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)||Outsourcing||Temporary employment|
|Cost per hour||$12.00||$18.00||$10.00||$10.00|
|Average quality level||99%||98%||94%||90%|
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