Development of mathematical models for integration of lot sizing and flow shop scheduling with lot streaming

In manufacturing industries, production planning and scheduling strategy usually flow in a hierarchical direction. In this direction, the production planning problem is solved first; then the scheduling problem is solved to meet the production targets. This often generates an infeasible production plan because of not considering the details of scheduling. Therefore, it is necessary to develop models that can integrate production planning and scheduling. For manufacturing companies that have identical units of single products and are often grouped in production batches (lots), lot streaming can be used as a scheduling technique. However, there has been no model to integrate production planning (lot sizing) and scheduling, using lot streaming technique which can accelerate production. The main objective of this research is to develop mixedinteger mathematical models for integration of lot sizing and flowshop lot streaming problems such as variable sublots, consistent and equal sublots, scheduling with learning effects and the possibility of preventive maintenance tasks. The objective of these mathematical models is minimization of total costs and also, five goals of problem can simultaneously be solved, namely: determining the sequence among sublots, optimal number of sublots for each lot, size of each lot, inventory levels and size of individual sublots. The second objective of this research is to propose a solution procedure for problems when data are fuzzy. Finally, the third research objective is to validate the proposed model through a case study. Three software are used to extract the results of mathematical models and validate the solution procedure. The name of these software are: LINGO, MINITAB and MATLAB. In this research, the author proposes the first mixed-integer mathematical models for integration of lot sizing and lot streaming problems. By these proposed models, not only sequencing and timing decisions of multiple products are calculated but also lot size of each product, work-in-process and inventory levels of finished products are calculated when lots can be split into smaller sublots. To get the results of mathematical models, in three examples, 70 randomlygenerated problems are solved by LINGO solver. Moreover, a two-way ANOVA test as a statistical method is applied to validate the mathematical model, using four examples consisting sixteen problems, by MINITAB software. The NDM Company is used as a case study. The mathematical models are used to solve NDM company’s problems by LINGO solver. The results showed 32 percent (77.66 hours) reduction in makespan compared to non-integrated mathematical model. Validation of the proposed solution procedure is achieved by comparison of results with max-min method results,using Shahab Shishe company data. The results of using the proposed mathematical models in this research are first to reduce cost by using these proposed models. Secondly is greater marginal benefits were obtained by intermingled sublot cases than non-intermingled sublot cases. It is concluded that better makespans were obtained by intermingled sublot cases than non-intermingled sublot case.

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