We developed a daily production schedule method for mixed-model assembly, in which multiple models with different workload are produced on a single line. In mixed-model assembly, it is necessary to determine the production ratio and production order considering two objectives, on-time shipping and production efficiency. In order to consider the objectives, divide the production planning problem into two procedures: (1) selecting the daily mix-flow ratio from the production ratio pattern using mixed integer programming, and (2) classifying production lots based on the workload and determining the production order so that the production of lots of the same classification is leveled. In this presentation, we show the contents of the method and the evaluation results.

This paper addresses the flexible job shop scheduling problem with sequencing flexibility and position-based learning effect. Unlike the classical case where a total order is imposed, in this variant of the flexible job shop scheduling problem, the precedence constraints of the operations comprising a job are given by an arbitrary directed acyclic graph. For this problem, a mixed integer programming model is first introduced, and constructive heuristics are introduced to provide an initial solution for the model's solvers. Next, local search strategies are examined. W show that the classical strategy of relocating only the operations that are part of the critical path can lose better quality neighbors, contrary to what happens in the case where there is no learning effect. Consequently, we analyzed an alternative type of neighborhood reduction that eliminates only neighbors that are no better than the current solution. Furthermore, we propose a neighborhood cut, and experimental results show that this greatly shrinks the neighborhood, bringing efficiency with minimal loss of effectiveness. Numerous numerical experiments are conducted. The proposed methods, as well as the instances and solutions found, are freely available.

In manufacturing industries, production and maintenance operations are closely linked but are generally planned and optimized separately. Planning preventive maintenance operations makes it possible to determine the appropriate periods for carrying out maintenance upstream of production. Then, production planning consists of determining the quantity and timing of production of several items over a time horizon. This study proposes new mathematical formulations as mixed-integer linear programs for a problem integrating preventive maintenance planning into the Capacitated Lot Sizing Problem (CLSP). One of these formulations (M1) is based on the redefinition of the variables linked to preventive maintenance planning and another is a Dantzig-Wolfe decomposition formulation (M2). We demonstrate that the formulation M1 gives a relaxation equivalent to the column generation based on M2. Subsequently, we use a relax-and-fix heuristic combined with fix-and-optimize to solve this problem. Relax-and-fix is used to build an initial solution and fix-and-optimize allows us to improve the built solution. Computational experiments evaluate the performance of the heuristics and the models solved with Gurobi. The results show that the solutions obtained by the heuristic are close to those obtained by the models in terms of gap and in a reduced time.

This study addresses large-scale personnel scheduling problems in the service industry by combining mathematical programming with data mining techniques to enhance efficiency. The studied problem aims at efficiently scheduling skilled employees over a one-week planning horizon, minimizing costs while meeting diverse job demands. In service industries, shift planning is intricately tied to customer presence, leading to a multitude of potential shifts and to a difficult optimization problem that cannot be easily solved using a commercial mixed-integer programming solver. Nevertheless, these problems are categorized as recurrent problems, where distinct instances share common characteristics and solution structures that differ only in a few parameters over time. Consequently, we propose to use a data mining technique, namely, the k-nearest neighbors algorithm, to expedite the solution process while upholding solution quality. In particular, we suggest using schedules of past solutions to reduce the problem size. Specifically, for an upcoming instance, we identify similar historical instances and streamline the enumeration of shifts to align with the comparable historical instances' schedules. This approach allows us to effectively address the problem using a commercial solver within a reasonable timeframe while preserving solution quality. Significantly, our methodology offers decision-makers the flexibility to determine the extent to which they wish to scale down the problem. Our experiments, conducted on a total of 80 instances with up to 12 jobs and 190 employees, yield an average removal of 85.5\% of decision variables. This resulted in a noteworthy average speedup factor of 15.5, with a marginal average cost increase of 1.2\%.