Cross-facility management of production and transportation planning problem

This paper studies an integrated production and transportation planning problem in a two-stage supply chain. This supply chain consists of a number of facilities, each capable of producing the final product, and a number of retailers. We assume that retailers’ demands are known deterministically and there are no production or transportation capacity constraints. We formulate the problem as a network flow problem with fixed charge costs. This is an NP  -hard problem. To solve the problem we propose a primal-dual based heuristic that generates upper and lower bounds and runs in O(FRT²)$O({\mathit{FRT}}^2)$. The quality of the upper and lower bounds is tested on a large set of randomly generated problems. The maximum error reported for these problems is 4.36% and the maximum running time is 7.65 cpu seconds.