Operations Research Assignment: Transportation & Assignment Problems

This document provides a comprehensive solution to an Operations Research assignment for an MBA-IB program. The assignment covers key concepts including transportation problems, assignment problems, and transshipment problems. It defines transportation problems and explains the use of dummy rows and columns in unbalanced scenarios. The solution further defines and explains assignment problems, highlighting their balancing techniques and applications, including machine allocation and sales territory assignments. The document also explores real-world applications of transportation problem-solving in human resources, inventory management, and media planning, emphasizing the importance of addressing transportation challenges. It differentiates between transportation and transshipment problems, defining transshipment nodes, pure supply nodes, and pure demand nodes. The solution provides a detailed analysis of each problem type, offering a clear understanding of the concepts involved.

Program Name
Mba-IB
Batch (2019 – 21)
Semester Number 2nd
Section D
Course Name
Operations research
Bhuvan Puri
2019003132
Assignment
Q1. Define transportation problem. When do we add a dummy row or dummy column in a
transportaion problem?
Answer: When the total supply of all the sources is not equal to the total demand of all destinations, the
problem is an unbalanced transportation problem.
Total supply ≠ Total demand

Demand Less than Supply
In real-life, supply and demand requirements will rarely be equal. This is because of variation in
production from the supplier end, and variations in forecast from the customer end. Supply variations
may be because of shortage of raw materials, labour problems, Transportation Model improper
planning and scheduling. Demand variations may be because of change in customer preference, change
in prices and introduction of new products by competitors.
These unbalanced problems can be easily solved by introducing dummy sources and dummy
destinations. If the total supply is greater than the total demand, a dummy destination (dummy
column) with demand equal to the supply surplus is added. If the total demand is greater than the total
supply, a dummy source (dummy row) with supply equal to the demand surplus is added. The unit
transportation cost for the dummy column and dummy row are assigned zero values, because no
shipment is actually made in case of a dummy source and dummy destination.
Q2. Define Assignment problem and how to balance the assignment problem. Give two areas of
application of assignment problem. The assignment problem is a special case of transportation
problem’. Explain.
Answer: An assignment problem is a unique type of LPP/transportation problem where the objective is
to find the optimum allocation of a number of tasks to an equal number of facilities in order to minimize
total cost/time involved or maximize total profit/sale of allocation. The problem of assignment arises
because available resources such as men, machines etc. have varying degrees of efficiency for
performing different activities, therefore, cost, profit or loss of performing the different activities is
different.
If an assignment problem has not the equal number of rows and columns, it is called an unbalanced
assignment problems. As we can solve only a balanced assignment problem, we have to convert it into a
balanced assignment problem by introducing dummy row or column with zero costs.
Though assignment problem has applications in various business situations, few of the important
applications are:
a. In assigning machines to factory orders.
b. In assigning contracts to bidders by systematic bid-evaluation.
c. In assigning sales/marketing people to sales territories.
Assignment problem is a special case of transportation problem as the number of rows equals number
of columns, all rim conditions are 1 and values of each decision variable is either 0 or 1. Here, the
integrality implies that every supplier will be assigned one destination and every destination will
have one supplier.
Q3. Explain with an example how the concept of solving transportaion problem be applied to solving
human resource problem, inventory problem and media planning problem?

Answer: There are a number of other business issues related to transportation problems, including
higher absenteeism, lower productivity and higher error rates. Clearly, companies need to seriously
consider any transportation problems for employees and put a comprehensive commuting policy into
place to address these issues. Handling transportation problems on an individual basis can lead to
charges of special treatment for certain employees.
A well-studied problem is the inventory-routing problem (IRP), which refers to developing a repeatable
distribution strategy that minimizes transportation costs and the number of stock-outs.
Based on SMART (Specific, Measurable, Attainable, Relevant and Timed) transport planning objectives
for the study have been established. This method of defining objectives provides a transparency to the
objective setting process and assists in focussing on the key aspects of the project. Therefore, to ensure
that the established transport planning objectives are consistent with other transport policy objectives.
Q4. What do you understand by transhipment nodes, pure supply nodes and pure demand nodes?
Also distinguish between transportation and transshipment problem?
Answer: In Transhipment Network, the nodes of the network that acts as both source and destination are
called transhipment nodes. The nodes of the network which acts as source only are called pure supply
nodes and the nodes which acts as destination only are called pure demand nodes.
Difference between transportation and transshipment problem:
 A transhipment problem is when you consider the shipment of goods to an intermediate
destination before the final destination (Transits). While for transportation problems you have
supply points (S) and demand points (D) and you have to ship units directly from points S to
points D. (No transits allowed, the units are directly shipped from supply to demand points) .
 Transshipment problems allow nodes in between the source and sink.
Whereas transportation models generally model the flow from supply nodes to demand nodes.
There are no intermediate nodes.