Sample Coursework Paper on Discussion 3

Implications of multiple optimal solutions in a transportation problem.

Transportation problems are part of linear programming models which are usually solved using either of the following methods: northwest corner method, minimum cost method, genetic algorithm, Vogel’s approximation method, row minimum method and column minimum method. However, trouble emerges when there are multiple optimal solutions in the transportation model. The occurrence of more than one objective to be optimized brings about complications when solving the problems (Sang 82). Ideally, in many business operations today, dealing with a single item does not guarantee many revenues for retailers. It is for this reason that many business persons in the field of transportation diversify their operations by carrying out multiple activities in order to maximize profits.

Optimal solutions are obtained when the opportunity costs for every unallocated cell are nil or negative. In the case where all solutions are zero, the solution obtained is unique. However, in cases where the solutions are not positive, but rather have one or more zeros, it implies that the problem has multiple optimal solutions. Typically, this is shown by the occurrence of more than one unoccupied cell having no value in the net cost of the optimal solution (Sam 87). Nevertheless, it can be daunting to try to route products in a situation where there are several supply locations and destinations for the minimization of total costs. Hence, distribution of the portions has to be done by filling in the box spaces whose values amount to zero and making the change to have no impacts on the transportation cost (Sam 74). The reallocations provide other solutions with similar values, however, with a different channel. The implication of this is that by obtaining new solutions, the management has more resilience in decision-making.

Works Cited

Sam, M. Lee.Goal Programming Methods for Multiple Objective Integer Programs.Operations Research Division, American Institute of Industrial Engineers, 1979. Print.

Sang, M. Lee, David L. Olson.Introduction to Management Science. 3edn. Thomson, 2006. Print