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Chapter 5 Question 4 An industrial machinery manufacturer produces shapers and drill presses

Operations Management

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Chapter 5 Question 4

An industrial machinery manufacturer produces shapers and drill presses. The manufacturer fore-casts that the demand for shapers for the next month will be at least 5 and the demand for drill presses for the next month will be at most 7. A shaper earns a profit of €40,000 and a drill press, €50,000. Both the shaper and the drill press use few common components like belts, electric motors, hydraulic drives, sensors, etc. A shaper needs 15 units of such common components and a drill press, 18 units. The store has 200 units of the components in stock. The cost of other parts is allocated from a common budget. A shaper needs €12,000 and a drill press needs €16,000 from the budget. The manufacturer has a budget of €150,000. The manufacturer wants to determine the number of shapers and drill presses to produce to maximize its profits. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer.

Question 8

Samsung sells its four flagship products—cell phones, TVs, computing devices, and memory storage devices—through its exclusive showroom in a city. To support sales, it has hired 20 per-sons and trained them to service every product. Depending on the nature of the job, the cost of overhead expenses varies. The overhead cost of the cellphone section of the showroom per day is £70, for the TV section is £65, for the computing device section is £60, and for the memory storage section is £25. The store has allotted a budget of £1,000 for the showroom per day. A cell phone serviceman generates a revenue of £480 a day, a TV serviceman, £480, a computing devices serviceman, £450, and a memory storage section serviceman, £300. Each section needs at least two servicemen. The outlet wants to determine the number of servicemen to be assigned to each section that will maximize the revenue. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer.

Question 20

The Terraco Motor Company has produced a lightweight, all-terrain vehicle code-named “J99 Terra” for the military. The company is now planning to sell the Terra to the public. It has five plants that manufacture the vehicle and four regional distribution centers. The company is unsure of public demand for the Terra, so it is considering reducing its fixed operating costs by closing one or more plants, even though it would incur an increase in transportation costs. The relevant costs for the problem are provided in the following table. The transportation costs are per thousand vehicles shipped; for example, the cost of shipping 1,000 vehicles from plant 1 to warehouse C is $32,000.

Formulate and solve an integer programming model for this problem to assist the company in determining which plants should remain open and which should be closed and the number of vehicles that should be shipped from each plant to each warehouse to minimize total cost.

Question 27

Six Sigma is a well-recognized quality management system that employs improvement projects to improve business processes to reduce product and service defects, reduce costs, and increase profits. Each project has a “champion” from upper management who is responsible for the proj-ect’s success. The project leader is known as a “black belt,” and project team members are called “green belts.” Simsun, a manufacturer of cell phone parts and components, has eight improvement projects under consideration, and six champions, 10 black belts, and 25 green belts available to be assigned to the projects. The following table shows for each of the projects the number of green belts required, the percent reduction in defects expected, the cost savings (in $ millions), and the profit improvement (in $ millions).