I. A manufacturing company produces products 1,2, and 3. The three products have

Question

I. A manufacturing company produces products 1,2, and 3. The three products have the followin urce requirements and produce the following profit Product Labor (hr./unit) Material (lb./unit) Profit (S/unit) 4 $3 4 At present, the firm has a daily labor capacity of 240 available hours and a daily supply of 400 pounds of material. The general linear programming formulation for this problem is as follows maximize Z 3xi + 5x2 2x3 subject to 5x + 22 +4x3 S 240 4x 623x3 S 400 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 $500 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 Formulate a goal programming model to determine the number of each product to produce to best satisfy the goals

Explanation / Answer

Goal programming model is following:

Standard variables: Let x1, x2, x3 be the number of products 1,2 and 3 to be poduced daily.

Deviation variables: Let di+ and di- be the positve and negative deviation variables for i-th goal.

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

Constraints:

5x1 + 2x2 + 4x3 + d1- - d1+ = 240   (goal 1)

3x1 + 5x2 + 2x3 + d2- - d2+ = 500   (goal 2)

5x1 + 2x2 + 4x3 - d3- + d3+ = 240   (goal 3)

5x1 + 6x2 + 3x3 - d4- + d4+ = 400   (goal 4)

All variables >= 0

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