Question

A manufacturing company produces products 1, 2, and 3. The three products have the following resource requirements and produce the following profit:

Profit Labor (hr/unit) Material (lb/unit) Profit ($/unit)
1 5 4 $3
2 2 6 5
3 4 3 2

At present, the firm has a daily labor capacity of 240 available hours and a daily supply of 400 pounds of material. Management has developed the following set of goals, arranged in order of their importance to the firm:

1. Because of recent labor relations difficulties, management wants to avoid underutilization of normal production capacity.
2. Management has established a satisfactory profit level of exist500 per day.
3. Overtime is to be minimized as much as possible.
4. Management wants to minimize the purchase of additional materials to avoid handling and storage problems.

Required:
Formulate a goal programming model (multi-criteria model) to determine the number of each product to produce to best satisfy the goals.

Answer 1

di+, di- are the deviation variables for i-th objectives.

Product_1, product_2, product_3 are respectively the products 1,2 and 3 to be produced in a day. Those are the Standard variables

goal: (1/400)*d4+ (2/240)*d3+ (3/500)*d2-+ Min (4/240)*d1-

variables are equal or bigger than zero

400 = 5*product_1 + 6*product_2 + 3*product_3 - d4- + d4+

240 = 5*product_1 + 2*product_2 + 4*product_3 - d3- + d3+

240 = 5*product_1 + 2*product_2 + 4*product_3 + d1- - d1+

500 = 3*product_1 + 5*product_2 + 2*product_3 + d2- - d2+