Question 21. A company is interested in developing a quarterly aggr

21. A company is interested in developing a quarterly aggregate production plan but they aren’t sure if level capacity or matching demand would be better. They have the following information available regarding their production operation:

Number of working days per quarter = 65 days

Number of hours per day per person = 8 hours

Labor standard to produce one unit = 3 hours

Demand for four quarters respectively:

40,000, 42,000, 41,000, and 44,000 units

a. Using a level capacity plan, how many workers would be needed each quarter?

b. For a level capacity plan, what is the beginning inventory in quarter 2?

c. Using a level capacity plan, in how many quarters are the machine requirements over capacity?

d. Using a matching demand plan, how many workers are needed for quarter 1?

e. How many additional workers are needed in quarter 2 under a matching demand plan?

22. A local company makes athletic clothing and they are preparing aggregate production plans on a quarterly basis for the coming year for their line of women’s wear. They have the following information available to develop a level capacity and a matching demand plan:

Number of working days per quarter = 65 days

Number of hours per day per person = 8 hours

Labor standard to produce one unit = 5 hours

Demand for four quarters respectively:

12,300, 12,500, 12,200, 13,000 units

Cost of hiring a worker = $800

Cost of laying off a worker = $500

Inventory carrying cost per unit per year = $60

a. Using a level capacity plan, how many workers are needed each quarter?

b. For a matching demand plan, how many workers are needed each quarter respectively?

c. What is the inventory carrying cost using a level capacity plan?

d. What is the total cost to hire workers under a matching demand plan?

23. Pacific Chemical Products, Inc. produces a liquid laundry detergent and is currently in the process of developing an aggregate plan for the upcoming year. They don’t know whether to use a level capacity or a matching demand approach. The costs that they are concerned with are the cost of hiring more workers, the cost of laying off workers, and the cost of carrying inventory. Currently at Pacific it costs $200 to hire a new worker, the cost of laying off one worker is $250, and the inventory carrying cost per unit per quarter is $4. The company has 65 working days per quarter and each person works only an 8 hour day. The labor standard for each gallon of detergent is 1.5 hours and the forecasted demand for the next four quarters is 30,000, 35,000, 47,000, 43,000 gallons.

a. Using a level capacity plan, how many workers are needed each quarter?

b. What is the average inventory level under the level capacity plan?

c. What is the total annual inventory cost under a level capacity plan?

d. Under a matching demand plan, how many workers are needed in the second quarter?

e. What is the total hiring and firing costs using a matching demand plan?

24. A cement company is considering how to expand its capacity and they are examining the use of overtime or subcontracting on a quarterly basis as possible options. They have the following information about their operation:

Aggregate demand = 30,000; 25,000; 27,000; and 31,000

Maximum capacity = 25,000 units

Labor standard = 2.45 hours/unit

Cost of overtime = $10.50/hour

Cost of subcontracting = $25.00/unit

a. What is the cost of overtime in quarter 1?

b. What is the total cost of subcontracting over four quarters?

25. A metal shop currently has a work force of 20 people and is considering hiring four more people for the next three weeks only. The cost of hiring and training one person is $200 and the cost of terminating one person is $100. Each employee can produce 40 units/week on regular time and four units/week on overtime, and each person must be paid to produce 40 units even if the demand is not sufficient enough to keep everyone busy. The cost of producing one unit on regular time is $20 while on overtime it is $30. The cost of subcontracting one unit is $40. Demand for the next three weeks is 800 units, 1200 units, and 1000 units. Because there is no storage available the shop has a policy that no inventory is to be carried over from week to week.

a. What is the total cost for week 1 if there are only 20 workers?

b. What is the total cost for all three weeks using only 20 workers?

c. What is the total cost for week 1 if the company uses 24 workers?

d. What is the total cost for all three weeks using all 24 workers?

26. A company is seeking to develop a master production schedule for its product. Their beginning inventory is 1000 units and they want to maintain a safety stock level of 1000 units. They produce the product in a fixed lot size of 1200 units. Information regarding weekly demand is shown below:

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