Question 2. Aggregate Production Plan (20 marks)

In order to satisfy the production requirement, the company can vary its capacity by hiring or laying off workers and running overtime production. The following assumptions are made.

• Inventory and backorder costs are calculated using ending inventory/backorder of each month.
• Hiring or layoff costs are incurred when the number of workers changes.
• The number of workers in each month should be an integer. Once scheduled, all workers will produce at their full potential each month.
• The ending inventory requirement of June stated in Cell B11 of the sheet Aggregate must be satisfied.
• Consider the following three different strategies.

(a) A chase strategy by varying the number of workers. That is, use the minimum number of workers in each month to make the ending inventory of each month non-negative. No overtime production.

(b) A level strategy to meet the overall production requirement. That is, use a constant number of workers for these 6 months; demand variations are absorbed by inventory and backorders. Hiring and layoff only happens at the beginning of January. No overtime production.

(c) Stable workforce with overtime so that there is no backorder in all months. That is, set a constant number of workers for these 6 months; do overtime production if necessary; no backorder is allowed at the end of each month. Hiring and layoff only happens at the beginning of January.

Develop three plans using the above three strategies, respectively. Your plans should be cost- effective among the plans that satisfy the requirements. (For example, using one thousand workers can satisfy some of the above requirements, but it is obviously not cost-effective, i.e., minimizing the cost.)

Period	1	2	3	4	5	6	Total
Demand
Number of workers
Beginning Inventory
Regular production quantity
Overtime production quantity
Ending Inventory (use negative for backorder)
Costs:
Hiring cost
Layoff cost
Regular labour cost
Overtime labour cost
Inventory holding cost
Backorder cost
Total cost:

	Planning Data	Numbers	Units of measure
	Initial number of workers	12
	Productivity	2	units per worker hour
	Regular hours per month	200	hours
	Regular time salary	14	$ per hour
	Overtime salary	19	$ per hour
	Inventory holding cost	2	$ per unit per month
	Backorder cost	11	$ per unit per month
	Hiring workers	4500	$ per worker
	Laying off workers	5000	$ per worker
	Beginning Inventory of January	300	units
	Required Ending Inventory of June	700	units (at least these many units)
	Chase strategy
	Period	1	2	3	4	5	6	Total
	Demand	6900	8600	8600	8800	7500	7300	47700
	Number of workers
	Aggregate Plan
	Beginning Inventory	300	0	0	0	0	0
	Regular production quantity	400
	Overtime production quantity
	Ending Inventory (use negative for backorder)						700
	Hiring cost
	Laying off cost
	Regular labor cost
	Overtime labor cost
	Inventory holding cost
	Backorder cost
							Total cost: