Exercise #1 Tillman Chemicals, Inc. case study
Exercise #1 Tillman Chemicals, Inc. has five production facilities, labelled A through E, that provide chemicals to five different regions, labelled 1 through 5. The production and shipping costs related to satisfying regional demand are listed in the following table: Demand Regions A B C D E Demand (Tankers/yr) 1 1885 4084 6283 3770 6911 810 2 3770 4398 6597 2513 7225 570 3 4084 1885 4398 4398 4084 600 4 6283 4398 9425 6597 3142 360 5 5341 4084 2827 6597 2513 300 Capacity (Tankers/yr) 555 1425 150 600 240 Prod. Costs per Tanker 31400 23500 52600 23000 29000 Tillman needs a production plan for the coming fiscal year. Answer the following questions: 1) If plants can produce however much they want to (infinite production capacity), how much should each plant produce, and what is the cost? 2) If plants can produce as much as they want to UP TO THEIR STATED CAPCITY, how much should each plant produce, and what is the cost? 3) If plants MUST produce at no less than 45% capacity, then what should each plant produce, and what is the cost? 4) What do you observe about the relationship between constraints in your model and cost? Exercise #2 Your company is choosing among several locations for its offices, each of which must serve multiple U.S. states. Your high-end products require regular servicing by repair technicians, who must report to the appropriate sales office. There are four potential sales office sites under consideration: San Diego, Dallas, Kansas City, and Seattle. The annual fixed cost of the San Diego office is $173,500, Dallas is $129,200, Kansas City is $142,000, and Seattle is $147,500. Repair technicians must make repair trips out of these offices, with costs per trip described in the following table: Travel Costs State San Diego Dallas Kansas City Seattle # of Trips Washington 225 325 275 100 40 Oregon 225 325 275 150 35 California 150 275 200 200 100 Idaho 225 275 200 200 25 Nevada 175 275 200 225 40 Montana 250 250 200 200 25 Wyoming 225 250 175 225 50 Utah 225 225 175 275 30 Arizona 150 275 175 325 50 New Mexico 200 200 150 375 40 N. Dakota 375 275 225 275 30 S. Dakota 375 250 200 275 20 Nebraska 325 175 200 325 30 Kansas 325 150 150 375 40 Oklahoma 325 100 200 375 55 Colorado 225 225 175 325 65 Each technician may make up to 25 repair calls each year. Answer the following: Assuming that, at most, 10 technicians are allowed at any one office, where should the offices be, and how many technicians should be at each office? Now assume that unlimited technicians are allowed at each office. Where should the offices be, and how many technicians should be at each office? How confident are you that the answer for #2 represents the best possible solutions? Explain your answer, and, if appropriate, suggest what might constitute a better solution. Exercise # 1 Demand Regions A B C D E Capacity (Tankers/yr) Prod. Cost per Tanker 1 1885 4084 6283 3770 6911 555 31400 2 3770 4398 6597 2513 7225 1425 23500 3 4084 1885 4398 4398 4084 150 52600 4 6283 4398 9425 6597 3142 600 2300 5 5341 4084 2827 6597 2513 240 2900 Demand (Tanker/yr) 810 570 600 360 300 Decision Variables Demand Regions A B C D E 1 2 3 4 5 Capacity (Tankers/yr) Prod. Costs per Tanker Constrants Demand Regions Excess Capacity Excess Capacity Excess Capacity 1 2 3 4 5 Objective Function Cost $ Question # 1 - infinite production capacity Question # 2 - UP TO THEIR STATED CAPCITY Question # 3 - MUST produce at____________ to achieve no less than 45% capacity Exercise # 2 State San Diego Dallas Kansas City Seattle # of Trips Idaho 225 275 200 200 25 Nevada 175 275 200 225 40 Montana 250 250 200 200 25 Wyoming 225 250 175 225 50 Utah 225 225 175 275 30 Arizona 150 275 175 325 50 New Mexico 200 200 150 375 40 N. Dakota 375 275 225 275 30 S. Dakota 375 250 200 275 20 Nebraska 325 175 200 325 30 Kansas 325 150 150 375 40 Oklahoma 325 100 200 375 55 Colorado 225 225 175 325 65 Decision Variables State San Diego Dallas Kansas City Seattle # of Trips Idaho Nevada Montana Wyoming Utah Arizona New Mexico N. Dakota S. Dakota Nebraska Kansas Oklahoma Colorado Constrants State San Diego Dallas Kansas City Seattle # of Trips Idaho Nevada Montana Wyoming Utah Arizona New Mexico N. Dakota S. Dakota Nebraska Kansas Oklahoma Colorado Objective Function Cost $ Questions Question # 1 - 10 technicians are allowed at any one office Question # 2 - unlimited technicians are allowed at each office Question # 3 - How confident are you that the answer for #2 represents the best possible solutions? Explain your answer, and, if appropriate, suggest what might constitute a better solution.