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
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
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
Word file contains solution for Transportation, Assignment, and Transshipment problems.
Transportation, Transshipment, and Assignment Problem
I need help trying to find the answer. I have tried about 20 different constraints and all of them are wrong. I don't know what I am doing wrong. Some of the constraints that I have tried are x4 + x6 = 175 and x6 + 0 = 175 just to give you an idea of the way that I am thinking. Evidently it is wrong. Please guide me in the right direction
The question is as follows:
In setting up the an intermediate (transshipment) node constraint, assume that there are three sources, two intermediate nodes, and two destinations, and travel is possible between all sources and the intermediate nodes and between all intermediate nodes and all destinations for a given transshipment problem. In, addition, assume that no travel is possible between source nodes, between intermediate nodes and between destination nodes and no direct travel from source nodes to destination nodes. Let the source nodes be labeled as 1, 2, and 3, the intermediate nodes be labeled as 4 and 5, and the destination nodes be labeled as 6 and 7. If there are 175 units demanded at destination 6, state the constraint for destination 6.
Your answer should look like :
x12 + x34 = 500, with the correct numbers filled in