Introduction To Operations Research By Frederick Hillier 10th Edition- Test Bank

Introduction To Operations Research By Frederick Hillier 10th Edition- Test Bank

Test Bank for Chapter 10

Problem 10-1:

Heart Beats is a manufacturer of medical equipment. The company’s primary product is a device used to monitor the heart during medical procedures. This device is produced in two factories and shipped to two warehouses. The product is then shipped on demand to four third-party wholesalers. All shipping is done by truck. The product distribution network is shown below. The annual production capacity at Factories 1 and 2 is 400 and 250, respectively. The annual demand at Wholesalers 1, 2, 3, and 4 is 200, 100, 150, and 200, respectively. The cost of shipping one unit in each shipping lane is shown on the arcs. Due to limited truck capacity, at most 250 units can be shipped from Factory 1 to Warehouse 1 each year. Formulate and solve a network optimization model in a spreadsheet to determine how to distribute the product at the lowest possible annual cost.

Solution for Problem 10-1:

This is a minimum-cost flow problem. To set up a spreadsheet model, first list all of the arcs as shown in B4:C11, along with their capacity (F4) and unit cost (G4:G11). Only the arc from F1 to WH1 is capacitated. Then list all of the nodes as shown in I4:I11 along with each node’s supply or demand (L4:L11).

The changing cells are the amount of flow to send through each arc. These are shown in Flow (D4:D11) below, with an arbitrary value of 10 entered for each. The flow through the arc from F1 to WH1 must be less than the capacity of 250, as indicated by the constraint D4 <= F4.