Multistage bulk commodity distribution: development of decomposition lagrangian relaxation based algorithm

Abstract

Bulk commodity distribution is an important problem in large countries. Huge expenses are incurred in warehousing and transportation. Situation is characterized by multistage location of warehouses and location and transportation decisions are taken in a multiperiod context. Ne provide a formulation o4 the bulk commodity distribution problem which results in a large sized mixed zero—one integer linear program. Solution methodology which takes advantage of its special structure and is computationally efficient is developed. Solution method employed is the modified Bender's decomposition which works with the primal problem and includes a set of constraints in the pure zero-one integer program which ensures necessary conditions for primal feasibility to be met. Primal problem is attempted by two different -methods, i) Heuristic and ii) Lagrangian Relaxation which gives near optimal solution. This solution is placed in the framework of Danzig Wolfe decomposition to extract the dual variables needed to prepare additional integer constraint for the pure zero—one integer linear program. The above algorithm was coded and implemented. Computational performance of the algorithm is presented.