Question

Data Equipment Inc. produces two models of a retail price scanner, a sophisticated model that can be networked to a central processing unit and a stand-alone model for small retailers. The major limitations of the manufacturing of these two products are labor and material capacities. The following table summarizes the usages and capacities associated with each product.

Product

Labor

Materials

Profit

Hr/Unit

Components/Unit

$/Unit

Network (X1)

8

20

$160

Basic (X2)

5

7

$95

Capacity

800 hr/day

1,500 comp/day

The typical LP formulation for this problem is:

Maximize

$160 X1 + $95 X2

Subject to:  8 X1 + 5 X2 ? 800
20 X1 + 7 X2 ? 1500
X1, X2 ? 0

However, the management of DEI has prioritized several goals that are to be attained by manufacturing:
Since the labor situation at the plant is uneasy (i.e., there are rumors that a local union is considering an organizing campaign), management wants to assure full employment of all its employees.
Management has established a profit goal of $12,000 per day.
Due to the high prices of components from nonroutine suppliers, management wants to minimize the purchase of additional materials.

Given the above additional information, set this up as a goal programming problem.

Answer 1

Data Equipment Inc. produces two models of a retail price scanner. The major limitations of the manufacturing of these two products are labor and material capacities. The following table summarizes the usages and capacities associated with each product.

Product	Labor Hr/Unit	Materials Components/Unit	Profit $/Unit
Network (X1)	8	20	160
Basic(X2)	5	7	95
Capacity	800hr/day	1500 comp/day

The typical LP formulation for this problem is:

Maximize:

Subject to:

However, the management of DEI has prioritized several goals that are to be attained by manufacturing:

1. Since the labor situation at the plant is uneasy (i.e., there are rumors that a local union is considering an organizing campaign), management wants to assure full employment of all its employees.
2. Management has established a profit goal of $12,000 per day.
3. Due to the high prices of components from nonroutine suppliers, management wants to minimize the purchase of additional materials.

Using the above information lets set up the goal programming problem.

Let,

the underachievement of the full employment goal

the overachievement of the full employment goal

the underachievement of profit target

the overachievement of profit target

unused components

an additional amount of components needed

Minimize:

Subject to:

Constraint on labor and taking into account the goal that management wants to assure full employment of all its employees.

Management has established a profit goal of $12,000 per day.

Constraint on material capacities and unused and additional amount of components. Goal: Due to the high prices of components from nonroutine suppliers, management wants to minimize the purchase of additional materials.