Page 132 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 6: Transportation Problem – Optimality Tests

Each of these nodes in turn supply to other destinations. The objective of the transshipment Notes
problem is to determine how many units should be shipped over each node so that all the
demand requirements are met with the minimum transportation cost.
Considering a company with its manufacturing facilities situated at two places, Coimbatore and
Pune. The units produced at each facility are shipped to either of the company’s warehouse hubs
located at Chennai and Mumbai. The company has its own retail outlets in Delhi, Hyderabad,
Bangalore and Thiruvananthapuram. The network diagram representing the nodes and
transportation per unit cost is shown in Figure 6.1. The supply and demand requirements are
also given.

Figure 6.1: Network Representation of Transshipment Problem

Manufacturing Warehouses Retail outlets Demand
facility (Origin nodes) (Transshipment nodes ) (Destination nodes)

Delhi
5

Coimbatore Chennai
1 3

Hyderabad
6

Supply Demand

Bangalore
Mumbai
Pune 4 7
2

Thiruvanantha
puram
8

Solving Transshipment Problem using Linear Programming

Let
X be the number of units shipped from node i to node j,
ij
X be the number of units shipped from Coimbatore to Chennai,
13
X be the number of units shipped from Pune to Mumbai, and so on
24
Table 6.2 shows the unit transportation cost from sources to destination.

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