# ILP Transportation Problem

The table below indicates required supplies delivered to four destinations.

Destinations

Port D1 D2 D3 D4

A 70 80 90 56

B 100 75 100 85

C 42 60 89 62

Demand 500 600 450 700

The ports are supplied by one of two stock suppliers. Supplier 1 carries 1200 tonnes of supplies while Supplier 2 carries 1120 tons of supplies. These suppliers can only offer a single port and each port can only accommodate one supplier. Assume the costs for a supplier to supply are not part of the objective function. Formulate the ILP for this problem capturing the supplier choice of port and the transportation from the port to the destinations.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please view the attached files (one Word document and one Excel file) as these will help you answer your question. I have attached an Excel file which solves the problem using Excel Solver. Go to Data - > Solver to see the objective function, decision variables and constraints. Optimal solution is available in the file.

Port-Supplier Selection - ILP

Problem definition: A commodity needs to be supplied to four destinations. The commodity can be supplied from three ports and two suppliers. A supplier can choose one of the ports and port can have only one supplier.

Objective is to minimize total ton-miles wherein total demand for each destination is provided along with distance between each port and a destination.

As the problem states that a supplier can choose only on port and a port can have only one supplier, the mathematical formulation would be integer linear with some of the decision variables allowed t take only integer values.

There are two types of integer linear formulations: 1) decision variables can take any integer value (0, 1 2, 3...), 2) decision variables can take only 0 or 1 (such variables are called binary or Boolean variables). First type is called integer programs and second type is called binary integer programs. Typically a formulation will have mix of integer and real variables, hence it is termed as mixed integer linear programs (MILP)

Formulating a mathematical program requires following

1. Defining decision variables

2. Formulating objective function

3. Formulating constraints

Step 1: Defining decision variables

There are two types of variables for the stated problem.

a. Port-Supplier selection variables

b. Quantity to be supplied from each supplier

Let

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