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.

Optimization algorithms for transportation problems with stochastic demand

“…The transportation problem gets rid of distributing a specific commodity from its supply center, which is called sources, to a group of reception centers, which are called destinations, in a way that minimizes the cost of the total distribution, as the goods are distributed from the source to his destination after determining the demand or the number of units by the exporter in order to be able to The destinations arrange this in a timely manner and bypass some of the problems that occur during the transport process, including the non-movement of the commodity or the goods directly, but rather passes through several transport points during the road, which disrupts the arrival of the goods to the distribution centers as well as the increase in the cost of transport, which leads to the failure of the transport process and failure Application of the model in addition to other problems that supply centers may face, which are the lack of clarity of demand by sources or the difference in supply from the quantity that was previously determined [4], [8]. Some companies may face the problem of transporting perishable items such as eggs and others, as this requires reducing fractions and reducing costs during the transportation process and trying to accomplish this in the shortest possible time without damaging the goods because increasing the speed may lead to an increase in the elements of breakage, and this is the biggest problem that may be exposed to it.…”

“…What requires setting the important objectives required in the transportation process and transporting the goods in a suitable time and at an appropriate cost and the least losses for perishable goods. In this case, we may resort to reducing the total distance for such transport of such type of goods [1], [4], [5]. The transportation problem is a special type of operations research problem and it plays an important role in logistics and supply chains, the purpose of which is to minimize the cost of shipment of goods from one location to another or from one point to another to meet the arrival of needs (demand) in an appropriate time and cost without any problems during the transport process through Many methods are the most important and most prominent of these methods is the Vogel method, which depends on the penalty cost, which means the difference between the largest cost in the class and the largest cost in the column.…”

“…The mathematical model for stochastic variables for the optimization problem under uncertainty takes the following mathematical form [3], [4], [6]- [8]:…”