The Ohio Truck Company produces two models of trucks at its factory in Columbus, Ohio: large...

 

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The Ohio Truck Company produces two models of trucks at its factory in Columbus, Ohio: large trucks (the Warrior model) and small trucks (the Chomper model). The factory can produce only one type of truck every month, and so the production planning department needs to determine which model and how many of that model to produce each month. If the plant switches from producing one model one month to the other model the next month, they incur a switch-over cost of $25 million. Historically, the demand for both models has fluctuated significantly over the calendar year. It is now December, and the end-of-December inventory of trucks is expected to be 50,000 Warrior models and 50,000 Chomper models. The table below shows the forecasted demand for the Warrior and the Chomper models for the next twelve months. Month January February March April May June July August September October November December Warrior model (in 1,000) 34 39 40 31 30 33 32 41 Forecasted Demand 40 38 41 40 Chomper model (in 1,000) 45 46 38 36 43 42 41 44 47 The variable unit production cost for the first six months of next year is expected to be $7,000 for the Warrior model and $6,000 for the Chomper model. It is expected that these costs will increase by 10% after the first six months of next year due to anticipated higher labor costs under a new union contract. The factory can produce up to 100,000 Warrior models each month, or up to 110,000 Chomper models each month. The unit storage cost per month is $700 per truck for the Warrior and $600 per truck for the Chomper. (a) Assume that it is now December and that the factory is producing Warriors this month. Construct a discrete optimization model to determine the production schedule of Warrior and Chomper model trucks for the coming year that will minimize the total cost of production, storage, and switch-over costs. IMPORTANT: The objective function and constraints must be LINEAR in the decision variables. (b) What is the optimal production schedule for Warrior and Chomper model trucks? What is the optimal cost? IMPORTANT: You must use SIMPLEX LP as your solution method. The Ohio Truck Company produces two models of trucks at its factory in Columbus, Ohio: large trucks (the Warrior model) and small trucks (the Chomper model). The factory can produce only one type of truck every month, and so the production planning department needs to determine which model and how many of that model to produce each month. If the plant switches from producing one model one month to the other model the next month, they incur a switch-over cost of $25 million. Historically, the demand for both models has fluctuated significantly over the calendar year. It is now December, and the end-of-December inventory of trucks is expected to be 50,000 Warrior models and 50,000 Chomper models. The table below shows the forecasted demand for the Warrior and the Chomper models for the next twelve months. Month January February March April May June July August September October November December Warrior model (in 1,000) 34 39 40 31 30 33 32 41 Forecasted Demand 40 38 41 40 Chomper model (in 1,000) 45 46 38 36 43 42 41 44 47 The variable unit production cost for the first six months of next year is expected to be $7,000 for the Warrior model and $6,000 for the Chomper model. It is expected that these costs will increase by 10% after the first six months of next year due to anticipated higher labor costs under a new union contract. The factory can produce up to 100,000 Warrior models each month, or up to 110,000 Chomper models each month. The unit storage cost per month is $700 per truck for the Warrior and $600 per truck for the Chomper. (a) Assume that it is now December and that the factory is producing Warriors this month. Construct a discrete optimization model to determine the production schedule of Warrior and Chomper model trucks for the coming year that will minimize the total cost of production, storage, and switch-over costs. IMPORTANT: The objective function and constraints must be LINEAR in the decision variables. (b) What is the optimal production schedule for Warrior and Chomper model trucks? What is the optimal cost? IMPORTANT: You must use SIMPLEX LP as your solution method.

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a Discrete Optimization Model Decision Variables Wi Number of Warrior trucks produc... View the full answer