Boston University Supply Chain Management Worksheet

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Vietnam Japan Mexico Ohio Poduction Yield 90% 100% 90% 95% Salvage Revenue $2.40 $2.40 $2.40 $2.40 $32.00 $32.00 $32.00 $32.00 3000 3000 3000 3000 37.5% 30.0% 22.5% 12.5% Lead Time (Weeks) 40 35 25 15 Gross Product Cost $12.00 $14.00 $14.00 $17.00 Net Product Cost $13.33 $14.00 $15.56 $17.89 Sales Revenue Demand Forecast Forecast CV AD680 Global Supply Chains Problem Set #3: Optimization You have been hired by a vendor who is preparing for an upcoming K-Pop (Korean pop music) concert featuring the singer IU (Lee Ji-eun) in Cincinnati. The concert organizer is allowing vendors to sell IU paraphernalia. You determine that certain one-size-fits-all winter hats featuring IU’s image will be sold. You have four choices for OEM suppliers of the hats. Due to their locations, their lead times differ, along with your costs. Based on past concerts, the product sales forecast is for 3000 hats, but this estimate is uncertain depending on the concert attendance. Each hat will sell for $32. Once the concert ends, products not sold will be bought by a discounter at a heavily reduced price of $2.40 per hat. Sales forecasts will be more accurate as the concert approaches (forecast CV’s are available based on past forecasting performance). Production quality varies according to location, which is expressed as an expected production yield. Production costs are adjusted to account for these yields(and shown below as net product cost). Because the products all require careful handling, there will be an inventory holding cost that will apply as soon as the order is placed. However, the annual holding percentage is unknown at this time. The table below summarizes the important information regarding the locations under consideration. Vietnam Japan Mexico Ohio Poduction Yield 90% 100% 90% 95% Salvage Revenue $2.40 $2.40 $2.40 $2.40 $32.00 $32.00 $32.00 $32.00 3000 3000 3000 3000 37.5% 30.0% 22.5% 12.5% Lead Time (Weeks) 40 35 25 15 Gross Product Cost $12.00 $14.00 $14.00 $17.00 Net Product Cost $13.33 $14.00 $15.56 $17.89 Sales Revenue Demand Forecast Forecast CV Create a spreadsheet that determines, for each manufacturing location, the expected profits and how many units the vendor should order from each manufacturer. Assume that demand variation is normally distributed. Vary the annual holding cost percentage and show how the expected profits and order quantities for a range of holding rates from 10% to 40%. Show these results in tabular and graphical form. Clearly organize and label the spreadsheet to show inputs and results (i.e., a user may wish to modify inputs later as more information becomes available). The assessment of this work will be based on the accuracy and clarity of your spreadsheet. Attach one Excel file, using a file name Lastname_PS3. Boston University Metropolitan College AD680: Global Supply Chains Live Session Module 5/Week 5 David L. Rainey, Ph.D. Spring 2020 Module 5 Agenda ● Discussion Board Review ● Preview of Lecture 9 (Supply Chain Optimization) ● Review Problem Set 2 ● Preview of Lecture 10 (Business Function Integration) ● Preview of Assignments/Assessments ● Questions and Answers 2 Module 5: Highlights Topics & Readings: Lecture 9: Supply Chain Optimization • Importance of Assumptions to Ensure Model Accuracy • News-Vendor Model with Holding Costs • Simulation Modeling in Supply Chains • Integration of Optimization Models and Decision Making Lecture 10: Business Function Integration • Concept of Linked Activities • Incentive System Integration • Supply Chain Management Software • Comprehensive Examples Module 3 Study Guide February 4 - 10 Discussion: Group Discussion #5: Rapid-Fire Fulfillment (Article). Postings end Monday, February 24 at 11:59 PM ET Assignment: Problem Set #3: Using an optimization model to choose supplier and determine order quantity. Due Monday, February 24, at 11:59 PM ET Assessment: Quiz #5: Available from 9:00 AM ET Saturday, February 22, through 11:59 PM ET Monday, February 24 3 Boston University Metropolitan College AD680: Global Supply Chains Lecture 9 Supply Chain Optimization David L. Rainey, Ph.D. Spring 2020 Lecture 9 Agenda ● Preview of Lecture 9 Supply Chain Optimization ● Review of Problem Set 3 ● Questions and Answers 5 Lecture 9 Agenda Lecture 9: Learning Outcomes As a result of completing this lecture, students will be able to: 1. Communicate the various types of models used in the analysis of supply chains. 2. Calculate optimal order quantities for newsvendor problems with or without the inclusion of holding costs. 3. Calculate expected profits under optimal conditions with or without the inclusion of holding costs in newsvendor models. 4. Compare alterative profit expectations for various lead time. 5. Choose between optimization models and simulation models in supply chain analyses. 6. Describe simulation models in terms of their inputs and outputs (See video on Blackboard). 7. Develop a basic Monte Carlo simulation using Excel (Blackboard). 6 Overview This lecture concerns two important uses of models in a supply chain related to optimization. The first use of a supply chain model will be for mathematical optimization. That is, the model will be used to find the best solution under an assumed set of conditions. “Optimization models" are more complex. The calculations can be done manually, but Excel is a great tool. The second use of a supply chain model will be for exploring how the supply chain system will respond to various decisions, which can indirectly lead to optimizing of performance. 7 Applications Just about everyone uses a model (albeit often a simple heuristic model) to support decision making – for example, you may want to estimate the cost of a car trip (e.g., 500 miles) by dividing the number of miles by an assumed miles per gallon (mpg) of gasoline (e.g., 25 mpg) and then multiplying the result by the expected price per gallon of gasoline (e.g., $2.00/gallon). – Cost =(500 miles ÷25mpg) x $2.00 = $40 8 Limitations ● Although models can be useful, they have certain limitations that must be understood prior to their use. – for the car cost model, what happens if snow causes you to drive a lot slower and the car’s mpg is lower than assumed? ● Every model has an underlying set of “assumptions” that are required to create a manageable model. – buffering models often assume that the demand distribution is normal – EOQ assumes that holding costs and ordering costs are the primary cost considerations ● Models that include uncertainty are called “stochastic” models while those that do not include uncertainty are called 9 “deterministic models.” Deterministic & Stochastic Models ● Deterministic models (e.g., linear programming, EOQ) tend to provide solutions to problems that may be complex but do not consider uncertainties. – running the model with “what if” scenarios allows for limited analysis of uncertainty. (example, what if the rate changes?) ● Stochastic models (e.g., inventory safety stock (ss) or capacity buffering) tend to provide solutions to problems that consider uncertainty but tend to be very simple. – in supply chains, stochastic models tend to be focused specifically on one stage of supply, usually for one product, without capacity or other constraints. 10 Newsvendor Model ● The “newsvendor model” is a stochastic model that is used to determine the optimal inventory level when there is a single order placed just prior to a selling period, and no other orders may be placed to satisfy demand. – originally referred to as the “newsboy” model, the assumed scenario would represent the daily decision making of a person selling newspapers. ● Other applications include: – perishable food items on a cruise ship, clothing or other items associated with a special event, seasonal items that cannot be stored for next season, ….. 11 Notation c = production cost or seller’s purchase price per unit p = retail price or seller’s revenue per unit s = salvage price per unit (applies to all overstocked units) Q = Order quantity (Q* is the optimal order quantity) D = Actual demand CU = p – c: Understock cost per unit CO = c – s: Overstock cost per unit CSL = Cycle Service Level (CSL* is optimal CSL) 12 Example The Sunday newspaper retails for $2.50/newspaper, costs the seller $1.00/newspaper, and unsold newspapers can be sold to a recycler at $0.25/newspaper. c = $1 p = $2.5 s = $0.25 CO = 1 – 0.25 = 0.75 ($0.75/newspaper) CU = 2.5 – 1 = 1.50 ($1.50/newspaper) CO = 0.5 Cu 13 Cost Function For a given value of demand (D), the cost function is: For the newsvendor, if 40 newspapers are obtained by the seller (i.e., Q=40): Cost = (0.75) max(0,40 − D) + (1.50) max(0, D − 40) 14 For the newsvendor, if 40 newspaper are bought and actual demand is 65 newspapers, the cost to the seller is $37.50: Cost = (0.75) max(0,40 − 65) + (1.50) max(0,65 − 40) Cost = (0.75)(0) + (1.50)(25) = 37.5 if 40 newspaper are obtained by the seller and actual demand is 15 newspapers, the cost to the seller is $18.75: Cost = (0.75) max(0,40 − 15) + (1.50) max(0,15 − 40) Cost = (0.75)(25) + (1.50)(0) = 18.75 15 Example ● Consider a single season scenario (with newsvendor assumptions) where the following costs are incurred, and the demand forecast is 1000 units with a CV of 40%: c = $45, p = $60, s = $35, CO = $10; CU = $15 ● Note, if the seller orders 1000 units (i.e., the forecast), we have: – If actual demand is 200 less than forecast (D = 800), the resulting cost is $2000 Cost = ($10) max (0,1000-800) + ($15) max (0,800-1000) = $2000 – If actual demand is 200 more than forecast (D = 1200), the resulting cost is $3000 Cost = ($10) max (0,1000-1200) + ($15) max (0,1200-1000) = $3000 16 Optimal Cycle Service Level By balancing expected overstock and understock costs, the optimal service cycle level is obtained: Cu CSL* = Cu + C o c = production cost or seller’s purchase price per unit p = retail price or seller’s revenue per unit s = salvage price per unit (applies to all overstocked Q = Order quantity (Q* is the optimal order quantity) D = Actual demand CU = p – c: Understock cost per unit CO = c – s: Overstock cost per unit CSL = Cycle Service Level (CSL* is optimal CSL) Note that: When Co = Cu, CSL* = 0.5 (order same as forecast) When Co > Cu, CSL* < 0.5 (order less than forecast) When Co < Cu, CSL* > 0.5 (order more than forecast) 17 Optimal Order Quantity (Normal) Q* = NORMINV(CSL*,m,s) m = the forecast (i.e., mean) s = the forecast standard deviation CSL* Q* 18 A daily newspaper retails for $2.50/newspaper, costs the seller $1.00/newspaper, and unsold newspapers can be sold to a recycler at $0.25/newspaper. As previously described, we have: c = 1, p = 2.5, s = 0.25, CO =c-s= 0.75, CU = p-c =1.50 If the demand is forecasted to be normally distributed with a mean of 50 units and a standard deviation of 10, the optimal order quantity will be 54 newspapers: Cu 1.5 CSL* = = = 0.667 Cu + Co 1.5 + 0.75 Q* = NORMINV(0.667,50,10) = 50 + (10 x 0.44) = 54 NORMINV- Also use Excel: Formulas; More Functions, Statistical. 19 Z=norminv(CSL,0,1) CSL Z CSL Z CSL Z CSL Z CSL Z 50% 0.000 60% 0.253 70% 0.524 80% 0.842 90% 1.282 51% 0.025 61% 0.279 71% 0.553 81% 0.878 91% 1.341 52% 0.050 62% 0.305 72% 0.583 82% 0.915 92% 1.405 53% 0.075 63% 0.332 73% 0.613 83% 0.954 93% 1.476 54% 0.100 64% 0.358 74% 0.643 84% 0.994 94% 1.555 55% 0.126 65% 0.385 75% 0.674 85% 1.036 95% 1.645 56% 0.151 66% 0.412 76% 0.706 86% 1.080 96% 1.751 57% 0.176 67% 0.440 77% 0.739 87% 1.126 97% 1.881 58% 0.202 68% 0.468 78% 0.772 88% 1.175 98% 2.054 59% 0.228 69% 0.496 79% 0.806 89% 1.227 99% 2.326 20 Q* = NORMINV(0.667,50,10) = 54 Q* = 50+z x std dev= 50+0.44 x 10 = 50 + 4.4 = 54 50 54 21 Consider a single season scenario (with newsvendor assumptions) where the following costs are incurred, and the demand forecast is 1000 units with a CV of 40%: c = $45, p = $60, s = $35, CO = c-s = $10; CU = p-c = $15 The optimal order quantity will be 1101 products: Cu 15 CSL* = = = 0.6 Cu + Co 15 + 10 Q* = NORMINV(0.6,1000,400) = 1101 Q* = 1000+z x std dev= 1000+ (0.253 x 400) = 1000 + 101 = 1101 22 Z=norminv(CSL,0,1) CSL Z CSL Z CSL Z CSL Z CSL Z 50% 0.000 60% 0.253 70% 0.524 80% 0.842 90% 1.282 51% 0.025 61% 0.279 71% 0.553 81% 0.878 91% 1.341 52% 0.050 62% 0.305 72% 0.583 82% 0.915 92% 1.405 53% 0.075 63% 0.332 73% 0.613 83% 0.954 93% 1.476 54% 0.100 64% 0.358 74% 0.643 84% 0.994 94% 1.555 55% 0.126 65% 0.385 75% 0.674 85% 1.036 95% 1.645 56% 0.151 66% 0.412 76% 0.706 86% 1.080 96% 1.751 57% 0.176 67% 0.440 77% 0.739 87% 1.126 97% 1.881 58% 0.202 68% 0.468 78% 0.772 88% 1.175 98% 2.054 59% 0.228 69% 0.496 79% 0.806 89% 1.227 99% 2.326 23 Expected Profit (Normal Case) When the order quantity is Q and demand is normally distributed, the expected profit in the newsvendor case is shown below. Be careful to distinguish between the order quantity (Q) and the number zero (0). Expected Profit =EP= (p-s)*m*NORMDIST((Q-m)/s,0,1,1)– (p-s)*s*NORMDIST((Q-m)/s,0,1,0)– Q*(c-s)*NORMDIST(Q,m,s,1)+ Q*(p-c)*(1-NORMDIST(Q,m,s,1)) NORMDIST - Use Excel: Formulas. More Functions, Statistical 24 Expected Profit (Normal Case) A daily newspaper retails for $2.50/newspaper, costs the seller $1.00/newspaper, and unsold newspapers can be sold to a recycler at $0.25/newspaper. As previously described, we have: c = 1, p = 2.5, s = 0.25, CO = 0.75, CU = 1.50 If the demand is forecasted to be normally distributed with a mean of 50 units and a standard deviation of 10, the optimal order quantity will be 54 newspapers (shown earlier) and the expected profit is $668.19. 2.25 50 2.25*50*NORMDIST(0.4,0,1,1)– 2.25 10 54 0.75 2.25*10*NORMDIST(0.4,0,1,0)– 54 1.5 54*0.75*NORMDIST(54,50,10,1)+ 54*1.5*(1-NORMDIST(54,50,10,1))=668.19 0.6554217 0.3682701 0.6554217 0.3445783 - 737.3 82.9 265.4 279.1 668.2 25 Consider a single season scenario (with newsvendor assumptions) where the following costs are incurred, and the demand forecast is 1000 units with a CV of 40%: c = $45, p = $60, s = $35, CO = $10; CU = $15 With an optimal order quantity of 1101 units (shown earlier) the expected profit would be $11,137: 25 25 1101 1101 1000 400 10 15 25*1000*NORMDIST(0.2525,0,1,1)– 25*400*NORMDIST(0.2525,0,1,0)– 1101*10*NORMDIST(1101,1000,400,1)+ 1101*15*(1-NORMDIST(1101,1000,400,1))=11136.57 0.5996727 0.3864253 0.5996727 1-0.5996727 14991.82 - 3864.25 - 6602.40 6611.40 11136.57 Expected Profit =EP= (p-s)*m*NORMDIST((Q-m)/s,0,1,1)– (p-s)*s*NORMDIST((Q-m)/s,0,1,0)– Q*(c-s)*NORMDIST(Q,m,s,1)+ Q*(p-c)*(1-NORMDIST(Q,m,s,1)) 26 Modified Newsvendor Model ● An inventory model can be modified to represent certain conditions, for example: – quantity discounts – continuously stocked items – backorders ● The addition of holding costs is easy to accomplish, representing a scenario where there is one order placed well ahead of the selling season; this would cause additional costs that are not accounted for the traditional newsvendor model: – security, warehousing, taxes, storage, etc. 27 Modified Newsvendor Model Note that a new cost is added: CH = Unit cost for holding product ordered (must be consistent with length of the time period prior to demand realization). The optimal CSL is: Cu − C H CSL* = Cu + Co The optimal order quantity is determined in the same way (as the classical model) and expected profit is modified by adding the product of CH and the order quantity. 28 Modified Newsvendor Model Consider a product with a cost of $25 that incurs an annual holding rate of 20%. For an analysis of production 6 months ahead of the selling season, the value of CH be $2.50: C H = (0.2)(25)(0.5) = 2.5 20% annual holding cost percentage Product cost per unit Portion of year products are held 29 Consider a single season scenario (with newsvendor assumptions plus holding costs) where the demand forecast is 1000 units with a CV of 40%, the product has an annual holding rate of 20%, the order must be placed 3 months in advance of sales, and the following costs are incurred: c = $45, p = $60, s = $35, CO = $10; CU = $15 Note that the holding cost (CH is $2.25/unit). C H = (0.2)(45)(0.25) = 2.25 The optimal order quantity will be 1010 products: Cu − C H 15 − 2.25 CSL* = = = 0.51 Cu + Co 15 + 10 O* = NORMINV(0.51,1000,400) = 1010 See Excel – Formulas; More Functions, Statistical. 30 Z=norminv(CSL,0,1) CSL Z CSL Z CSL Z CSL Z CSL Z 50% 0.000 60% 0.253 70% 0.524 80% 0.842 90% 1.282 51% 0.025 61% 0.279 71% 0.553 81% 0.878 91% 1.341 52% 0.050 62% 0.305 72% 0.583 82% 0.915 92% 1.405 53% 0.075 63% 0.332 73% 0.613 83% 0.954 93% 1.476 54% 0.100 64% 0.358 74% 0.643 84% 0.994 94% 1.555 55% 0.126 65% 0.385 75% 0.674 85% 1.036 95% 1.645 56% 0.151 66% 0.412 76% 0.706 86% 1.080 96% 1.751 57% 0.176 67% 0.440 77% 0.739 87% 1.126 97% 1.881 58% 0.202 68% 0.468 78% 0.772 88% 1.175 98% 2.054 59% 0.228 69% 0.496 79% 0.806 89% 1.227 99% 2.326 31 Optimal CSL w/Holding Cost With the addition of holding costs, the expected profit when ordering O units is: The expected profit with holding costs (normally distributed demand) is: E(P)= (p−s) × μ × NORMDIST(Q−μ/σ,0,1,1) −(p−s) × σ × NORMDIST(Q−μ/σ,0,1,0) −Q × (c−s) × NORMDIST(Q,μ,σ,1) +Q × (p−c) × (1−NORMDIST(Q,μ,σ,1)) −CH x Q 32 Optimal CSL w/Holding Cost Note that, as expected, the optimal order quantity decreases with the inclusion of holding costs. With an optimal order quantity of 1010 units, the expected profit with holding cost would be $8,762 (a reduction from $11,137 without holding costs): 25*1000*NORMDIST(0.025,0,1,1)– 25*400*NORMDIST(0.025,0,1,0)– 1010*10*NORMDIST(1010,1000,400,1)+ 1010*15*(1-NORMDIST(1010,1000,400,1)) – 2.25*1010=8761.83 33 Simulation Modeling ● When problems become too complex for a stochastic model, a “simulation” model can be employed. – simulation models are also useful when an analyst does not know the existence of a more sophisticated model. ● Simulation models mimic the problem under study; monte carlo simulation is a simulation that uses random numbers to mimic uncertainty. – the key to this development is the ability to generate random numbers that are consistent with an assumed statistical distribution, and to “run” the simulation a large number of “iterations.” (See video on Blackboard) 34 Problem Set 3 Assignment Optimization You have been hired by a vendor who is preparing for an upcoming K-Pop (Korean pop music) concert featuring the singer IU (Lee Ji-eun) in Cincinnati. The concert organizer is allowing vendors to sell IU paraphernalia. You determine that certain one-size-fits-all winter hats featuring IU’s image will be sold. You have four choices for OEM suppliers of the hats. Due to their locations, their lead times differ, along with your costs. Based on past concerts, the product sales forecast is for 3000 hats, but this estimate is uncertain depending on the concert attendance. Each hat will sell for $32. Once the concert ends, products not sold will be bought by a discounter at a heavily reduced price of $2.40 per hat. Sales forecasts will be more accurate as the concert approaches(forecast CV’s are available based on past forecasting performance). Production quality varies according to location, which is expressed as an expected production yield. 35 Problem Set 3 Assignment Optimization Production quality varies according to location, which is expressed as an expected production yield. Production costs are adjusted to account for these yields (and shown below as net product cost). Because the products all require careful handling, there will be an inventory holding cost that will apply as soon as the order is placed. However, the annual holding percentage is unknown at this time. The table below summarizes the important information regarding the locations under consideration. 36 Problem Set 3 Assignment Optimization Vietnam Japan Mexico Ohio Production Yield 90% 100% 90% 95% Salvage Revenue $2.40 $2.40 $2.40 $2.40 $32.00 $32.00 $32.00 $32.00 3000 3000 3000 3000 37.5% 30.0% 22.5% 12.5% Lead Time (Weeks) 40 35 25 15 Gross Product Cost $12.00 $14.00 $14.00 $17.00 Net Product Cost $13.33 $14.00 $15.56 $17.89 Sales Revenue Demand Forecast Forecast CV 37 Problem Set 3 Assignment Optimization Create a spreadsheet that determines, for each manufacturing location, the expected profits and how many units the vendor should order from each manufacturer. Assume that demand variation is normally distributed. Vary the annual holding cost percentage and show how the expected profits and order quantities for a range of holding rates from 10% to 40%. Show these results in tabular and graphical form. Clearly organize and label the spreadsheet to show inputs and results (i.e., a user may wish to modify inputs later as more information becomes available). The assessment of this work will be based on the accuracy and clarity of your spreadsheet. Attach one Excel file, using a file name Lastname_PS3. 38 Boston University Metropolitan College AD680: Global Supply Chains Lecture 10 Business Function Integration David L. Rainey, Ph.D. Spring 2020 Lecture 10 Agenda ● Preview of Lecture 9 Business Function Integration ● Preview of Article #3 ● Questions and Answers 40 Lecture 10 Agenda Lecture 10: Learning Outcomes As a result of completing this lecture, students will be able to: • Appreciate the impact that linked activities have on business effectiveness. • Project the impact that activates in any business process has on supply chain effectiveness. • Design incentive systems that promote better performance of the whole, with little chance of gaming. • Choose a supply chain management (SCM) software system that meets the needs of the global supply chain. • Provide specific examples of effective business process integration and why this integration is critical. • Develop and deploy business function integration across the 41 supply chains. Overview Business Integration Integration in a global supply chain necessitates that every business activity within the firm is aligned with the strategic focus of the firm’s supply chain. “Linked" activities would take place in operations-related functions. A full integrated supply chain would also integrate all administrative, support, and other business functions. Full integration also requires that all internal systems and processes are aligned and consistent with the supply chain focus. 42 Overview Connectedness The global economy is a complex structure that engenders both opportunities and challenges. It is the linking of economies, markets, and customers through the expansion of trade and the liberalization of market restrictions. Global supply chains and the management thereof require innovative strategies for managing the complex array of forces that impinge on supply chain management (SCM) decisionmaking. Markets and customers expect customized, sophisticated, high quality products and services with exceptional value. Markets and stakeholder expectations often cross industry lines43 Business Function Integration Connectedness Many factors can complicate successful business process integration in supply chains. First, many corporate leaders can lack enough understanding of the complex supply chain system (like in the Honda case). Thus, they may consider the supply chain to be a selfcontained function that operates independently of the firm’s other business functions. Second, there are facets of supply chain performance that are directly affected by decisions made in seemingly unrelated business functions. 44 Business Function Integration Connectedness Function Executive Other Names or Purposes Leadership, Management Operations Production, Manufacturing Planning IT Finance Scheduling, Forecasting Information Services, Computing Accounting, Investing, Payroll, Accounts Procurement Purchasing, Supplier Management Sales Customer Relationship Management Marketing Demand Management, Promotions Quality Logistics Design HR Legal Performance, Accreditation, Certification Warehousing, Transportation Engineering, Innovation Management Personnel, Talent Management Law, Contract Management 45 Incentive System Integration One of the main features of a fully integrated supply chain is the alignment of incentives. Challenges exist, however, due to the diversity of supply chain members. Often, "hidden" information and actions exist that some members choose not to disclose for proprietary or competitive reasons. Poorly designed incentive systems are those that are geared towards "local" optimization, those that are shortsighted, and those that promote "gaming." Ideally, by using effective metrics, a strong sense of cooperation (rather than competition) will permeate the supply chain. 46 Incentive System Examples Types of Incentives Merit pay impacted by quantity of cost savings in Six Sigma projects. Salesforce incentive system that pays percentage of revenue. “Piecework” pay for each unit made by production workers. Bonus to service employee based on satisfaction survey results. Although some practitioners tend to like and others dislike individualized incentives, both would agree that if used, they should align with system goals and be resistant to “gaming.” 47 Better Alignment Incentive Merit pay impacted by quantity of cost savings in Six Sigma projects. Salesforce incentive system that pays percentage of revenue. “Piecework” pay for each unit made by production workers. Bonus to service employee based on satisfaction survey results. When projects deal with easily quantifiable problems. For innovative products in a responsive system. When quality goals are is easy to meet and inventory is buffered. When sample sizes are large & server has sole control over service. 48 Worse Alignment Incentive Merit pay impacted by quantity of cost savings in Six Sigma projects. Salesforce incentive system that pays percentage of revenue. “Piecework” pay for each unit made by production workers. Bonus to service employee based on satisfaction survey results. When project effects are difficult to quantify precisely. For products whose production is based on level loading. When it is important for operators to pay attention to quality. When sample sizes are small or server is a just a “cog in the wheel.” 49 SCM Integration Linking Business Functions As the number of entities (especially in supply chains) increases, integration becomes even more critical. For example, fragmented linkages often characterized the traditional supply chains. Each entity in a given process may have fulfilled its responsibilities without much input or considerations from the other participants in the system. Networking with suppliers, distributors, partners, allies, customers, and stakeholders requires sharing information, knowledge, and experiences about products, materials, parts, components and waste streams, and the requisite interfaces between the entities. The intent of business function integration, with respect to external entities, is to facilitate cooperation, collaboration, and communications among entities. SCM Integration Connecting with Supply Networks Connecting with suppliers allows the producers and service providers to acquire a more complete understanding the flows of goods, services and information that go into the products and the implications and impacts of choices and decisions. Despite the sophistication of modern SCM, most global corporations have only limited information about the processes and activities of their suppliers, especially of suppliers of suppliers and beyond. While it is seemingly impossible to keep track of all external entities, the whole business enterprise can function more effectively if it is properly linked and there is a common ground of understanding among the entities and participants. SCM Integration Connecting with Supply Networks Steps Identifying and Defining Identifying reality and determining the driving forces in the business environment. Elements -Identifying the driving forces in the business environment. -Identifying the regulatory mandates that pertain to suppliers and the business enterprise. -Defining environment, health and safety concerns -Determining key stakeholders involved in the flow of goods and information -Determining their objectives, needs, and expectations. -Identifying the information requirements. -Identifying trade associations and industry groups that can provide information and support. -Obtaining related research from academic communities. Analyzing -Assessing the key issues, concerns and mandates. Assessing driving -Benchmarking important peers and competitors. forces and -Determining the needs and requirements related to supply chain aspects. supply chain -Assessing the main strategic suppliers and distributors. capabilities, -Determining supply chain uncertainties, risks, vulnerabilities and potential resources and disruptions. performance -Developing alternative sources of supply, especially considering potential disruptions. SCM Integration Connecting with Supply Networks Steps Elements Goal Setting Defining the short-term and long-term goals, including the actions required for improving the processes. -Determining and prioritizing the opportunities for improvements. -Reviewing media reports and the literature to determine the most critical needs & expectations. -Listing specific targets for improvements. -Identifying the most relevant social, economic and environmental objectives. -Identifying ways for improving compliance and eliminating the need for it. -Defining targets for reducing uncertainties and risks. -Setting the goals and objectives. -Developing appropriate metrics. -Establishing protocols and information sharing systems to link the participants. -Linking supply chains to the business enterprise. -Creating short-term success outcomes to build momentum. -Educating supply chains. -Changing attitudes about the expectations. -Building a spirit of cooperation, collaboration, and commitment across the enterprise. -Preparing actions plans and long-term initiatives Articulating Action Plans Establishing the initiatives to improve outcomes, reduce impacts, and obtain success. SCM Integration Connecting with Supply Networks Steps Implementing and Sustaining Implementing initiatives and programs to achieve balanced solutions; building awareness, acceptance and confidence in the making improvements and ongoing progress. Elements -Changing mindsets about the value proposition. -Establishing new criteria for materials, parts, components, and goods including requirements for minimizing resources utilization, degradation, disruptions, and impacts and improving end-of-life considerations by facilitating recycling. -Communicating the program to suppliers, distributors, customers, stakeholders and communities. -Auditing progress over time and taking corrective actions. -Evaluating ongoing results and making improvements -Reporting on the progress and ongoing challenges. -Celebrating and rewarding outstanding achievements. -Continuing the process. SCM Integration Connecting with Supply Networks Suggested Goal Setting Items Types of Business Function Integration Determining a Model for Business Function Integration The multidimensional perspectives involve sophisticated management systems, proactive strategies, cutting-edge product development, and innovative methods that are developed and deployed to enhance the positive aspects and eliminate the negative aspects of the social, political, economic, technological, environmental, and ethical forces. Business function integration requires advanced information and communications technologies; cost-effective means and mechanisms for designing, producing and transporting goods; sophisticated business models; and new-to-the-world solutions. It is based on the realization that success depends on all the entities and participants engaged in the business transactions. Reflections Successful and sustainable global supply chain integration requires leaders and professionals who are knowledgeable, confident, and technical astute. They take a long-term, holistic perspective while navigating the day-to-day functions, issues and challenges. They also have to be decision makers who play a role in strategic planning, operational development, and leadership. Although the professionals who are assigned to these positions are generally skilled in one or more technical competencies, they are often not prepared to fully appreciate the myriad functional requirements, issues and navigate the various challenges. Discussion Article #3 Article: Rapid Fire Fulfillment by Ferdows, Lewis, and Machuca For this group discussion, read the article listed above and that illustrates the integration of business functions and other decisions in a responsive supply chain. The article states that, although Zara’s supply chain practices seem crazy when considered individually, their overall supply chain system is very effective. That is, as stated in the article, Zara’s supply chain approach can be said to be “penny foolish, and pound wise.” Consider any or all business functions including planning, production, procurement, quality, logistics, sales, marketing, finance, HR, accounting, engineering, design, and IT. 58 Processing math: 100% Module 5 This is a single, concatenated file, suitable for printing or saving as a PDF for offline viewing. Please note that some animations or images may not work. Module 5 Study Guide February 18 - 24 Topics & Lecture 9: Supply Chain Optimization Readings: • Importance of Assumptions to Ensure Model Accuracy • News-Vendor Model with Holding Costs • Simulation Modeling in Supply Chains • Integration of Optimization Models and Decision Making Lecture 10: Business Function Integration Discussions: • Concept of Linked Activities • Incentive System Integration • Supply Chain Management Software • Comprehensive Examples Group Discussion #5: Rapid-Fire Fulfillment (Article). Postings end Monday, February 24, at 11:59 PM ET Assignments: Problem Set #3: Using an optimization model to choose supplier and determine order quantity. Due Monday, February 24, at 11:59 PM ET Assessments: Quiz #5 - available from 9:00 AM ET Saturday, February 22 through 11:59 PM ET Monday, February 24 Live Tuesday, February 18, at 7:00 PM ET Classrooms: (will be recorded) Lecture 9: Supply Chain Optimization Lecture 9: Supply Chain Optimization Sections: 1. Learning Objectives 2. Traditional Newsvendor Model 3. Modified Newsvendor Model 4. Simulation Modeling 5. References Learning Objectives As a result of completing this lecture, students will be able to: 1. Communicate the various types of models used in the analysis of supply chains. 2. Calculate optimal order quantities for newsvendor problems with or without the inclusion of holding costs. 3. Calculate expected profits under optimal conditions with or without the inclusion of holding costs in newsvendor models. 4. Compare alterative profit expectations for various lead-time supply chains. 5. Choose between optimization models and simulation models in supply chain analyses. 6. Describe simulation models in terms of their inputs and outputs. 7. Develop a basic Monte Carlo simulation using Excel. Background This course has highlighted the use of analytical approaches to support supply chain decision making. These approaches have included forecasting, performance metric analysis, inventory aggregation, and buffer size determination. More complex approaches have been developed that consider a broader perspective. These approaches require that a supply chain "model" is specified that represents the operation of a supply chain. The models include both complex versions of the forecasting and buffering models contained in this course (e.g., buffering in a multistage inventory system) and models that "optimize" supply chain operations. It is important to clarify that the term optimization always applies to a model. This model should adequately represent the real-world system under study but will not be a perfectly accurate representation. That is, a model is only as good as the assumptions that underlie its use. For example, many models covered in this course assume that uncertainty can accurately be modeled by the normal distribution. Although this is often a valid assumption in many cases, the normality assumption can also be violated in many real-world supply chains. Any user of a model must be cognizant of its underlying assumptions, and must also ensure that the assumptions are consistent with the real world. This is not to say that models must always be a perfect representation of reality. By use of "what if" or "sensitivity analysis," an analyst can explore how the supply chain would function under a range of assumptions rather than relying on a single assumption that is subject to uncertainty. This lecture concerns two important uses of models in a supply chain related to optimization. The first use of a supply chain model will be for mathematical optimization. That is, the model will be used to find the best solution under an assumed set of conditions. We have already done some of this earlier, such as the calculation of optimize buffer sizes. Here, these "optimization models" will be more complex. The second use of a supply chain model will be for exploring how the supply chain system will respond to various decisions, which can indirectly lead to optimizing of performance. These "simulation models" are usually used for even more complex scenarios and for those that do not have mathematically optimal results. Other phrases used in supply chain modeling include deterministic modeling (usually optimization modeling with uncertainty not accounted for in the model); stochastic modeling (usually optimization modeling with uncertainty accounted for in the model); and heuristic modeling (the use of rules of thumb or simplified solutions that have been shown to work well in some situations). Traditional Newsvendor Model The newsvendor model (formerly known as the newsboy model) is a stochastic model that is used to determine the optional order quantity when there is a single order placed just prior to a single selling period; no other orders may be placed to satisfy demand during the period. The phrase is derived from the problem faced by a traditional newspaper vendor. This vendor sells newspapers that are bought from a publisher and sold to consumers. The seller must discard unsold newspapers at the end of the day (or sell them to a recycler). The preferred order quantity needs to strike a balance between the cost of underestimating demand (lost sales opportunities) and the cost of overestimating demand (leftover newspapers). The newsvendor model has many real-world applications. They include sellers of highly perishable food (e.g., a sushi restaurant, food on a cruise ship); high-fashion clothing (i.e., one selling season and an offshore vendor with a long lead time, precluding more than one order); souvenirs and other targeted products at a special event (e.g., Expo, World’s Fair, concert tour); or any products sold in short seasons with long production or procurement lead times. In addition, minor variations of the newsvendor model’s assumptions can be incorporated. For example, in this module, we will incorporate an assumption of holding cost (which applies when the products need to be ordered ahead of time and held in storage until the selling season commences). It should be noted, however, that each expanded application brings more complexity and often the necessity of simplifying certain assumptions. Table 1 provides notation that will be used in the newsvendor model. For example, if a daily newspaper retails for $2.50 and costs the seller $1.00 per newspaper and unsold newspapers are sold to a recycler for $0.25 per newspaper, we have: c=1, p=2.5, s=0.25, Co=0.75 and Cu=1.5. Note that Cu=p−c is the per unit lost opportunity to make a profit and Co=c−s is the difference between the procurement cost and the salvage value. Table 1: Newsvendor Model Notation Notation c Description Procurement or production cost (seller’s purchase price per unit) p Retail price or seller’s revenue per unit s Salvage price per unit (applies to all overstocks) Q Order quantity (Q∗ denotes the optimal value of Q) D Actual demand (units) Cu=p−c Understock cost per unit Co=c−s Overstock cost per unit CSL Cycle service level (CSL∗ denotes the optimal value of CSL) The revenue to the newsvendor is simply the product of the number of newspapers sold and the selling price. As shown in Equation 1, the quantity sold is either D (the actual demand) or Q (the amount ordered), depending on whether the order quantity exceeds the actual demand. For example, if 450 products are ordered and demand is 500, the revenue will be $1,125 --- the product of the selling price (p=2.5) and the order quantity (Q=450). If, on the other hand, 450 products are ordered and demand is 400, the revenue will be $1000 --- the product of the selling price (p=2.5) and the actual demand (D=400). Revenue =p×min(Q,D)[1] The cost to the newsvendor depends on whether or not there are overstocks or understocks at the end of the day. This cost function is shown as Equation 2. For example, if 450 newspapers are ordered and demand is 500, the cost will be $75 –-- the product of the understock cost (1.5) and the understock quantity (D−Q=50). If, on the other hand, 450 newspapers are ordered and demand is 400, the cost will be $37.5 –-- the product of the overstock cost (0.75) and the overstock quantity (Q−D=50). Cost =Comax(0,Q−D)+Cumax(0,D−Q)[2] The calculation for the order quantity that minimizes Equation 2 (called the optimal order quantity) is provided as Equation 3, where CSL is called the cycle service level. Note that, when CO equals CU, there is indifference between understocks and overstocks. In this case, the optimal CSL is 0.5 –-- and therefore the optimal order quantity will be the median demand. When CO< CU, the optimal CSL will be higher than 0.5, and therefore the optimal order quantity would be higher than the demand forecast. Correspondingly, the optimal order quantity will be lower than the forecast when CO> CU. CSL∗=CuCu+Co[3] When demand is normally distributed, the optimal order quantity (Q*) is easily derived. In Excel, the function shown as Equation 4 is used to obtain the optimal order quantity. When demand follows other distributions, the optimal order quantity is found in a similar manner (using the Excel function for that distribution). NORMINV(CSL∗,μ,σ)[4] The optimal order quantity (Q*) for a normally distributed demand scenario is shown in Figure 1. Specifically, the area to the left of the optimal order quantity would be equal to the optimal CSL (CSL∗). Figure 1: Optimal Order Quantity (Normal Demand)s Example 1 For the example stated earlier: A daily newspaper retails for $2.50 and costs the seller $1.00 per newspaper and unsold newspapers are sold to a recycler for $0.25 per newspaper. As shown earlier: c=1, p=2.5, s=0.25, CO=0.75 and CU=1.5. Demand is assumed to be normal with a forecast (i.e., mean) of 500 newspapers and a standard deviation FOP 100 newspapers. The value of CSL∗ is 0.667 (Equation 3) and the optimal order quantity (Q*) is 543 units (Equation 4). The result is illustrated in Figure 2. Note that the order quantity is always an integer (i.e., it is rounded from the Excel function result). Figure 2: Optimal Order Quantity (Example 1) Example 2 Consider a single-season scenario (with newsvendor assumptions) in which the revenue per product is $60, the procurement cost is $45 and the salvage value is $35 per unit. Demand is forecasted to follow a normal distribution with a mean of 1000 units and a coefficient of variation (CV) of 40%. We have: c=45, p=60, s=35, CO=10, CU=15, μ=1000, and σ=400. Prior to doing the optimization calculations, it is always a good idea to predict the correct answer. This will prevent mistakes (i.e., incorrect calculations) and can help to understand the methodology (when the estimate is incorrect, but the calculations are correct). In this case, because the understock cost is higher that the overstock cost, we expected that the optimal order quantity would be greater than the forecast (to avoid understocks). In any case, for this problem the value of CSL∗ is 0.600 (Equation 3) and the optimal order quantity (Q∗) is 1101 units (Equation 4). The result is illustrated in Figure 3. Figure 3: Optimal Order Quantity (Example 2) For an order quantity, the mathematical expectation for the profit, E(P), can be calculated when demand is normally distributed. The Excel version of this equation is shown in Equation 5. Equation 5 E(P)=(p-s)*μ*NORMDIST((Q-μ)/σ,0,1,1)-(p-s)*σ*NORMDIST((Q-μ)/σ,0,1,0)Q*(c-s)*NORMDIST(Q,μ,σ,1)+Q*(p-c)*(1-NORMDIST(Q,μ,σ,1)) Example 1 (Revisited) For the first example stated earlier: A daily newspaper retails for $2.50 and costs the seller $1.00 per newspaper and unsold newspapers are sold to a recycler for $0.25 per newspaper. Demand is assumed to be normal with a forecast of 500 newspapers and a standard deviation of 100 newspapers. The value of CSL∗ is 0.667 and the optimal order quantity (Q∗) is 543 units. The expected profit is $66.82, obtained using Equation 5. Example 2 (Revisited) For the second example stated earlier: A single-season scenario (with newsvendor assumptions) in which the revenue per product is $60, the procurement cost is $45 and the salvage value is $35 per unit. Demand forecasted to follow a normal distribution with a mean of 1000 units and a coefficient of variation (CV) of 40%. The value of CSL∗ is 0.600 and the optimal order quantity (Q∗) is 1101 units. The expected profit is $11,137, obtained using Equation 5. Test Yourself The traditional newsvendor model requires the following inputs: a. Variation of the demand forecast. b. Fixed ordering costs. c. Cycle service level (CSL). d. All of the above. Show Answer Modified Newsvendor Model A supply chain optimization model can sometimes be modified to represent unique conditions. Some examples of modifications would include quantity discounts, continuously stocked items, backorders, non-normal demand, and multi-stage storage. At times, the resulting model can be solved mathematically. Although mathematical expertise is required, this approach is generally fast and can be applied relatively quickly. At other times, the problem can be solved only by using a simulation approach, discussed later in this module. The inclusion of holding costs in an otherwise traditional newsvendor model is relatively easy to accomplish (Maleyeff, 2014). The resulting model can be solved mathematically. In this scenario, one order is placed well ahead of the selling season. The long lead time would cause additional costs that are not accounted for in the traditional newsvendor model. These costs, called holding costs or carrying costs, would include security, warehousing, taxes, and storage, as well as the cost of capital (i.e., money that could have been earned by putting the same funds to productive use). The model that includes holding costs will be used to assist in decision making regarding the production or procurement of goods for a single selling season. It will help a supply chain planner compare more efficient long lead time ordering with responsive short lead time ordering. The main reason for long lead time ordering is to minimize manufacturing costs by smoothing production or reducing procurement costs by offshoring. However, ordering goods in this way will would typically result in higher holding costs and the need to accommodate higher forecast uncertainty. But more responsive later ordering would often require a more expensive supply chain. The newsvendor model with holding costs would use a modified cost function as shown in Equation 6. Cost=CHQ+COmax(0,Q−D)+CUmax(0,D−Q)[6] The value of CH (holding cost) must be consistent with the length of time that the item will be held in storage prior to being sold. Its calculation is shown as Equation 7, where h is the annual holding cost rate, c remains as defined earlier, and t is the relevant length of time (expressed as a fraction of a year). CH=h×c×t[7] For example, consider a product with a cost of $25 that incurs an annual holding rate of 20%. For an analysis of production six months ahead of the selling season, the value of CH be $2.50 -p the product of 0.2 (h), 25 (c), and 0.5 (t). When holding cost is included, the optimal order quantity is derived using Equation 8. Notice that, as expected, when the holding cost increases, the optimal order quantity will decrease. CSL∗=CU−CHCU+CO[8] The expected profit with holding costs (normally distributed demand) is shown as Equation 9. E(P)= (p−s)×μ×NORMDIST ( Q−μσ,0,1,1 [9]−(p−s)×σ×NORMDIST ) ( NORMDIST(Q,μ,σ,1)+Q×(p−c)×(1−NORMDIST(Q,μ,σ,1))−CHQ Example 2 (Revisited) Q−μσ,0,1,0 ) −Q×(c−s)× For the second example stated earlier: A single-season scenario (with newsvendor assumptions) in which the revenue per product is $60, the procurement cost is $45 and the salvage value is $35 per unit. Demand forecasted to follow a normal distribution with a mean of 1000 units and a coefficient of variation (CV) of 40%. Assuming that the product has an annual holding rate of 20%, the product must be ordered three months in advance of sales and held in storage for that time frame. The following costs are incurred: c=45, p=60, s=35, CO=10 and CU=15. In addition, μ=1000, σ=400, and the value of CH is 2.25 --- the product of 0.2 (h), 45 (c), and 0.25 (t), using Equation 7. The value of CSL* is 0.510 using Equation 8 (this value is reduced from 0.600 --- its value without holding costs). The value of Q* is 1010 units using Equation 4 (this value is reduced from 1101 units --- its value without holding costs). Finally, the expected profit is $8,762, obtained using Equation 9 (this value is reduced from $11137 --- its value without holding costs). The incorporation of holding cost has had a profound effect on the results of the optimization. This is the type of analysis used by Maleyeff (2014) in evaluating the advantages of moving from an efficient supply chain to a responsive supply chain when a manufacturer changes from selling commodity (i.e., functional) products to fashion (i.e., innovative) products. Comprehensive Exercise A manufacturer is attempting to determine the benefits of postponing production of new wood products. Forecasters can do a better job of forecasting if they have more time to study consumer preferences by organizing focus groups, surveying potential customers, or doing other forms of market research. Specifically, the forecast CV is expected to be 40% when products are produced nine months ahead of sales, 25% when products are ordered six months ahead of sales, and 15% when products are ordered three months ahead of sales. For the sake of comparison, the analysis will assume a forecast of 100,000 units, with revenue averaging $125 per unit sold. Three options are available: (1) offshoring (a nine-month lead time), with a production cost of $37.50; (2) outsourcing domestically (a six-month lead time), with a production cost of $44; and (3) in-house production (a three-month lead time), with a production cost of $50. The annual holding rate is estimated at 35% (it is high due to climate controls required during storage of wood products). Overstocked items will be sold at a heavy discount (to a reseller such as overstock.com) estimated to be $12.50 per unsold unit. The results of applying the model are shown in Table 2 (readers should confirm all calculations). Based on this analysis, the best solution would be to produce the product in-house, because it has the highest expected profit. Table 2: Inputs and Results (Comprehensive Exercise) (1) Offshoring (2) Outsourcing (3) In-House Lead Time 9 6 3 t 0.75 0.5 0.25 c 37.5 44 50 p 125 125 125 s 12.5 12.5 12.5 h 0.35 0.35 0.35 CU 87.5 81 75 CO 25 31.5 37.5 CH 9.844 7.700 4.375 CSL* 0.6903 0.6516 0.6278 CV 0.400 0.250 0.150 μ 100,000 100,000 100,000 σ 40,000 25,000 15,000 Q* 119,868 109,741 104,890 E(P) $6,178,668 $6,289,948 $6,424,119 Often an analysis is based on estimates that may not all be highly reliable. In these instances, the analyst can do a sensitivity analysis based on one or more key uncertain factors. The effect of these factors can be evaluated as they are changed across a range of potential values. For this scenario, it is likely that the main uncertain factors may include the forecast, the CV of the forecast, and the holding rate. As an example, we can adjust the value for the holding rate while keeping all other variables consistent with their assumed values. The results of this analysis are shown in Figure 4. It is clear that, as the holding rate changes, the preferred production location (and associated lead time) changes. It appears that outsourcing domestically is never the optimal option. The offshoring option is preferred when the holding rate is about 22%23% or below; otherwise the in-house option is preferred. The analyst should confirm the most accurate value of holding rate (even if a study needs to be undertaken) before presenting a firm recommendation. Figure 4: Sensitivity Analysis (Comprehensive Example) Simulation Modeling When problems become too complex for an optimization model, a simulation model can be employed. Simulation models are also useful when an analyst does not know of the existence of a more sophisticated model. Simulation models mimic the problem under study, Monte Carlo simulation is a simulation that uses random numbers to mimic uncertainty. Simulations generally contain random input variables, the logic that represents the system under study, and the tabulation of results. The simulation is "run" for a large number of "iterations" (i.e., the simulation can mimic the actual system thousands or even millions of times). Like all models, the key to their effectiveness is the accuracy between the model and the real system being analyzed. AD 680 Lecture 9 Video 1 shows a supply chain facility that would be well suited for simulation. It includes a multistage system, many random input variables, and other uncertainties across the many variables that influence performance. (Source: Tour of Fulfillment by Amazon (FBA)) msm_ad680_17_su1_jmaleyeff_mod9_v1 video cannot be displayed here Random Number Generation Simulations include the generation of random numbers that mimic real distributions of uncertainty, for example customer demand, production or service times, and product quality (rejects, rework). The generation of random numbers that fit any random probability distribution is not difficult. The main requirement is the capability to generation random data for a continuous uniform distribution between 0 and 1, called the U(0,1) random function. In Excel, for example, the U(0,1) random function is generated as follows (F9 generates new sets of random data). A simple example of simulation logic would be the generation of defect data in a manufacturing simulation (or, similarly, mistake data in a service simulation). For example, if a defect or mistake occurs 10% of the time, the user would input the following expression into an Excel cell: =if(rand()
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Explanation & Answer

Attached.

Vietnam

Japan

Mexico

Ohio

Poduction Yield

90%

100%

90%

95%

Salvage Revenue

$2.40

$2.40

$2.40

$2.40

$32.00

$32.00

$32.00

$32.00

3000

3000

3000

3000

37.5%

30.0%

22.5%

12.5%

Lead Time (Weeks)

40

35

25

15

Gross Product Cost

$12.00

$14.00

$14.00

$17.00

Net Product Cost

$13.33

$14.00

$15.56

$17.89

Sales Revenue
Demand Forecast
Forecast CV

INPUTS
Poduction Yield
Salvage Revenue
Sales Revenue
Demand Forecast
Forecast CV
Lead T...


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