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A manufacturer of over 75 grades of styrenic resins — used to make DVD cases, refrigerator trays, packaging materials and auto parts — faces a “transition loss” each time it switches production from one grade to another. A transition loss for each grade arises from the initial 16 metric tons produced, which are sub-standard and unsuitable for usage by customers. To the company, this implies a loss of resources (raw material and production cost) and a disposal fee ($10,000) to remove each sub-standard production.
The case illustrates a sample of 15 grades for which data on their requirements for machine time usage, raw materials and labour hours are provided, as well as their production cost, selling price and market demand. Some of these grades must also be sold jointly in specific ratios. A newly hired sales executive must present an optimization template that would meet the company’s production constraints and maximize its profitability. Which grades of styrenic resins should be produced? Furthermore, how much of each grade should be produced?
This case can be viewed as an interesting extension of the optimal production problem. Specifically, the fixed $10,000 disposal fee for the initial sub-standard 16 metric tons produced for each grade adds a layer of complexity.
The case is suitable as an intermediate optimal production planning problem for advanced undergraduates and MBAs in analytics, management science and operations courses. It requires the use of optimization software, such as Excel Solver.
Singapore, Large, 2013
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