4. Further Development: Mathematical Model 2 (MM2) and a Comprehensive Heuristic for Capacitated Lot Sizing Problem with Production Carryover and Setup Crossover Across Periods for Process Industries

In the previous chapter, a mathematical model and a heuristic are applied to the CLSP in process industries which can be applied to real-life situations in process industries such as production carryover across periods and setup crossover across periods. The heuristic proposed in Chap. 3Capacitated Lot Sizing Problem with Production Carryover and Setup Crossover Across Periods (CLSP:PCSC): Mathematical Model 1 (MM1) and a Heuristic for Process Industrieschapter.38.3 with respect to MM1:CLSP-PCSC can be easily applied when identical capacity is present across periods. However, in reality the capacity across periods may be varying. When non-identical capacity is present across periods, for allowing shift of setup/production for more periods ahead of or after the current time period, the extension of the heuristic based on MM1:CLSP-PCSC becomes tedious. In such cases the heuristic proposed in this chapter is easier to apply. Hence, in this chapter we propose a second mathematical model (MM2:CLSP-PCSC) for the CLSP-PCSC followed by a heuristic using the second mathematical model. The proposed model in this chapter is not constrained by the consideration of long setup products. The model is flexible enough to handle the process industries with small bucket setups and long bucket production runs or the scenario with large bucket setups and small production runs or a mixture of both. In other words, the proposed mathematical model and heuristic approach are flexible enough to handle or address situations in the conventional process industries such as cement and sugar industries (associated with small bucket setups and long bucket production runs), large bucket setups and small bucket production runs (associated with highly technological intensive big bucket setups and small bucket production runs such as those in highly specialized pharmaceutical processes), or a mixture of scenarios in a single process industry. Also, depending upon the industry the definition of a period may vary. It is to be noted that in all these scenarios we have real-life restrictions that once a process starts there is no interruption with the production run length, and the production has to start immediately after the completion of setup. In this book we address such a variety or mix of process-industry scenarios and the restriction in terms of continuous production and production commencement immediately after setup. This book is primarily motivated by the literature on CLSP based on the nature of continuous manufacturing industries such as chemical manufacturing, cement manufacturing, sugar industries, pharmaceuticals, hot rolling process, heat treatment, casting and injection moulding, and a real-life case study in a batch processing industry. Referring to the benchmark literature (e.g. Sung and Maravelias (2008) and Belo-Filho et al. (2013)), we find that no existing work has attempted such a mix of industrial scenarios and associated real-life constraints such as continuous production with no interruption and production commencement immediately after setup completion. Therefore, the proposed mathematical model in this chapter is also generalized in nature.