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Transportation and Transshipment Nodes

Problem attached
Consider a transshipment problem consisting of three origin nodes, two transshipment nodes, and four destination nodes. The supplies at the origin nodes and the demands at the destination nodes are as follow:

Origin Supply Destination Demand
1 400 1 200
2 450 2 500
3 350 3 300
4 200

The shipping costs per unit ($) are provided in the follwoing table:

(see attached file)

a. Draw the network representation of this problem
b. Formulate the appropriate linear programming problem
c. Solve for the optimal solution

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Solution Preview


Kindly see the steps and solution below. It is also attached as word file. Hope this is useful to you.
a. Network representation: Following is the network representation. For the sake of simplicity and clarity while LP formulation I have denoted transshipment nodes as 4 and 5, and destination nodes as 6, 7, 8, and 9. Arrows show transportation routes

d. Formulate the appropriate linear programming problem
Let us look at decision variables first. Decision variable should convey quantity to be shipped along the specific routes.
x14 be the quantity shipped from source node 1 to transshipment node 4. Similarly we define x15, x24, x25, x34, x35.
Let x46 be the quantity shipped from transshipment node 4 to destination node 6. Similarly we define x47, x48, x49, x56, x57, x58, and x59

Solution Summary

Word file contains solution for Transportation, Assignment, and Transshipment problems.