Question

The production manager has developed an aggregate forecast
Month	Demand
1	55
2	44
3	50
4	40
5	50
6	60
7	51
8	45
9	35
10	54
11	60
12	60
Use the following information to develop an aggregate plan
Beginning inventory: 5 units
Beginning workforce: 5 workers
Unit per worker: 8 units per month
Inventory Holding cost: $7 per unit per month
Regular production cost: $80 per unit
Overtime production cost: $110 per unit
Subcontracting cost: $120 per unit
Overtime capacity: 5 units per month
Subcontracting capacity: 12 units per month
Hiring and firing costs: 500
Develop an aggregate plan using linear programming while the number of workers cannot exceed 6.
Use overtime and subcontracting as needed within the capacity.
What is the minimum cost of the optimal solution? ****Please use solver and show steps thank you***

Answer 1

Excel formulation and solver setup

Solution

Month	Demand	Workers	Hire	Layoff	OT production	SubCont units	Ending inventory	Regular production	Total output	Output + B.I - E.I.	OT capacity	SubCont capacity
12		5					5
1	55	6	1	0	2	0	0	48	50	55	5	12
2	44	6	0	0	0	0	4	48	48	44	5	12
3	50	6	0	0	0	0	2	48	48	50	5	12
4	40	6	0	0	0	0	10	48	48	40	5	12
5	50	6	0	0	0	0	8	48	48	50	5	12
6	60	6	0	0	4	0	0	48	52	60	5	12
7	51	6	0	0	3	0	0	48	51	51	5	12
8	45	6	0	0	0	0	3	48	48	45	5	12
9	35	6	0	0	0	0	16	48	48	35	5	12
10	54	6	0	0	0	0	10	48	48	54	5	12
11	60	6	0	0	5	0	3	48	53	60	5	12
12	60	6	0	0	5	4	0	48	57	60	5	12
Totals			1	0	19	4	56	576
Marginal costs			$500	$500	$110	$120	$7	$80	Total cost
Cost			$500	$0	$2,090	$480	$392	$46,080	$49,542