Solving Solid Transportation Problem with Multi-Choice Cost and Stochastic Supply and Demand

Abstract

This paper proposes a new approach to analyze the solid transportation problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming which is incorporated in three constraints namely sources, destinations and capacities constraints followed by Cauchy's distribution for solid transportation problem. The multi-choice programming and stochastic programming are combined into solid transportation problem and this new problem is called multi-choice stochastic solid transportation problem (MCSSTP). The solution concepts behind the MCSSTP are based on a new transformation technique which will select an appropriate choice from a set of multi-choice which optimizes the objective function. The stochastic constraints of STP convert into deterministic constraints by stochastic programming approach. Finally, the authors have constructed a non-linear programming problem for MCSSTP and have derived an optimal solution of the specified problem. A realistic example on STP is considered to illustrate the methodology.