# Aggregate Planning

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Industrial Design
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University of Florida
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ESI6323 Models for Supply Chain Management
2021 Summer
1
Homework 4 Aggregate Planning in a Supply Chain &
Sales and Operations Planning in a Supply Chain
Homework Questions
Problem 1
Gator Bike, a major bike manufacturer, is making production plans for the coming year. Gator
Bike has worked with its customers (the service providers) to come up with forecasts of monthly
requirements (in thousands of bikes) as shown in Table 1.
Gator Bike’s manufacturing is mainly an assembly operation, and its capacity is governed by the
number of people on the assembly line. The plant operates for 22 days a month, 7 hours each day.
One worker can assemble a bike every 10 minutes. Workers are paid 25 dollars per hour and 50%
premium for overtime. The plant currently employs 1,200 workers. Component costs for each bike
total 40 dollars. Given the rapid decline in component and finished product prices, carrying
inventory from one month to the next incurs a cost of 10 dollars per bike per month. Gator Bike
currently has a no-layoff policy in place. Overtime is limited to a maximum of 30 hours per month
per employee. Assume that Gator Bike has a starting inventory of 50,000 units and wants to end
the year with the same level of inventory.
Table 1. Mostly demand for bike, in thousands.
Month
Demand
January
800
February
900
March
1,100
April
1,300
May
1,800
June
1,700
July
1,400
August
900
September
1,500
October
1,400
November
1,100
December
900
a. Assuming no backlogs, no subcontracting, and no new hires, what is the optimal production
schedule? What is the annual cost of this schedule? (20 pts)

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ESI6323 Models for Supply Chain Management
2021 Summer
2
The Optimal Production Schedule is:
Month
Production (in 1000 Units)
January
1001.2
February
1324.8
March
1324.8
April
1324.8
May
1324.8
June
1324.8
July
1324.8
August
1150.4
September
1324.8
October
1324.8
November
1100
December
950
The annual cost of this schedule is $695,048,000. b. Is there any value for management to negotiate an increase of allowed overtime per employee per month from 30 hours to 40? You can use the sheet you made in Problem 1- a. (15 pts) Answer: Increasing the maximum allowed overtime per employee per month from 30 hours to 40 reduced the overall cost to$ 681,786,000. Hence, it is negotiable for management to consider
this as it minimizes the objective.
c. Reconsider part (a) and (b) if Gator Bike starts with only 1,180 employees. Reconsider part
(a) and (b) if Gator Bike starts with only 1,220 employees. What happened to the value of
additional overtime as the workforce size decreases? You can use the sheet you made in
Problem 1-a. (15 pts)
When the Gator Bike starts with only 1,180 employees with overtime of 30 and 40 hours per
employee per month, the aggregate costs are $699,966,200 and$ 685,745,900, respectively.
Additionally, with the increase in employees to 1220 and overtime of 30 and 40 hours per
employee per month, the aggregate costs are $690,592,800 and$679,214,200, respectively. Hence,

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ESI6323 Models for Supply Chain Management 2021 Summer Homework 4 – Aggregate Planning in a Supply Chain & Sales and Operations Planning in a Supply Chain Homework Questions Problem 1 Gator Bike, a major bike manufacturer, is making production plans for the coming year. Gator Bike has worked with its customers (the service providers) to come up with forecasts of monthly requirements (in thousands of bikes) as shown in Table 1. Gator Bike’s manufacturing is mainly an assembly operation, and its capacity is governed by the number of people on the assembly line. The plant operates for 22 days a month, 7 hours each day. One worker can assemble a bike every 10 minutes. Workers are paid 25 dollars per hour and 50% premium for overtime. The plant currently employs 1,200 workers. Component costs for each bike total 40 dollars. Given the rapid decline in component and finished product prices, carrying inventory from one month to the next incurs a cost of 10 dollars per bike per month. Gator Bike currently has a no-layoff policy in place. Overtime is limited to a maximum of 30 hours per month per employee. Assume that Gator Bike has a starting inventory of 50,000 units and wants to end the year with the same level of inventory. Table 1. Mostly demand for bike, in thousands. Month January February March April May June July August September October November December Demand 800 900 1,100 1,300 1,800 1,700 1,400 900 1,500 1,400 1,100 900 a. Assuming no backlogs, no subcontracting, ...
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