Mixed-model sequencing problem under capacity and machine idle time constraints in JIT production systems

Sequencing problems in mixed-model production systems assume a negligible set-up time that permits unconstrained product interspersing. This assumption offers better production sequences in terms of just-in-time objectives such as minimizing parts usage rate variation and minimizing Production Rate Variation (PRV). However, set-up times turn out to be critical in many realistic situations. The present paper addresses the sequencing problem in mixed-model production systems, where internal and external set-up times are considerable measures. Internal set-up time limits free mixing of products, resulting in batching of products; while external set-up time causes machine idle time. The authors present a mathematical model for the problem to find sequences that minimize PRV, satisfying capacity and zero machine idle time constraints. LINGO 15.0 solver could solve the model for small-size problems in a reasonable computational time. For large-size problems, a modified bit-wise mutation algorithm that uses a single unary genetic operator has been developed. The authors have applied the algorithm for diverse problem instances at different production capacities. The same problems are also analyzed by relaxing the zero machine idle time constraint. Results demonstrate how the constraints on capacity and machine idle time disturb the leveling of sequences in mixed-model production systems. The model provides decision makers with the opportunity to select smooth sequences based on the available production time and acceptable machine idle time.