MGT 425 Saudi Electronic University Autonomous Decision Making Process Questions

User Generated

Nyv_xuna

Health Medical

mgt 425

Saudi electronic university

MGT

Description

Unformatted Attachment Preview

1 Ethical Issues in a Health Assessment Giovanna Skylar Institutional Affiliation HHA3002 Dr. Tilman July 26th, 2022 2 Ethical Issues in a Health Assessment Question 1 The reporting of a client's health status must abide by the disclosure policies and procedures provided in the health and medical standards. After my client has tested positive, I will report her health status to the state health departments. The information is supposed to help public health officials monitor the state's health status. It is fundamental to report this information as the federal and state funding for HIV services is often targeted to regions under severe attacks by the epidemic (HIV.gov, 2017). The second party that should be notified of the status is the new boyfriend in the waiting room, who should be notified under the client's consent. The non-disclosure of this information will likely put the new boyfriend at risk of being infected. As suggested by the HPCSA, for information to be disclosed, the potential for causing harm to third parties must be high enough to surpass the patient's right to privacy. The information should, however, be disclosed through the counseling process to make them understand the importance of extending care to the patients. Question 2 Confidentiality of the client data is essential in communication between the health worker and the client. Confidentiality is especially useful in the process of counseling and treatment services. Although health workers' professional ethics recommend adherence to patient confidentiality, observing these guidelines strictly may risk the client's significant other and the public. Therefore, I will use the counseling approach to help the client realize the dangers that might find her significant others. The lack of disclosure by the client is based on the assumption the information could cause her separation from her new relationship. However, previous studies suggest that couple counseling schemes have successfully reduced the number of marriage 3 separations after the HIV status diagnosis (Dessalegn et al., 2019). The impact the infection can cause on a partner would be severe, and it is necessary to create awareness on this matter. I will take this approach because counseling may enable my client to provide individual consent for the disclosure, thus avoiding the breach of confidentiality. Question 3 The first action that must be taken to protect the confidentiality of the patient's information is to prohibit sharing information without informed consent. Strict rules should be implemented to help share information where there are exceptions (Liz Stokes, 2019). In this case, exceptions should only be permitted when a person's life is endangered, in case there is a legal requirement, or where the non-disclosure threatens the public. This information should also be limited to relevant entities, such as the public health department. Some policies that must be implemented should include informing the patient through writing regarding the information to be released, the party to release the information, and the individuals who will receive the information (Liz Stokes, 2019). The second action that can help to protect patient data confidentiality is offering education to staff concerning potential areas of misuse of patient information. The health centers should implement policies regarding the improper use of information (Araújo et al., 2020). For example, the policies should address areas such as personal electronic data devices, emails, and electronic transmission of data. 4 References Araújo, W. J. S., Bragagnollo, G. R., Nascimento, K. C. D., Camargo, R. A. A. D., Tavares, C. M., & Monteiro, E. M. L. M. (2020). Educational intervention on HIV/AIDS with elderly individuals: a quasi-experimental study. Texto & Contexto-Enfermagem, 29. Dessalegn, N. G., Hailemichael, R. G., Shewa-Amare, A., Sawleshwarkar, S., Lodebo, B., Amberbir, A., & Hillman, R. J. (2019). HIV Disclosure: HIV-positive status disclosure to sexual partners among individuals receiving HIV care in Addis Ababa, Ethiopia. PloS one, 14(2), e0211967. Liz Stokes, J. D. (2019). ANA position statement: Nursing advocacy for LGBTQ+ populations. Online Journal of Issues in Nursing, 24(1), 1-6. HIV.gov. (2017, August 31). Limits on Confidentiality. HIV.gov. https://www.hiv.gov/hivbasics/living-well-with-hiv/your-legal-rights/limits-on-confidentiality 1 Pre-Assessment Giovanna Skylar Walden University HA3002 2 Pre-Assessment Provision of the Code of Ethics for Nurses Code of Ethics for Nurses provides an ethical framework to guide the decision-making in ethical dilemmas. Besides, the code ensures nurses provide quality care through ethically guided action that places the patient at the center of the care process. In this context, Provision 3 of the code of ethics stipulates that nurse promotes, advocates for, and protects the patient's rights and safety (American Nurses Association, 2019). In this provision, nurses are ethically obligated to protect patient's privacy and confidentiality. In this regard, the nurse has the moral responsibility to provide a safe and private environment to engage in conversation with the patient. In the current case, the need-to-know basis would be appropriate to ensure quality care. Studies by Stutterheim et al. (2014) revealed that explicit breaches of confidentiality and carelessness were common violations of patient privacy and confidentiality for those diagnosed with HIV. In part, eases of access to patient files, use of the nurse notes, and unnecessary referral increased stigma and perception of poor quality. In this regard, the need to know will form the basis of sharing the patient HIV status with other professionals. At the same time, documentation and file storage will align with hospital standards of data protection and privacy policies. Holistic Approach Holistic approaches to the assessment of people with HIV should be longitudinal. In particular, new complications and challenges tend to arise during the cause of the treatment. HIV disclosure to the patient partner is vital in social support groups and has positive and negative consequences. In part, disclosure can increase the risk of relationship dissolution, while on the other hand, disclosure has the potential to increase social support and the subsequent adherence to antiretroviral therapy (ART). Besides, the motivation to disclose among HIV patients is 3 related to various factors. Notably, when the patient considers the personal and interpersonal gains for others, the likelihood of self-disclosure is high. Thus, the narrative therapy approach offers a viable model for providing holistic care. In particular, the narrative approach addresses the need to establish closeness, the fear of rejection, and privacy concerns. In the narrative approach, the patient gains the ability to externalize the problem rather than internalize the problems. In this case, the approach relies on the patient's skills and the sense of purpose as a resource during difficult times. The patients' need is addressed through the after-mentioned strategy, considering both the emotional aspects. Alignment with the Code of Ethics Research has consistently shown that the barrier to disclosing HIV is linked to the fear of stigma. In essence, fear of discrimination, relationship dissolution, and intimate partner violence are cited as the primary motive for withholding HIV serostatus (Xiao et al., 2015). Besides, the legal mandate for self-disclosure further violates the patient's rights to privacy and increases emotional distress. On the other hand, the perception of control over privacy issues and the perception of interpersonal and personal gain is associated with a higher willingness to disclose HIV status to partners and friends. In this regard, the narrative approach aligns with ANA provision 3. In this case, the nurse focuses on protecting the patient's right to privacy and confidentiality. In the narrative approach, the patient needs and privacy concerns are fully addressed in that the potential of a breach of confidentiality is limited (Obermeyer et al., 2011). Instead, patients leverage on own skills to find the motivation to disclose while receiving emotional and social support from the health care providers. Compared to mandatory reporting set by legal provisions, the narrative approach is holistic. It addresses other underlying issues, such as adherence to ART and overcoming distress 4 due to violating individual privacy. Hence, rather than resorting to legal means, enabling the patient to externalize the problem will increase the motivation to disclose the serostatus based on the positive perception of support from the health care provider and total control over personal privacy. 5 References American Nurses Association. (2019). American nurses association code of ethics for nurses. https://nursing.rutgers.edu/wp-content/uploads/2019/06/ANA-Code-of-Ethics-forNurses.pdf Obermeyer, C. M., Baijal, P., & Pegurri, E. (2011). Facilitating HIV disclosure across diverse settings: A review. American Journal of Public Health, 101(6), 1011–1023. https://doi.org/10.2105/ajph.2010.300102 Stutterheim, S. E., Sicking, L., Brands, R., Baas, I., Roberts, H., van Brakel, W. H., Lechner, L., Kok, G., & Bos, A. E. R. (2014). Patient and provider perspectives on HIV and hivrelated stigma in dutch health care settings. AIDS Patient Care and STDs, 28(12), 652– 665. https://doi.org/10.1089/apc.2014.0226 Xiao, Z., Li, X., Qiao, S., Zhou, Y., Shen, Z., & Tang, Z. (2015). Using communication privacy management theory to examine HIV disclosure to sexual partners/spouses among PLHIV in guangxi. AIDS Care, 27(sup1), 73–82. https://doi.org/10.1080/09540121.2015.1055229 STEPHEN G. POWELL KENNETH R. BAKER MANAGEMENT SCIENCE CHAPTER 8 POWERPOINT NONLINEAR OPTIMIZATION The Art of Modeling with Spreadsheets Compatible with Analytic Solver Platform FOURTH EDITION OPTIMIZATION • Find the best set of decisions for a particular measure of performance • Includes: – The goal of finding the best set – The algorithms (procedures) to accomplish this goal Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 2 EXCEL OPTIMIZATION SOFTWARE • Solver – Standard with Excel • Analytic Solver Platform – Comes with text – install off text CD – More advanced than standard solver – Is preferred tool throughout text Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 3 DECISION VARIABLES • Levers used to improve performance • Want to find the best values for the variables • Finding these best values can be challenging – Need Solver’s sophisticated software – Still relatively easy to construct models beyond Solver’s capabilities Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 4 SOLVER WINDOW Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 5 FORMULATION • Decision variables – What must be decided? Be explicit with units • Objective function – What measure compares decision variables? – Use only one measure (as a “yardstick”) – put in target cell • Constraints – What restrictions limit our choice of decision variables? Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 6 CONSTRAINTS • Left-hand-side (LHS) – Usually a function • Right-hand-side (RHS) – Usually a number (i.e., a parameter) • Three types of constraints – LHS = RHS – LHS = RHS Chapter 8 (less-than [LT] constraint) (Greater than [GT] constraint) (Equality [EQ] constraint) Copyright © 2013 John Wiley & Sons, Inc. 7 TYPES OF CONSTRAINTS • LT constraints (LHSRHS) – Commitments or thresholds • EQ constraints (LHS=RHS) – Material balance – Define related variables consistently Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 8 LAYOUT • Standard model template is advisable • Enhances ability to communicate – Provides common language – Reinforces understanding how models shaped • Improves ability to spot modeling errors • Enables “scaling up” more easily Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 9 LAYOUT • Organize worksheet in modules – Decision variables, objective function, constraints • Place decision variables in single row (or column) • Use color or border highlighting • Place objective in single highlighted cell • Arrange constraints for visual comparison of LHS and RHS Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 10 SOLVER TIP: RANGES FOR DECISION VARIABLES • Arrange worksheet with all decision variables in adjacent cells – Enables a single reference to their range – Makes data entry efficient – Reduces clutter in Solver interface – Makes task pane description easier to interpret Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 11 INTERPRETING RESULTS • Optimal values of decision variables – Best course of action for the model • Optimal value of objective function – Best level of performance possible • Constraint outcomes – Constraint is tight or binding if LHS=RHS in LT or GT constraint – Throughout optimization, generally only some constraints are binding Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 12 INTERPRETING RESULTS: OPTIMIZATION SOLUTION • Tactical information – Plan for decision variables • Strategic information – What factors could lead to better levels of performance? – Binding constraints are economic factors that restrict the value of the objective. Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 13 MODEL CLASSIFICATION AND THE NONLINEAR SOLVER • Linear optimization or linear programming – Objective and all constraints are linear functions of the decision variables • Nonlinear optimization or nonlinear programming – Either objective or a constraint (or both) are nonlinear functions of the decision variables • Techniques for solving linear models are more powerful – Use wherever possible Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 14 “HILL CLIMBING” • Technique used by Solver for nonlinear optimization • Called LSGRG (Large-Scale Generalized Reduced Gradient) algorithm • Hill climbing in a fog – Try to follow steepest path going up – After each step, or group of steps, again find steepest path and follow it – Stop if no path leads up Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 15 LOCAL AND GLOBAL OPTIMUM • The highest peak is the global optimum. – What we want to find • Any peak higher than all points around it is a local optimum. – What the LSGRG algorithm locates – Except in special circumstances, there is no way to guarantee that a local optimum is the global optimum. – If multiple local optima, then which is found depends on starting point for decision variables – may want to run Solver starting from multiple points Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 16 PROGRAMMING EXAMPLES • Facility location • Revenue maximization – Maximize revenue in the presence of a demand curve • Curve fitting – Fit a function to observed data points • Economic Order Quantity – Trade-off ordering and carrying costs for inventory Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 17 SOLVER TIP: SOLUTIONS FROM THE LSGRG ALGORITHM • When the GRG algorithm concludes with the convergence message, “Solver has converged to the current solution, all constraints are satisfied”, the algorithm should be rerun from the stopping point. • This message may then reappear, in which case Solver should be rerun once more. • Eventually, the algorithm should conclude with the optimality message, “Solver found a solution, all constraints and optimality conditions are satisfied”, which signifies that it has found a local optimum. • To help determine whether the local optimum is also a global optimum, Solver should be restarted at a different set of decision variables and rerun. • If several widely differing starting solutions lead to the same local optimum, that is some evidence that the local optimum is likely to be a global optimum, but in general there is no way to know for sure. Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 18 SOLVER TIP: AVOID DISCONTINUOUS FUNCTIONS • A number of functions familiar to experienced Excel programmers should be avoided when using the nonlinear solver. • These include: – Logical functions (e.g., IF or AND) – Mathematical functions (e.g., ROUND or CEILING) – Lookup and reference functions (e.g., CHOOSE or VLOOKUP) – Statistical functions (e.g., RANK or COUNT). • In general, avoid using any function that changes discontinuously. Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 19 SENSITIVITY ANALYSIS FOR NONLINEAR PROGRAMS • Tests our initial assumptions to see what impact they have on our conclusions. • Analysis of one or two variables can lead to optimal values of those variables. – E.g., using the Parametric Sensitivity tool. • Solver tool for larger numbers of variables and constraints Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 20 SOLVER TIP: WHAT KIND OF SENSITIVITY ANALYSIS? • Easy to confuse parametric sensitivity with optimization sensitivity, which answer different questions: – Optimization sensitivity determines how the optimal solution changes with a change in parameter. – Parametric sensitivity answers how specific outputs change with parameters. • The Solver tool can answer questions about how specific outputs change with a change in one or two parameters. Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 21 THE PORTFOLIO OPTIMIZATION MODEL • The performance of a portfolio of stocks is measured in terms of return and risk. • When we create a portfolio of stocks, our goals are usually to maximize the mean return and to minimize the risk. • Both goals cannot be met simultaneously, but we can use optimization to explore the trade-offs involved. Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 22 *EXCEL MINI-LESSON: THE COVAR FUNCTION • The COVAR function in Excel calculates the covariance between two equal-sized sets of numbers representing observations of two variables. • The covariance measures the extent to which one variable tends to rise or fall with increases and decreases in the other variable. – If the two variables rise and fall in unison, their covariance is large and positive. – If the two variables move in opposite directions, then their covariance is negative. – If the two variables move independently, then their covariance is close to zero. Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 23 SUMMARY • Optimization: Answers “What values of the decision variables lead to the best possible value of the objective?” • Excel Solver: Collection of optimization procedures – Nonlinear Solver is Solver’s default choice • Steps: 1) formulating, 2) solving, and 3) interpreting optimization problems. Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 24 SUMMARY • These guidelines for model builders are the craft skills typically exhibited by experts: – Follow a standard form whenever possible. – Enter cell references in the Solver windows; keep numerical values in cells. – Try out some feasible (and infeasible) possibilities as a way of debugging the model and exploring the problem. – Test intuition and suggest hypotheses before running Solver. Chapter 8 Copyright © 2013 John Wiley & Sons, Inc. 25 COPYRIGHT © 2013 JOHN WILEY & SONS, INC. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein. 10 - 26 STEPHEN G. POWELL KENNETH R. BAKER MANAGEMENT SCIENCE CHAPTER 9 POWERPOINT LINEAR OPTIMIZATION The Art of Modeling with Spreadsheets Compatible with Analytic Solver Platform FOURTH EDITION MODEL CLASSIFICATION • Linear optimization or linear programming – Objective and all constraints are linear functions of the decision variables. • Nonlinear optimization or nonlinear programming – Either objective or a constraint (or both) are nonlinear functions of the decision variables. • Techniques for solving linear models are more powerful. – Use wherever possible. Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 2 PROPERTIES OF LINEAR FUNCTIONS • Term “linear” refers to a feature of the objective function and the constraints. • Linear function exhibits: – Additivity – Proportionality – Divisibility Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 3 EXCEL MINI-LESSON: THE SUMPRODUCT FUNCTION • The SUMPRODUCT function in Excel takes the pairwise products of two sets of numbers and sums the products. • SUMPRODUCT(Array1,Array2) – Array1 references the first set of numbers. – Array2 references the second set of numbers. • The two arrays must have identical layouts and be the same size. Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 4 THE SIMPLEX ALGORITHM FOR LINEAR OPTIMIZATION • Exploits special properties of linearity to find optimal solutions. • Imagine the surface of a diamond which represents feasible decision variables: – Starts with a feasible set of decision variables that corresponds to a corner on a diamond. – Checks to see if a feasible neighboring corner point is better. – If not, stops; otherwise moves to that better neighbor and return to step 2. Guaranteed to converge to the global optimal solution Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 5 LINEAR PROGRAMMING PROBLEMS • Allocation models – Maximize objective (e.g., profit) subject to LT constraints on capacity • Covering models – Minimize objective (e.g., cost) subject to GT constraints on required coverage • Blending models – E.g., in determining product mix; mix materials with different properties to find best blend • Network models – Describe patterns of flow in a connected system – Covered in Chapter 10 Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 6 SOLVER TIP: RESCALING THE MODEL • Consider scaling parameters to appear in thousands or millions • Saves work in data entry – decreases errors • Spreadsheet looks less crowded • Helps with Solver algorithms – Value of objective, constraints, and decision variables should not differ from each other by more than a factor of 1000, at most 10,000. • Can always display model output on separate sheet with separate units Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 7 AUTOMATIC SCALING • Use if scaling problems difficult to avoid • Consider when: – Solver claims no feasible solution when user is sure there is one. • Preferable for model-builder to do the scaling Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 8 SENSITIVITY ANALYSIS FOR LINEAR PROGRAMS • A distinct pattern to the change in the optimal solution when varying a coefficient in the objective function • In some interval around the base case – No change in optimal decisions – Objective will change if decision variable is positive • Outside this interval a different set of values is optimal for decision variables Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 9 SOLVER TIP: OPTIMIZATION SENSITIVITY AND SHADOW PRICES • Break-even price where attractive to acquire more of a scarce resource • Improvement in objective function from a unit increase (or decrease) in RHS of constraint • In linear programs, constant for some range of changes to RHS. Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 10 SENSITIVITY ANALYSIS FOR BINDING CAPACITY CONSTRAINTS • A distinct pattern in sensitivity tables when varying availability of scare resource • In some interval around the base case: – Marginal value (shadow price) of capacity remains constant – Some variables change linearly with capacity – Others remain the same • Below this interval the value decreases and eventually reaches zero. Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 11 PATTERNS IN LINEAR PROGRAMMING SOLUTIONS • The optimal solution tells a “story” about a pattern of economic priorities. – Leads to more convincing explanations for solutions – Can anticipate answers to “what-if” questions – Provides a level of understanding that enhances decision making • After optimization, should always try to discern the qualitative pattern in the solution. Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 12 CONSTRUCTING PATTERNS • Decision variables – Which are positive and which are zero? • Constraints – Which are binding and which are not? • “Construct” the optimal solution from the given parameters – Determine one variable at a time – Can be interpreted as a list of priorities which reveal the economic forces at work Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 13 DEFINING PATTERNS • Qualitative description • Pattern should be complete and unambiguous – Leads to full solution – Always leads to same solution • Ask where shadow prices come from – Should be able to trace the incremental changes to derive shadow price of constraint Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 14 *DATA ENVELOPMENT ANALYSIS • DEA is a linear programming application aimed at evaluating the efficiencies of similar organizational departments or decision-making units (DMUs). • DMUs are characterized in terms of inputs and outputs, not in terms of operating details. • A DMU is considered efficient if it gets the most output from its inputs. • The purpose of DEA is to identify inefficient DMUs when there are multiple outputs and multiple inputs. Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 15 EXCEL MINI-LESSON: THE INDEX FUNCTION • The INDEX function finds a value in a rectangular array according to the row number and column number of its location. • The basic form of the function, as we use it for DEA models, is the following: – INDEX(Array, Row, Column) • Array references a rectangular array. • Row specifies a row number in the array. • Column specifies a column number in the array. If Array has just one column, then this argument can be omitted. Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 16 SUMMARY • Linear programming represents the most widely used optimization technique in practice. • The special features of a linear program are a linear objective function and linear constraints. • Linearity in the optimization model allows us to apply the simplex method as a solution procedure, which in turn guarantees finding a global optimum whenever an optimum of any kind exists. • Therefore, when we have a choice, we are better off with a linear formulation of a problem than with a nonlinear formulation. Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 17 SUMMARY • While optimization is a powerful technique, we should not assume that a solution that is optimal for a model is also optimal for the real world. • Often, the realities of the application will force changes in the optimal solution determined by the model. • One powerful method for making this translation is to look for the pattern, or the economic priorities, in the optimal solution. • These economic priorities are often more valuable to decision makers than the precise solution to a particular instance of the model. Chapter 9 Copyright © 2013 John Wiley & Sons, Inc. 18 COPYRIGHT © 2013 JOHN WILEY & SONS, INC. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein. 11 - 19 STEPHEN G. POWELL KENNETH R. BAKER MANAGEMENT SCIENCE CHAPTER 10 POWERPOINT NETWORK MODELS The Art of Modeling with Spreadsheets Compatible with Analytic Solver Platform FOURTH EDITION THE NETWORK MODEL • Describes patterns of flow in a connected system, where the flow might involve material, people, or funds • System elements may be locations (e.g., cities, warehouses, or assembly lines), or points in time. • We construct diagrams to represent such systems with elements are represented by nodes (circles). The paths of flow are represented by arcs or arrows. Chapter 10 Copyright © 2013 John Wiley & Sons, Inc. 2 THE TRANSPORTATION MODEL • A very common supply chain involves the shipment of goods from suppliers at one set of locations to customers at another set of locations. • The classic transportation model is characterized by a set of supply sources (each with known capacities), a set of demand locations (each with known requirements) and the unit costs of transportation between supply-demand pairs. Chapter 10 Copyright © 2013 John Wiley & Sons, Inc. 3 TRANSPORTATION PROBLEM: MODEL FORMULATION • The transportation model has two kinds of constraints: – Less-than capacity constraints and – Greater-than demand constraints • If total capacity equals total demand, both capacity and demand constraints are “=”. • If capacity exceeds demand, the capacity constraints are “”. • If demand exceeds capacity, the capacity constraints are “>” and the demand constraints are “ 1 • Project 2, or Project 5, or both, will be selected, thus satisfying the requirement of at least one selection. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 14 RELATIONSHIP: AT MOST N PROJECTS MUST BE SELECTED • y4 + y5 < 1 • Project 4, or Project 5, or neither, but not both will be selected, thus satisfying the requirement of at most one selection. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 15 RELATIONSHIP: EXACTLY K PROJECTS MUST BE SELECTED • y4 + y5 = 1 • Exactly one of either Project 4 or Project 5 will be selected, thus satisfying the requirement of exactly one selection. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 16 RELATIONSHIP: SOME PROJECTS HAVE CONTINGENCY RELATIONSHIPS • y3 – y5 > 0 • If Project 5 is selected, then project 3 must be as well. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 17 LINKING CONSTRAINTS AND FIXED COSTS • We commonly encounter situations in which activity costs are composed of fixed costs and variable costs, with only the variable costs being proportional to activity level. • With an integer programming model, we can also integrate the fixed component of cost. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 18 LINKING CONSTRAINTS AND FIXED COSTS • We separate the fixed and variable components of cost. • In algebraic terms, we write cost as: Cost = Fy + cx where F represents the fixed cost, and c represents the linear variable cost. • The variables x and y are decision variables, where x is a normal (continuous) variable, and y is a binary variable. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 19 LINKING CONSTRAINTS AND FIXED COSTS • To achieve consistent linking of the two variables, we add the following generic linking constraint to the model: x < My where the number M represents an upper bound on the variable x. • In other words, M is at least as large as any value we can feasibly choose for x. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 20 LINKING CONSTRAINT: X < MY • When y = 0 (and therefore no fixed cost is incurred), the righthand side becomes zero, and Solver interprets the constraint as x = 0, these two constraints together force x to be zero. – Thus, when y = 0, it will be consistent to avoid the fixed cost. • On the other hand, when y = 1, the right-hand side will be so large that Solver does not need to restrict x at all, permitting its value to be positive while we incur the fixed cost. – Thus, when y = 1, it will be consistent to incur the fixed cost. • Of course, because we are optimizing, Solver will never produce a solution with the combination of y = 1 and x = 0, because it would always be preferable to set y = 0. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 21 SOLVER TIP: LOGICAL FUNCTIONS AND INTEGER PROGRAMMING • Experienced Excel programmers might be tempted to use the logical functions (IF, AND, OR, etc.) to express certain relationships. • Unfortunately, the linear solver does not always detect the nonlinearity caused by the use of logical functions, so it is important to remember never to use an IF function in a model built for the linear solver. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 22 THRESHOLD LEVELS AND QUANTITY DISCOUNTS • Threshold level requirement: a decision variable is either at least as large as a specified minimum, or else it is zero. • The existence of a threshold level does not directly affect the objective function of a model, and it can be represented in the constraints with the help of binary variables. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 23 THRESHOLD LEVELS • Suppose we have a variable x that is subject to a threshold requirement. Let m denote the minimum feasible value of x if it is nonzero. Then we can capture this structure in an integer programming model by including the following pair of constraints: x – my > 0 x – My < 0 where, as before, M is a large number that is greater than or equal to any value x could feasibly take. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 24 *THE FACILITY LOCATION MODEL • The transportation model (discussed in Chapter 10) is typically used to find optimal shipping schedules in supply chains and logistics systems. • The applications of the model can be viewed as tactical problems, in the sense that the time interval of interest is usually short, say a week or a month. • Over that time period, the supply capacities and locations are unlikely to change at all, and the demands can be predicted with reasonable precision. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 25 *THE FACILITY LOCATION MODEL • Over a longer time frame, a strategic version of the problem arises. In this setting, the decisions relate to the selection of supply locations as well as the shipment schedule. • These decisions are strategic in the sense that, once determined, they influence the system for a relatively long time interval. • The basic model for choosing supply locations is called the facility location model. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 26 THE CAPACITATED PROBLEM • Conceptually, we can think of this problem as having two stages. • In the first stage, decisions must be made about how many warehouses to open and where they should be. • Then, once we know where the warehouses are, we can construct a transportation model to optimize the actual shipments. • The costs at stake are also of two types: fixed costs associated with keeping a warehouse open and variable transportation costs associated with shipments from the open warehouses. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 27 THE UNCAPACITATED PROBLEM • Once we see how to solve the facility location problem with capacities given, it is not difficult to adapt the model to the uncapacitated case. • Obviously, we could choose a virtual capacity for each warehouse that is as large as total demand, so that capacity would never interfere with the optimization. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 28 THE ASSORTMENT MODEL • The facility location model, with or without capacity constraints, clearly has direct application to the design of supply chains and the choice of locations from a discrete set of alternatives. • But the model can actually be used in other types of problems because it captures the essential trade-off between fixed costs and variable costs. • An example from the field of Marketing is the assortment problem, which asks which items in a product line should be carried, when customers are willing to substitute. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 29 SUMMARY • Integer programming problems are optimization problems in which at least one of the variables is required to be an integer. • Solver’s solutions to linear integer programs are reliable: a global optimal solution always occurs as long as the Integer Tolerance parameter has been set to zero. • Binary variables can represent all-or-nothing decisions that allow only accept/reject alternatives. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 30 SUMMARY • Binary variables can also be instrumental in capturing complicated logic in linear form so that we can harness the linear solver to find solutions. • Binary variables make it possible to accommodate problem information on: – Contingency conditions between projects – Mutual exclusivity among projects – Linking constraints for consistency – Threshold constraints for minimum activity levels • With the capability of formulating these kinds of relationships in optimization problems, our modeling abilities expand well beyond the basic capabilities of the linear and nonlinear solvers. Chapter 11 Copyright © 2013 John Wiley & Sons, Inc. 31 COPYRIGHT © 2013 JOHN WILEY & SONS, INC. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein. 13 - 32 STEPHEN G. POWELL KENNETH R. BAKER MANAGEMENT SCIENCE CHAPTER 12 POWERPOINT NON-SMOOTH MODELS The Art of Modeling with Spreadsheets Compatible with Analytic Solver Platform FOURTH EDITION INTRODUCTION • Evolutionary solver is a Solver algorithm that can be effective on models that cannot be optimized in any other way. • The evolutionary solver is particularly suited to models containing nonsmooth objective functions. • Because the evolutionary solver makes virtually no assumptions about the nature of the objective function, it is not able to identify an optimal solution. Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 2 INTRODUCTION (CONT’D) • This method conducts a systematic search with random elements, comparing the solutions encountered along the way and retaining the better ones. • The best solution it finds may not be optimal, although it may be a very good solution. • This type of procedure is called a heuristic procedure, meaning that it is a systematic procedure for identifying good solutions, but not guaranteed optimal solutions. Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 3 FEATURES OF THE EVOLUTIONARY SOLVER • The evolutionary solver is designed to mimic the process of biological evolution in certain ways. • The algorithm proceeds through a series of stages, which are analogous to generations in a biological population. In each generation the approach considers not a single solution, but a population of perhaps 25 or 50 solutions. • New members are introduced to this population through a process that mimics mating in that offspring solutions combine the traits of their parent solutions. • Occasional mutations occur in the form of offspring solutions with some random characteristics that do not come from their parents. Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 4 FEATURES OF THE EVOLUTIONARY SOLVER (CONT’D) • The ‘‘fitness’’ of each member of the population is determined by the value of its objective function. • Members of the population that are less fit (have a relatively worse value of the objective function) are removed from the population by a process that mimics natural selection. • This process of selection propels the population toward better levels of fitness (better values of the objective function). • The procedure stops when there is evidence that the population is no longer improving (or if one of the userdesignated stopping conditions is met). • When it stops, the procedure displays the bes tmember of the final population as the solution. Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 5 THE ENGINE TAB FOR THE EVOLUTIONARY SOLVER Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 6 THE ADVERTISING BUDGET PROBLEM • The decision variables in this problem are the quarterly expenditures on advertising. • The objective function is nonlinear but smooth, since there are diminishing returns to advertising Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 7 ADVERTISING BUDGET MODEL WITH UNIT COST TABLE Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 8 OPTIMAL ALLOCATION FROM THE NONLINEAR SOLVER Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 9 OPTIMAL ALLOCATION FROM THE EVOLUTIONARY SOLVER Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 10 RESULTS OF USING EVOLUTIONARY SOLVER • The evolutionary solver finds a solution with a profit of $87,541, which is 63 percent higher than the base case and 25 percent higher than the solution found by the nonlinear solver. • The advertising expenditures in this solution focus on the fourth quarter. • Repeated runs of Scatter Search fail to improve on this solution significantly, so we can accept it as optimal or nearly so. • This example demonstrates that even a modest alteration to one function in a model (here, the product’s cost) can fundamentally change the approach required for optimization. • The lesson for model building: recognize that the choice of Excel functions may affect the most suitable optimization algorithms to use and the results that can be achieved. Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 11 THE CAPITAL BUDGETING PROBLEM • Although the evolutionary solver can work with constraints, it is less efficient when constraints are present, and performance tends to deteriorate as the number of constraints increases. • Rather than imposing an explicit constraint, we add a term to the objective function that penalizes the solution for violations of a constraint. Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 12 WORKSHEET FOR THE MODIFIED MARR CORPORATION EXAMPLE Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 13 RESULTS OF RUNNING EVOLUTIONARY SOLVER ON THIS MODEL • A solution of $35 million, which is better than the optimum in the base case. • If the previous run stopped because of convergence, we should expand the population size. • If it stopped because improvement was impossible, then the Max time without Improvement parameter should be increased or the Tolerance parameter should be reduced to zero. • If this stopping condition persists, then it is a good idea to start the search with a different set of decision variables. • If we simply run into the time limit, then the maximum time parameter should be increased to 60 seconds (and beyond, if we have the time). • It appears that an objective function of $35 million is the best we can achieve. Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 14 SUMMARY • The evolutionary solver contains an algorithm that complements the nonlinear solver, the linear solver, and the integer solver. • Evolutionary solver can often find good, near-optimal solutions to very difficult problems, and it may be the only effective procedure when there is a nonsmooth objective function. • The evolutionary solver works with a set of specialized parameters. • Practice and experience using the evolutionary solver are the key ingredients in effective parameter selection. • We usually reserve the use of the evolutionary solver for only the most difficult problems, when the other solvers would fail or when we cannot build a suitable model with a smooth objective function. Chapter 12 Copyright © 2013 John Wiley & Sons, Inc. 15 COPYRIGHT © 2013 JOHN WILEY & SONS, INC. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein. 14 - 16 STEPHEN G. POWELL KENNETH R. BAKER MANAGEMENT SCIENCE CHAPTER 13 POWERPOINT DECISION ANALYSIS The Art of Modeling with Spreadsheets Compatible with Analytic Solver Platform FOURTH EDITION INTRODUCTION • Many business problems contain uncertain elements that are impossible to ignore without losing the essence of the situation. • In this chapter, we introduce some basic methods for analyzing decisions affected by uncertainty. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 2 UNCERTAIN PARAMETERS • Now, we broaden our viewpoint to include uncertain inputs— parameter values subject to uncertainty. • Uncertain parameters become known only after a decision is made. • When a parameter is uncertain, we treat it as if it could take on two or more values, depending on influences beyond our control. • These influences are called states of nature, or more simply, states. • In many instances, we can list the possible states, and for each one, the corresponding value of the parameter. • Finally, we can assign probabilities to each of the states so that the parameter outcomes form a probability distribution. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 3 PAYOFF TABLES AND DECISION CRITERIA • For each action-state combination, the entry in the table is a measure of the economic result. • Typically, the payoffs are measured in monetary terms, but they need not be profit figures. • They could be costs or revenues in other applications, so we use the more general term payoff. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 4 BENCHMARK CRITERIA • The Maximax payoff criterion seeks the largest of the maximum payoffs among the actions. • The maximin payoff criterion seeks the largest of the minimum payoffs among the actions. • The minimax regret criterion seeks the smallest of the maximum regrets among the actions. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 5 INCORPORATING PROBABILITIES • We can immediately translate this information into probability distributions for the payoffs corresponding to each of the potential actions. • We use the notation EP to represent an expected payoff (e.g., an expected profit). • Note that the expected payoff calculation ignores no information: all outcomes and probabilities are incorporated into the result. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 6 USING TREES TO MODEL DECISIONS • A probability tree depicts one or more random factors • The node from which the branches emanate is called a chance node, and each branch represents one of the possible states that could occur. • Each state, therefore, is a possible resolution of the uncertainty represented by the chance node. • Eventually, we’ll specify probabilities for each of the states and create a probability distribution to describe uncertainty at the chance node. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 7 SIMPLE PROBABILITY TREE Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 8 THREE CHANCE NODES IN TELEGRAPHIC FORM Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 9 DECISION TREES • Decision-tree models offer a visual tool that can represent the key elements in a model for decision making under uncertainty and help organize those elements by distinguishing between decisions (controllable variables) and random events (uncontrollable variables). • In a decision tree, we describe the choices and uncertainties facing a single decision-making agent. • This usually means a single decision maker, but it could also mean a decision-making group or a company. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 10 REPRESENTING DECISIONS • In a decision tree, we represent decisions as square nodes (boxes), and for each decision, the alternative choices are represented as branches emanating from the decision node. • These are potential actions that are available to the decision maker. • In addition, for each uncertain event, the possible alternative states are represented as branches emanating from a chance node, labeled with their respective probabilities. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 11 ANALYZING THE DECISION TREE • Whereas we build the tree left to right, to reflect the temporal sequence in which a decision is followed by a chance event, we evaluate the tree in the reverse direction. • At each chance node, we can calculate the expected payoff represented by the probability distribution at the node. • This value becomes associated with the corresponding action branch of the decision node. • Then, at the decision node, we calculate the largest expected payoff to determine the best action. • This process of making the calculations is usually referred to as rolling back the tree. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 12 DECISION TREES: RISK PROFILES • The distribution associated with a particular action is called its risk profile. • The risk profile shows all the possible economic outcomes and provides the probability of each: It is a probability distribution for the principal output of the model. • This form reinforces the notion that, when some of the input parameters are described in probabilistic terms, we should examine the outputs in probabilistic terms. • After we determine the optimal decision, we can use a probability model to describe the profit outcome. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 13 DECISION TREES FOR A SERIES OF DECISIONS • Decision trees are especially useful in situations where there are multiple sources of uncertainty and a sequence of decisions to make. • For example, suppose that we are introducing a new product and that the first decision determines which channel to use during test-marketing. • When this decision is implemented, and we make an initial commitment to a marketing channel, we can begin to develop estimates of demand based on our test. • At the end of the test period, we might reconsider our channel choice, and we may decide to switch to another channel. • Then, in the full-scale introduction, we attain a level of profit that depends, at least in part, on the channel we chose initially. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 14 EXAMPLE • In the following example, we have depicted (in telegraphic form) a situation in which we choose our channel initially, observe the test market, reconsider our choice of a channel, and finally observe the demand during full-scale introduction. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 15 DECISION TREE WITH SEQUENTIAL DECISIONS Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 16 PRINCIPLES FOR BUILDING AND ANALYZING DECISION TREES 1. 2. 3. 4. 5. 6. 7. Determine the essential decisions and uncertainties. Place the decisions and uncertainties in the appropriate temporal sequence. Start the tree with a decision node representing the first decision. Select a representative (but not necessarily exhaustive) number of possible choices for the decision node. For each choice, draw a chance node representing the first uncertain event that follows the initial decision. Select a representative (but not necessarily exhaustive) number of possible states for the chance node. Continue to expand the tree with additional decision nodes and chance nodes until the overall outcome can be evaluated. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 17 ROLLBACK PROCEDURE FOR ANALYZING TREES 1. 2. 3. 4. 5. 6. 7. Start from the last set of nodes—those leading to the ends of the paths. For each chance node, calculate the expected payoff as a probability-weighted average of the values corresponding to its branches. Replace each chance node by its expected value. For each decision node, find the best expected value (maximum benefit or minimum cost) among the choices corresponding to its branches. Replace each decision node by the best value, and note which choice is best. Continue evaluating chance nodes and decision nodes, backward in sequence, until the optimal outcome at the first node is determined. Construct its risk profile. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 18 THE COST OF UNCERTAINTY • An action must be chosen before learning how an uncertain event will unfold. • The situation would be much more manageable if we could learn about the uncertain event first and then choose an action. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 19 IMPERFECT VS. PERFECT INFORMATION • When we have to make a decision before uncertainty is resolved, we are operating with imperfect information (uncertain knowledge) about the state of nature. • When we can make a decision after uncertainty is resolved, we can respond to perfect information about the state of nature. • Our probability assessments of event outcomes remain unchanged, and we are still dealing with expected values. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 20 EXPECTED VALUE OF PERFECT INFORMATION (EVPI) • The expected payoff with perfect information must always be at least as good as the expected payoff from following the optimal policy in the original problem, and it will usually be better. • The EVPI measures the difference, or the gain due to perfect information. • The calculation of EVPI can also be represented with a tree structure, where we reverse the sequence of decision and chance event in the tree diagram, just as we did in the calculations. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 21 DECISION TREE FOR THE EVPI CALCULATION Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 22 USING DECISION TREE SOFTWARE • It is often difficult to create a layout for the calculations that is tailored to the features of a particular example. • For that reason, it makes sense to take advantage of software that has been designed expressly for representing decision trees in Excel. • Decision Tree is a tool contained in Analytic Solver Platform for constructing and analyzing decision tree. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 23 DECISION TREE MENU Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 24 DEFAULT INITIAL TREE PRODUCED BY DECISION TREE Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 25 DETAILS FOR THE FIRST DECISION NODE Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 26 EXPANDED INITIAL TREE DIAGRAM Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 27 NODE WINDOW FOR THE FIRST EVENT NODE Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 28 FIRST EVENT NODE PRODUCED BY DECISION TREE Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 29 EXPANDED DIAGRAM WITH SECOND EVENT NODE COPIED Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 30 FULL DIAGRAM Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 31 SENSITIVITY ANALYSIS WITH TREEPLAN • A decision-tree analysis retains the properties of a spreadsheet. • The worksheet produced by Decision Tree contains inputs, formulas, and outputs, just as in any welldesigned model. • Thus, we can perform sensitivity analyses in the usual ways. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 32 SENSITIVITY ANALYSIS FOR THE EXAMPLE MODEL Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 33 MINIMIZING EXPECTED COSTS WITH DECISION TREE • We could just as easily apply Decision Tree to a problem involving the criterion of expected costs by treating all costs as negative profits and finding the maximum expected profit. • However, Decision Tree can accommodate costs in a more direct fashion and simply minimize expected cost. • To do so, we enter the task pane on the Model tab, select the root node (Decision Tree) in the main window, and in the table below, find the Decision Node parameter and use its pull-down menu to switch from Maximize to Minimize. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 34 LOCATION OF THE MAXIMIZATION SETTING ON THE TASK PANE Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 35 *MAXIMIZING EXPECTED UTILITY WITH DECISION TREE • What if we wish to incorporate some aversion to risk in our decision making? • Suppose that we could evaluate payoffs in some risk-adjusted manner—that is, with a measure that combines notions of monetary value along with the risk of an undesired outcome. • To contrast this measure with the measure of pure dollars unadjusted for risk, we’ll adopt the name utils for this new scale. • With this scale available, the decision maker can compute the value of a particular action in utils and select as the optimal decision the action with the largest such value. • The value of an action, measured in utils, incorporates both outcomes and probabilities, just as expected value does, but it also acknowledges risk. • We say that a decision maker who is behaving in this way seeks to maximize expected utility. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 36 EXPONENTIAL UTILITY FUNCTION • Although there are many ways of converting dollars to utils, one straightforward method uses an exponential utility function: U = a – b exp (–D/R) where D is the value of the outcome in dollars; U is the utility value, or the value of an outcome in utils; and a, b, and R represent parameters of the utility function. Parameters a and b are essentially scaling parameters; R influences the shape of the curve and is known as the risk tolerance. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 37 ANALYSIS WITH UTILITIES • To carry out the analysis, we use this function to convert each monetary outcome from dollars to utils, and then we determine the action that achieves the maximum expected utility. • Although Decision Tree allows the flexibility of setting three different parameters, we usually advise setting a = b = 1. • This choice ensures that the function passes through the origin, so that our remaining task is finding a value of R that captures the decision maker’s preferences. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 38 GRAPH OF UTILITY FUNCTION FOR THE EXAMPLE Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 39 USING TREE PLAN WITH EXPONENTIAL UTILITY FUNCTION • In Decision Tree, it is necessary to specify the three parameters in the exponential utility function. • These three values must be entered in the task pane on the Model tab, along with designating the value for Certainty Equivalents to be the Exponential Utility Function. • After the user designates the use of Exponential Utility Function, Decision Tree displays additional calculations in columns B, F, and J. Immediately below the monetary payoffs the display shows the same figures converted to utils. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 40 MODIFICATION OF THE EXAMPLE MODEL FOR EXPONENTIAL UTILITIES Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 41 SUMMARY • A decision tree is a specialized model for recognizing the role of uncertainties in a decision-making situation. • Trees help us distinguish between decisions and random events, and more importantly, they help us sort out the sequence in which they occur. • Probability trees provide us with an opportunity to consider the possible states in a random environment when there are several sources of uncertainty, and they become components of decision trees. • The key elements of decision trees are decisions and chance events. A decision is the selection of a particular action from a given list of possibilities. • A chance event gives rise to a set of possible states, and each action-state pair results in an economic payoff. • In the simplest cases, these relationships can be displayed in a payoff table, but in complex situations, a decision tree tends to be a more flexible way to represent the relationships and consequences of decisions made under uncertainty. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 42 SUMMARY (CONT’D) • The choice of a criterion is a critical step in solving a decision problem when uncertainty is involved. • There are benchmark criteria for optimistic and pessimistic decision making, but these are somewhat extreme criteria. They ignore some available information, including probabilities, in order to simplify the task of choosing a decision. • The more common approach is to use probability assessments and then to take the criterion to be maximizing the expected payoff, which in the business context translates into maximizing expected profit or minimizing expected cost. • Using the rollback procedure, we can identify those decisions that optimize the expected value of our criterion. Furthermore, we can produce information in the form of a probability distribution to help assess the risk associated with any decision in the tree. • Decision Tree is a straightforward spreadsheet program that assists in the structuring of decision trees and in the calculations required for a quantitative analysis. Chapter 13 Copyright © 2013 John Wiley & Sons, Inc. 43 COPYRIGHT © 2013 JOHN WILEY & SONS, INC. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein. STEPHEN G. POWELL KENNETH R. BAKER MANAGEMENT SCIENCE CHAPTER 1 POWERPOINT INTRODUCTION The Art of Modeling with Spreadsheets Compatible with Analytic Solver Platform FOURTH EDITION WHAT IS MODELING? • Creating a simplified version of reality – Maps • Working with this version to understand or control some aspect of the world Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 2 TYPES OF MODELS • Mental • Visual • Physical • Mathematical – Algebra – Calculus – Spreadsheets Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 3 WHY STUDY MODELING? • Models generate insight which leads to better decisions. • Modeling improves thinking skills: – Break problems down into components – Make assumptions explicit • Modeling improves quantitative skills: – Ballpark estimation, number sense, sensitivity analysis • Modeling is widely used by business analysts: – Finance, marketing, operations Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 4 MODELS IN BUSINESS: TYPES • One time decision models (usually built by the decision maker) – Will be the primary focus in this text • Decision support models • Embedded models – A computer makes the decision without the user being explicitly aware • Models used in business education Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 5 BENEFITS OF BUSINESS MODELS • Modeling allows us to make inexpensive errors. • Allows exploration of the impossible • Improves business intuition • Provides timely information • Reduces costs Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 6 ROLE OF SPREADSHEETS • Principal vehicle for modeling in business • Mathematics at an accessible level – Versus calculus, algebra • Correspond nicely to accounting statements • “The Swiss Army knife of business analysis” Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 7 SPREADSHEETS: “THE SWISS ARMY KNIFE OF BUSINESS ANALYSIS” • Prior to the 1980s, modeling was performed only by specialists using demanding software on expensive hardware. – Spreadsheets changed all this in the 1990s • The “second best” way to do many kinds of analysis – Many specialized decision tools exist (e.g., simulation software, optimization software, etc.). • The best way to do most modeling – An effective modeler should know its limitations and when to call in specialists. Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 8 RISKS OF SPREADSHEET USE • Spreadsheets contain internal errors, and more errors are introduced as these spreadsheets are used and modified. • A sampling of errors with serious ramifications: – Sorting a spreadsheet improperly – Careless naming of spreadsheet files – Copy-and-paste error in a spreadsheet – Erroneous numerical input in a spreadsheet – Numbers entered as text in a spreadsheet – Shifting a spreadsheet so the wrong numbers appear in the wrong columns – Incorrect references in a spreadsheet formula Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 9 WHY ARE ERRORS SO COMMON? • Traditional computer programming is carried out largely by trained professionals. • It uses elaborate and formalized development methods. • Very few corporations (and even fewer individuals) employ even the most basic design and inspection procedures. Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 10 CHALLENGES FOR SPREADSHEET USERS • End-user spreadsheets frequently have bugs. • End-users are overconfident about the quality of their spreadsheets. • Development process is inefficient • Most productive methods for generating insights not employed Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 11 END USER INEFFICIENCIES • Lack of planning causes extensive rework • No prototyping; too much complexity too soon • Users rarely spend time debugging • Users rarely seek review • Do not use Excel’s best tools for clearest insights (even advanced users) Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 12 BASIC KNOWLEDGE FOR SPREADSHEET MODELING • Basic algebra – e.g., quadratic, exponential, logarithmic functions • Simple logic – e.g., IF statements or MAX functions • Basic probability – e.g., distributions and sampling • Basic familiarity with Excel – e.g., entering and formatting text, using functions Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 13 REAL WORLD PROBLEM STATEMENT MODEL WORLD FORMULATION ASSUMPTIONS and MODEL STRUCTURES ANALYSIS SOLUTION INTERPRETATION — translation — communication RESULTS and CONCLUSIONS THE REAL WORLD AND THE MODEL WORLD Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 14 MODEL FORMULATION • Decisions – Possible choices or actions to take • Outcomes – Consequences of the decisions • Structure – Logic that links elements of the model together • Data – Numerical assumptions in model Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 15 FIVE ASPECTS OF MODELING ACTIVITY • Problem context – Situation from which modeler’s problem arises • Model structure – Building the model • Model realization – Fitting model to available data and calculating results • Model assessment – Evaluating model’s correctness, feasibility, and acceptability • Model implementation – Working with client to derive value from the model Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 16 HABITS OF EXPERT MODELERS • Experts: – Frequently switched among the five aspects of modeling – Spent 60% of activity time on model structure with frequent switches between model structure and model assessment. – Used model structure as the organizing principle around which the related activities were arrayed • Conclusion: Craft skills are as essential as technical skills in effective modeling. Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 17 RANKING OF MODELING SKILLS • Creativity, sensitivity to client needs, persistence • Communication, teamwork skills, etc. • Technical expertise • Knowledge of the industry or problem-type • Above ranking confirms the importance of craft skills alongside technical skills in modeling. Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 18 BEHAVIORS THAT LIMIT MODELING EFFECTIVENESS • Over-reliance on given numerical data • Taking shortcuts to an answer • Insufficient use of abstract variables and relationships • Ineffective self-regulation • Overuse of brainstorming relative to structured problem solving Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 19 ORGANIZATION OF TEXT • Spreadsheet engineering – How to design build, test and perform analysis with a spreadsheet model • Modeling craft – Effective abstraction, model debugging, and translating models into managerial insights • Data analysis – Exploring datasets and basic techniques for classification, prediction • Management science – Optimization – Simulation Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 20 SUMMARY OF TEXT PHILOSOPHY • Modeling is a necessary skill for every business analyst. • Spreadsheets are the modeling platform of choice. • Basic spreadsheet modeling skills are an essential foundation. • End-user modeling is cost-effective. • Craft skills are essential to the effective modeler. • Analysts can learn the required modeling skills. • Management science/statistics are important advanced tools. Chapter 1 Copyright © 2013 John Wiley & Sons, Inc. 21 COPYRIGHT © 2013 JOHN WILEY & SONS, INC. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein. STEPHEN G. POWELL KENNETH R. BAKER MANAGEMENT SCIENCE CHAPTER 2 POWERPOINT MODELING IN A PROBLEM-SOLVING FRAMEWORK The Art of Modeling with Spreadsheets Compatible with Analytic Solver Platform FOURTH EDITION MODELERS’ ROLES IN THE PROBLEM-SOLVING PROCESS • End user – Identifies problems, develops model, uses model, and implements results – Often the modeler • Team member – Communication skills critical – Whole team must understand model and assumptions • Independent consultant – Model is for a client – Model must be consistent with client’s goals Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 2 KEY TERMS: “PROBLEM” VERSUS A “MESS” • A problem is a well-defined situation that is capable of resolution. • A mess is a morass of unsettling symptoms, causes, data, pressures, shortfalls, opportunities, etc. • Identifying a problem in the mess is the first step in the creative problem solving process. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 3 PROBLEM STATEMENTS • A statement in the form “In what ways might…?” – Focuses on defining the problem to be solved – Example: “In what ways might we increase revenues to keep pace with costs?” • Solutions will differ based on the problem statement, so: – Pay close attention to the problem definition. – Take any problem definition as tentative. – Prepare to alter the definition if evidence suggests a different statement would be more effective. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 4 CHARACTERISTICS OF WELL-STRUCTURED PROBLEMS • The objectives of the analysis are clear. • The assumptions that must be made are obvious. • All the necessary data are readily available. • The logical structure behind the analysis is well understood. • Example: Algebra problems are typically well- structured problems. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 5 ILL-STRUCTURED PROBLEMS • Objectives, assumptions, data, and structure of the problem are all unclear. • Examples: – Should the Red Cross institute a policy of paying for blood donations? – Should Boeing’s next major commercial airliner be a small supersonic jet or a slower jumbo jet? – Should an advertiser spend more money on the creative aspects of an ad campaign or on the delivery of the ad? – How much should a mid-career executive save out of current income toward retirement? • Require exploration more than solutions. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 6 EXPLORATION • With an inquiring mind and a spirit of discovery, exploration involves: – formulating hypotheses – making assumptions – building simple models – deriving tentative conclusions • It often reveals aspects of the problem that are not obvious at first glance. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 7 DIVERGENT AND CONVERGENT THINKING • Divergent thinking – Thinking in different directions – Searching for a variety of answers to questions that may have many right answers – Brainstorming • Convergent thinking – Directed toward achieving a goal or single solution – Involves trying to find the one best answer – Emphasis shifts from idea generation to evaluation • Decision makers need to be clear as to which they use at a given time, and balance the two. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 8 THE SIX-STAGE PROBLEM-SOLVING PROCESS 1. Exploring the mess Divergent phase Search the mess for problems and opportunities. Convergent phase Accept a challenge and undertake systematic efforts to respond to it. 2. Searching for information Divergent phase Gather data, impressions, feelings, observations; examine the situation from many different viewpoints. Convergent phase Identify the most important information. 3. Identifying a problem Divergent phase Generate many different potential problem statements. Convergent phase Choose a working problem statement. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 9 THE SIX-STAGE PROBLEM-SOLVING PROCESS (CONT’D) 4. Searching for solutions Divergent phase Develop many different alternatives and possibilities for solutions. Convergent phase Select one or a few ideas that seem most promising. 5. Evaluating solutions Divergent phase Formulate criteria for reviewing and evaluating ideas. Convergent phase Select the most important criteria; use them to evaluate, strengthen, and refine ideas. 6. Implementing a solution Divergent phase Consider possible sources of assistance and resistance to proposed solution. Identify implementation steps and required resources. Convergent phase Prepare the most promising solution for implementation. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 10 EXAMPLE: INVIVO DIAGNOSTICS • A $300M pharmaceutical company built on the strength of a single product that accounts for over 75% of revenues. • In 18 months, the patent for this product will expire. • The CEO wants to explore ways to plug the expected $100-$200M revenue gap as revenues from this product decline. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 11 1. EXPLORING THE MESS • What problems or opportunities do we face? • Where is there a gap between the current situation and the desired one? • What are the stated and unstated goals? • This stage is complete when we have: – A description of the situation – Identified (not gathered) key facts and data Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 12 2. SEARCHING FOR INFORMATION • What are the symptoms and causes? • What measures of effectiveness seem appropriate? • What actions are available? • This stage is complete when we have: – Found and organized relevant data – Made initial hypotheses about problem causes and solutions Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 13 3. IDENTIFYING A PROBLEM • Which is the most important problem? • Is this problem like others we have dealt with? • What are the consequences of a broad versus narrow problem statement? • This stage is complete when we have produced a working problem statement. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 14 4. SEARCHING FOR SOLUTIONS • What decisions are open to us? • What solutions have been tried in similar situations? • How are the various candidate solutions linked to outcomes of interest? • This stage is complete when we have produced a list of potential solutions. – Perhaps also a list of advantages and disadvantages Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 15 5. EVALUATING SOLUTIONS • How does this solution impact each of the criteria? • What factors within our control could improve the outcomes? • What factors outside our control could alter the outcomes? • This stage is complete when we have produced a recommended course of action along with justification. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 16 6. IMPLEMENTING A SOLUTION • What are the barriers to successful implementation? • Where will there be support and motivation, or resistance and conflict? • Are the resources available for successful implementation? • This stage is complete when we have produced an implementation plan and begun execution. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 17 MENTAL MODELS (INFORMAL MODELING) • Help us to relate cause and effect – But often in a simplified, incomplete way • Help us determine what is feasible – But may be limited by personal experiences • Are influenced by our preferences for certain outcomes • Are useful but can be limiting • Problem solvers construct quick, informal mental models at many different points in the process. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 18 FORMAL MODELS • Provide the same kind of information as mental models – Link causes to effects, aid in evaluating solutions • Require a set of potential solutions and criteria to compare solutions to be identified • More costly and time consuming to build than mental models • Make assumptions, logic, and preferences explicit and open to debate Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 19 INFLUENCE CHARTS • A simple diagram to show outputs and how they are calculated from inputs • Tool of choice for complex, unstructured problems • Identifies main elements of a model • Delineates the boundaries of a model • Recommended for early stages of any problem formulation task • Flexible, support frequent revision Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 20 BUILDING AN INFLUENCE CHART • Built from right to left • Conventions on types of variables – Outputs – hexagons – Decisions – boxes – Inputs – triangles – Other variables – circles – Random variables – double circles – See Figure 2.3 Figure 2.3 Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 21 INFLUENCE CHART PRINCIPLES • Start with outcome measure • Decompose outcome measure into independent variables that directly determine it • Repeat decomposition for each variable in turn • Identify input data and decisions as they arise • Ensure each variable appears only once • Highlight special types of elements with consistent symbols Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 22 EXAMPLE 1: A PRICING DECISION • “Determine the price we should set for our product so as to generate the highest possible profit this coming year.” • See Figures 2.2a – 2.2f Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 23 EXAMPLE 1: A PRICING DECISION Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 24 EXAMPLE 1: A PRICING DECISION Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 25 EXAMPLE 1: A PRICING DECISION Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 26 EXAMPLE 2: THE SS KUNIANG1 • In the early 1980s, New England Electric System (NEES) was deciding how much to bid for the salvage rights to a grounded ship, the SS Kuniang. If the bid were successful, the ship could be repaired and outfitted to haul coal for the company’s power-generation stations. But the value of doing so depended on the outcome of a U.S. Coast Guard judgment about the salvage value of the ship. • See Figure 2.6 1D. E. Bell, “Bidding for the S.S. Kuniang,” Interfaces 14 (1984): 17–23. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 27 EXAMPLE 3: AUTOMOBILE LEASING • The primary challenge for companies offering a closedend lease is to select the residual value of the vehicle. • See Figure 2.7 Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 28 INFLUENCE CHARTS WRAP-UP • The goal is to develop a problem structure—not to solve the problem. • There is no one correct chart. • Charts ignore all available numerical data. • Charts rely on modeling assumptions that should be recorded as made. Chapter 2 Copyright © 2013 John Wiley & Sons, Inc. 29 CRAFT SKILLS FOR MODELING • Successful modelers draw on both techni...
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

View attached explanation and answer. Let me know if you have any questions.

1

Privacy and Confidentiality in Nursing
Student’s Name
Course
Date

2

Privacy and Confidentiality in Nursing
Confidentiality And Privacy
[The confidentiality laws apply to everyone involved in providing medical care. I am
responsible for following the HIV disclosure policies and procedures established by the
medical facility where I work because I am now evaluating an HIV-positive patient. The HIVpositive woman should, out of an abundance of caution, inform her partner and her medical
team about her diagnosis.
If HIV testing is required in your area, you might be obligated by law to tell everyone
you've shared a bed or had intercourse with that you're HIV positive. This responsibility can
also apply to you if you reside in an area where HIV testing is required. If so, you must act
quickly (either independently or with the assistance of a medical expert, such as a nurse or
doctor) (s). If you are HIV positive and don't tell your partner, you could be in trouble with the
law (Ranjan,2022). Even if you don't want your doctor or nurse to be aware of your sexual
partners or needle-sharing habits, specific laws demand that they do so. One of the most
common methods for transmitting HIV from person to person is sharing hypodermic needles
and syringes.
]
Approach
[She will keep telling me about HIV and how it impacts her health and the health of the
people she has sex with; if I keep giving her knowledge, she will keep telling me about it. To
resolve this dilemma, I intend to have a therapeutic dialogue. Now that I know more about

3

HIV, I can educate her on the precautions she should take to prevent spreading the illness to
others.
She appears to be in good health but has HIV and can potentially spread the disease to
others. One of two things can cause this: either sharing needles or engaging in sexual activity
without using any form of protection. There is a good likelihood that her partner will use
condoms to protect themselves. Additionally, this...


Anonymous
I was struggling with this subject, and this helped me a ton!

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags