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## Solving transportation and transhipment problems with restricted and enhanced flow [Research Assistant]

Professor Archana Khurana

Department: Mathematics

The Project

The transportation model, a sub class of linear programming problem, considers minimum-cost planning problems for shipping a product from some origins to other destinations, such as from factories to warehouses, or from warehouses to supermarkets, with the shipping cost from one location to another being a linear function of the number of units shipped. The amount to be sent from each origin, the amount to be received at each destination, and the cost per unit shipped from any origin to any destination are specified. In transportation problems, transhipment is not considered, that is, each point acts as shipper only or as a receiver only. We can extend this problem to permit transhipment with the additional feature that shipments may go via any sequence of points rather than being restricted to direct connections from one origin to one of the destination which would reduce the cost of transportation.
Both the transportation problem and the transhipment problem are also quite widely used for planning bulk distribution, especially in the USA where the (road) distances travelled are large. Transportation problem deals with distributing any commodity from any group of ‘sources’ to any group of destinations or ‘sinks’ in the most cost effective way with a given ‘supply’ and ‘demand’ constraints. There always exists an optimal solution to the balanced transportation problem.
In case of unbalanced transportation problem, the total availability is not equal of total demand, thus some of the source and/or destination constraints are satisfied as inequalities. For example, sometimes, one wishes to keep reserve stocks at the sources for emergencies thereby restricting the total transportation flow to a known specified level, it results in a transportation problem with impaired flow. For example, stockiest reserves the goods viz. medicines, food grains and other items at warehouses for emergencies. At this point of situation, some of the warehouses are forced to be closed down or are made to operate below their original operational level, while some still continue to maintain their original supplying behaviour which gives rise to transportation problem with restricted flow. Again sometimes, situations may arise when because of the extra demand in the market due to high storage cost at some sources or during festive /marriage seasons or during fire / military services, the total flow needs to be enhanced compelling some of the factories to increase their productions in order to meet this extra demand. This results in a transportation problem with enhanced flow. The optimal solution of such problems is of practical interest to the decision maker.
Moreover in literature, much effort has been concentrated on two-dimensional transportation problems as well as transhipment problems with equality constraints. However, when we have to transport heterogeneous commodities of products, then we need to formulate a solid transportation problem which involves three indices.
All the above scenarios of transportation and transhipment problem are of practical interest to decision maker. We shall be formulating and finding out the solution procedures for all such kinds of problems.

You would be formulating and developing solution procedures for transportation and transhipment problems with restricted and enhanced flow and you would also be required to study solid transportation and transhipment problems. You would be learning GAMS (General algebraic modelling system) software which is very useful to solve such linear programming problems.

Time Commitment: 7-9 hours per week

Contact Emailakhurana@email.gwu.edu