Industrial Engineering 335 Operations Research - Optimization Spring 2016 Due date: April 22, 2016 (beginning of class) Project 1 Problem description A manufacturer has two companies, one in Indiana and one in New York. In addition, it has other four factories in Ohio, Texas, Nevada, and Michigan, respectively. The manufacturer sells its product to six different customers C1, C2, . . . , C6. Customers can be supplied from either a factory or the company directly (see Figure 1) Figure 1: The relationship between the supplier and consumer The distribution costs for the manufacturer are given in Table 1 below (in $ per ton delivered). Table 1: The distribution costs Supplied to Factory Ohio Texas Nevada Michigan Indiana company New York company 0.5 0.5 1.0 0.2 0.3 0.5 0.2 Ohio factory Supplier Texas Nevada factory factory Customers C1 1.0 2.0 1.0 C2 1.5 0.5 C3 1.5 0.5 0.5 C4 2.0 1.5 1.0 C5 0.5 C6 1.0 1.0 A dash indicates the impossibility of certain suppliers for 1 Michigan factory 1.5 2.0 0.5 1.5 certain factories 0.2 1.5 0.5 1.5 or customers. The weekly capacity for each company is as follows (this quantity cannot be exceeded): Indiana New York 150000 tons 200000 tons For each factory the maximum weekly throughput is as follows (this quantity cannot be exceeded): Ohio Texas Nevada Michigan 70000 50000 100000 40000 tons tons tons tons There is a weekly demand that has to be met and it is given as follows: C1 C2 C3 C4 C5 C6 2 50000 10000 40000 35000 60000 20000 tons tons tons tons tons tons Problem Formulation (1) Formulate a LP model to help the manufacturer to determine what distribution pattern would minimize the overall cost. (2) Solve the LP problem using MATLAB (provide also the MATLAB script) Some hints: (i) You may want to define the following decision variables: xij = quantity sent from company i to factory j, for all i = 1, 2 and j = 1, 2, 3, 4. yij = quantity sent from company i to customer k, for all i = 1, 2 and k = 1, 2, . . . , 6. zij = quantity sent from factory j to customer k, for all j = 1, 2, 3, 4 and k = 1, 2, . . . , 6 There are 44 such variables. (ii) The constraints to include in the formulations are (on top of the nonnegativity constraints): 1. Company Capacities 2. Quantity into Factories 3. Quantity out of Factories 4. Customer Requirements 2