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# Aggregate production planning

Firm X projects the company's aggregate demand requirements over the next 8 months as shown in the table below. The operations manager is considering a new plan, which begins in January. Ignore any idle-time costs. We will call this Plan A. Plan A: Vary the workforce level to execute a "chase" strategy to produce only the quantity demanded each month. The December rate of production was 1,600 units per month. The cost of hiring additional workers is \$5,000 per 100 units. The cost of laying off workers is \$7,500 per 100 units. Evaluate this plan.

True or False

1. Because we have 200 units in beginning inventory, the demand to be met by production in January should be adjusted to only 1,200 units.
2. Firing costs in January are \$30,000.
3. Hiring costs in February are \$30,000.
4. Hiring costs in June are \$20,000.
5. The total cost of hiring and laying off workers in this plan is \$140,000.

Firm X (from the previous question) would like to consider other aggregate planning options. Plan B involves producing at a level production rate of 1,400 units per month. This should meet minimum monthly demands. If additional units are needed, use subcontracting to make them. Evaluate Plan B.

True of False

1.In a level production strategy, the demand to be met by production in January would be adjusted to only 1,200 units due to the beginning inventory.
2.Total cost of carrying inventory for Plan B is \$4,000.
3.Cost of subcontracting in February is \$15,000.
4.Cost of subcontracting in March is \$30,000.
5.From a cost standpoint, this plan is preferrable to Plan A.

Firm X wants to look at yet another option - let's call it Plan C. In plan C, Johnson wants to keep a stable workforce by maintaining a constant production rate equal to the average monthly demand for the eight month period and allow varying inventory levels. Beginning inventory, stockout costs, and holding costs are provided below and don't change from the Plan A and Plan B.

True or False

1.Ending inventory at the end of January is 575 units.
2.There were 125 stockouts in April.
3.May ended with 275 units in inventory.
4.Ending inventory for the month of August is zero.
5.Total cost of Plan C (inventory holding costs + stockout costs) is less than Plan A or Plan B.

Firm X wants to look at yet another option - let's call it Plan D. In plan D we will keep the current workforce stable at producing 1,600 units per month. This will be our "regular production" figure. Permit a maximum of 20% of regular production in overtime at an additional cost of \$50 per unit. However, there is a new twist: A warehouse now constrains the maximum allowable inventory on hand to 400 units or less. This implies there may be stock-outs in some months.

True or False

1.Ending inventory for March is 200 units.
2.200 units will have to be made on overtime in April.
3.This plan has a total of 560 stockouts across all months.
4.Costs for the month of of June involve both overtime expenses and stockout costs.
5.The costs associated with Plan D are less than Plan C.

Firm X wants to look at yet another option - let's call it Plan E. In plan E, we will keep the current workforce which is producing 1,600 units per month, and subcontract to meet the rest of the demand.

True or False

1.Ending inventory in Aug is 200 units.
2.Subcontracting for April costs \$4,000.
3.This plan involves subcontracting out production of 1,400 units.
4.Total cost of Plan E (holding costs + subcontracting) is \$117,000.
5.Of the five plans presented (A - E), the most economical is this one.

Month - Demand
January - 1400
Febuary - 1600
March - 1800
April - 1800
May - 2200
June - 2200
July - 1800
August - 1400

Stock out cost - \$100/unit
Inventory Holding Cost - \$20/unit/month
Beginning Inventory - 200 units
Ending inventory (Aug) - 0 units
Idle time cost - \$0
Cost to hire - \$5000/100 units
Cost to lay off - \$7500/100 units
Subcontracting - \$75/unit
Overtime - \$50/unit

Please explain in detail on how to solve the above problems.

#### Solution Summary

Excel file contains evaluations of various plans, step by step calculations and formulas.

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