ABC Inc. is a steel wholesaler and is considering the location of warehouses to use in its logistics system. The firm currently has a list of three warehouses it can lease. The cost per month to lease warehouse i, as well as the maximum number of trucks the warehouse i can handle per month, are shown in the table shown in the upper left corner of the Excel template TRANINT.xls. There are four sales districts and the typical monthly demand in district j (measured in terms of the number of TL shipments), along with the average cost of sending a truck from warehouse i to district j, are shown in the same table.
The firm wants to know which warehouses to lease and how many trucks to send from each warehouse to each district. A schematic representation of the problem is illustrated in the figure included in the TRANINT.xls template. In the template we see, for example, that it costs $7750 to lease warehouse A for a month and that up to 200 trucks (per month) can be dispatched from this warehouse. Also, the monthly demand in sales district 1 is 100 TLs. By the same token wee see, for example, that the cost of sending a truck from warehouse B to sales district 3 is $100. Keeping these points in mind, answer the following questions.
Question 1:
Formulate a linear mixed integer programming problem and solve the problem by using the solver optimization procedure available in Microsoft Excel. Give recommendation as to which warehouse should be leased and how many trucks are to be sent from each warehouse to each sales district.
Question 2:
Do question 1 by changing the monthly leasing cost for warehouse B to $1000. What is your recommendation now? Did the overall cost increase or decrease?
Question 3:
(Continuation of question 1, ignore question 2). Assume that, because of the road construction currently underway, the road connecting warehouse A to sales district 3 is temporally not usable. What is your shipment plan now? Did the overall cost increase or decrease compared to your solution to question 1?