Question

Wormwood, Ltd., produces a variety of furniture products. The planning committee wants to pre- pare an aggregate plan for the next six months using the following information:

Month
	1	2	3	4	5	6
Demand	160	150	160	180	170	140
Capacity:
Regular	150	150	150	150	160	160
Overtime	10	10	0	10	10	10

Cost per unit
Regular time	$50
Overtime	$75
Subcontract	$80
Inventory holding, per month	4

Subcontracting can handle a maximum of 10 units per month. Beginning inventory is zero. Develop a plan that minimizes total cost. No back orders are allowed. Regular capacity = Regular production.

1.  Because total capacity of regular and overtime is greater than the forecast, we don't need to use the subcontractor in this problem. True or false?

2.  To satisfy the requirement, not all over time will be used. True or false?

3. To minimize the total cost, we need to hold inventory by the end of which of following month(s)? Select all that apply. 1, 2, 3, 4, 5, and/or 6.

4.  To minimize the total cost, we need to use subcontractor in which of following month(s)? Select all that apply. 1, 2, 3, 4, 5, and/or 6.

5.  What is the minimized total cost for the plan?

Answer 1

Month	1	2	3	4	5	6
Demand	160	150	160	180	170	140
Capacity:
Regular	150	150	150	150	160	160
Overtime	10	10	0	10	10	10
Production:
Regular	150	150	150	150	160	140
Overtime	10	10	0	10	10	0
Subcontract	0	0	10	10	0	0
Inventory	0	10	10	0	0	0
Cost:
Regular	7500	7500	7500	7500	8000	7000
Overtime	750	750	0	750	750	0
Subcontract	0	0	800	800	0	0
Inventory	0	40	40	0	0	0
Total Cost	49680	(sum of all the costs given above)

In month 1: regular and overtime cover the demand

In month 2: Regular alone covers the demand, but overtime is used to cover the demand for next month and minimize cost. Hence inventory of 10 is carried forward.

In month 3: demand is covered using regular and inventory, subcontract is done to cover the demand of next month, hence inventory carried forward is 10

In month 4: Demand is covered using all regular, overtime, subcontract and inventory

In month 5: regular and overtime cover the demand

In month 6: Only regular is used to cover demand

The costs are calculated in above table:

regular = production*50

overtime = production*75

subcontract = units*80

inventory = units*4

1. False, we do need subcontract

2. True, overtime not used in month 6.

3. To minimize the total cost, we need to hold inventory by the end of month 2 and 3

4.  To minimize the total cost, we need to use subcontractor in month 3 &4

5. total cost = 49680