Abstract
We note that the Single Stage Single Period Multi Commodity Warehouse Location Problem (SSSPMCWLP) has been first attempted by Geoffrion and Graves [1], and that they use the weak formulation (in context of contribution of this paper). We give for the first time “strong” formulation of SSSPMCWLP. We notice advantages of strong formulation over weak formulation in terms of better bounds for yielding efficient Branch and Bound solutions. However, the computation time of “strong” formulation was discovered to be higher than that of the “weak” formulation, which was a major drawback in solving large size problems. To overcome this, we develop the hybrid strong formulation by adding only a few most promising demand and supply side strong constraints to the weak formulation of SSSPMCWLP. So, the formulations developed were put to test on various large size problems. Hybrid formulation is able to give better bound than the weak and takes much less CPU time than the strong formulation. So, a kind of trade off is achieved allowing efficiently solving large sized SSSPMCWLP in real times using hybrid formulation.
Highlights
Introduction and Literature SurveyWarehousing is a key component of today’s business supply chain
We develop in this work the strong constraints for the multi-commodity case of Single Stage Single Period Capacitated Warehouse Location Problem (SSSPMCWLP)
Single stage refers to the real life problems where commodities are stored at one intermediate stage between plants and markets, while in the multi-stage problems, food grain distribution system commodities are stored at multiple stages (Figure 1 shows the schematic representation of single stage)
Summary
Warehousing is a key component of today’s business supply chain. It is not just a place to store finished goods but. The sole objective in warehouse allocation problem is to minimize the total cost of transporting the goods from the manufacturing sites to the end customers via these warehouses. The problem faced by FCI is to choose an optimum number of regional warehouse locations with sufficient capacity so as to minimize the sum of location and transportation costs of distributing food grains from MANDIS to these large Regional warehouses, and subsequently to smaller warehouses or district distribution centres. Uncapacitated or Simple Plant Location Problems are those where it is assumed that facility has infinite storage space/handling capacity while the Capacitated Plant Location Problem implies that the capacity of the warehouse is limited and known in advance
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