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(Solved) Industrial Engineering 335 Operations Research - Optimization Spring 2016 Due date: April 22, 2016 (beginning of class) Project 1 Problem description...


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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

 


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