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Goal Programming

Sneed Manufacturing manufactures auxiliary gasoline tanks for 
subcompact cars. The company manufactures a type of tank that 
is used for various cars. At present, the company has a high 
demand and a fixed production capacity. With the intention of
satisfying the demand, the company is considering: 
(1) operating on the basis of various shifts in overtime, 
(2) subcontracting some orders with other companies 
and / or (3) hiring temporary employees.
Administrators are concerned about going to external 
subcontractors or hiring temporary employees because 
this could reduce the quality of work. Even, in some 
cases, the costs would be higher. The data in Table 1 
describe the labor requirements, costs and average quality
levels associated with the different alternatives. With 
the current workforce, the company can set up a total 
of 200 hours of operations (180 during normal hours and 
20 hours in overtime) per week. After this analysis, 
the company determined the following goals:

Goal 1: The current demand for the gas tank is 
100 units per week. The company would like to 
meet this demand; however, and due to limited 
storage capacities, the company would like to a
void overproduction. Administrators have decided 
that meeting demand is twice as important as avoiding
overproduction.

Goal 2: Reach an average quality level of 98%
Goal 3: Minimize the total costs associated with
all operations.
Set the goal programming model for the problem that 
indicates the number of units of each product that 
must be manufactured through each employment alternative.
Internal Operations (Normal)Internal Operations (Extra)OutsourcingTemporary employment
Hours required4.04.05.06.0
Cost per hour$12.00$18.00$10.00$10.00
Average quality level99%98%94%90%

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