A Heuristic Solution of Multi-item Single Level Capacitated Dynamic Lot-sizing Problem

The multi-item single level capacitated dynamic lot-sizing problem consists of scheduling N items over a horizon of T periods. The objective is to minimize the sum of setup and inventory holding costs over the horizon subject to a constraint on total capacity in each period. No backlogging is allowed. Only one machine is available with a fixed capacity in each period. In case of a single item production, an optimal solution algorithm exists. But for multi-item problems, optimal solution algorithms are not available. It has been proved that even the two-item problem with constant capacity is NP (nondeterministic polynomial)-hard. That is, it is in a class of problems that are extremely difficult to solve in a reasonable amount of time. This has called for searching good heuristic solutions. For a multi-item problem, it would be more realistic to consider an upper limit on the lot-size per setup for each item and this could be a very important parameter from practical point of view. The current research work has been directed toward the development of a model for multi-item problem considering this parameter. Based on the model a program has been executed and feasible solutions have been obtained.