Exact methods for the single-item multi-plantcapacitated lot sizing problem coupledwith transportation

In this paper we study the integration of production, transportation and storage decisions ina multi plant-distribution center supply chain structure. Multiple plants produce one type ofitem, each of them with different production capacity and costs, and send finished goods tothe distribution center (DC) using capacitated vehicles. Customer demand is known at DClevel and has to be satisfied without backlogging. This problem contains classicalcapacitated lot sizing problem as a subpart, which, in the general case, is NP-hard. Wepropose an exact pseudo-polynomial dynamic programming algorithm and show that theproblem is NP-hard in the ordinary sense. We then compare the computational time of thisdynamic program to that of a mixed integer linear program (MILP) which is selected among4 different MILP formulations based on its lower computational time.....