Inventory control with flexible demand: Cyclic case with multiple batch supply and demand processes

We introduce, and present methods for solving, the cyclic inventory control problem with multiple flexible batch supply and demand processes. The objective of this new problem is to minimize the average or maximum amount of inventory of a single item that is held during a cycle of given length in a buffer whose stock is replenished by multiple batch supply processes and consumed by multiple batch demand processes. The problem is noteworthy in that the decision maker has control over the timing and lot sizes of all supply and demand processes subject to (1) minimum frequency and batch size requirements for each demand process and (2) maximum frequency and batch size capabilities for each supply process. Thus, demand is flexible; it is a control action that the decision maker applies to optimize the system. We model this deterministic problem as an integer linear program; obtain theoretical insights concerning problem feasibility and solution optimality; and develop three heuristic methods for attacking large problem instances. Extensive experiments compare five methods for attacking the problem: pure integer programming using IBM ILOG CPLEX; integer programming where CPLEX is given an initial feasible solution; a genetic algorithm; simulated annealing; and a random algorithm. We find that CPLEX is a good option for solving small problem instances and the proposed genetic algorithm outperforms CPLEX on larger instances.