Push-based MRP and pull-based Kanban systems are effective production control policies for a wide range of manufacturing environment. Both of them, however, have certain limitations when they are implemented in different production environments. In recent years, CONWIP (CONstant Work-In-process), a hybrid push/pull control policy, was proposed and studied to take advantages of MRP and Kanban systems for optimal work-in-process (WIP) inventory control. CONWIP is a closed production system in which a constant number of containers traverse a closed loop that includes the entire production system.

In order to effectively implement CONWIP control in a manufacturing environment, several issues, such as the number of containers, lot sizes and job sequence, need to be addressed. This research aims at the development of mathematical models to address these issues and to help implement CONWIP systems in different manufacturing environments. Two mathematical programming models are developed to address issues on a single serial CONWIP line system. The first model can be used in a make-to-stock environment and the objective function of the model is to minimize the setup costs and the costs associated with an unbalanced workload at the bottleneck machine. The solution of the first model simultaneously determines the optimal job sequence on the part list and the lot size associated with each entry on the part list. The second model can be used in a make-to-order environment or in a make-to-stock environment with a known part list. The objective function of the second model is to minimize the system makespan. Two essential CONWIP system parameters, number of containers and job sequence can be determined by solving the second model. A third model is developed for an assembly-type CONWIP system with multiple fabrication lines feeding an assembly station. The objective of the third model is to synchronize system production by minimizing makespan differences among all the fabrication lines. The solution of the third model determines the number of the containers and job sequence for each of the fabrication lines.

The solution of such models is NP-hard. The general branch and bound approach used by most off-the-shelf optimization software cannot be used to solve real sized problems of this nature. In order to solve real sized problems efficiently, we develop a heuristic search method based on simulated annealing. Several example problems are used to test the developed models and algorithms. Computational results validate the modelling and computational efficiency of the solution methods.