Optimization of Sharpley Value Method of Cost Allocation in a Bimodal Transport- Supply Chain Distribution Via Dynamic Programming

Abstract

In this paper, we proposed a coalition between two modes of transportation, where one provides cargo train and the other provides trucks of capacity 453 tons respectively for the coalition. We have five grand coalitions and four coalitions. The coalitions were distributed along five paths across Nigeria and specialized in the distribution of agricultural produce from the north to the south. Each of the coalition was made up of four transport providers and composed of four legs. Since this is a cooperative game scenario, Sharpley's value method of cost allocation was used to obtain the gains accrued to the grand coalition. The coalition made a total savings of 1259.6 million naira within the period under study. The researchers further developed and applied a Dynamic programming model to the supply chain distribution and obtained an intelligent result. They discovered that if the five coalitions were distributed among the four legs, in this other (1, 1, 2, 1), the grand coalition would make an additional gain of 377.6 million naira. The distribution means that the allocation of the coalition to the third leg should be doubled while the other legs remain as they were. The introduction of the optimization method into the system brought additional revenue to the coalition and increased the total gain to 1637.3 million naira.