Lot-sizing and scheduling for flexible flow lines.
In this book the lot-sizing and scheduling problem for flexible flow line production facilities is considered. Flexible flow lines are flow lines with parallel machines on some or all production stages. They can be found in a vast number of industries. The goal of a lot-sizing and scheduling routine is to determine production quantities, machine assignments and product sequences. The latter two represent a schedule, while the former are the result of a lot-sizing procedure. The author presents an integrative solution approach for the combined lot-sizing and scheduling problem. The objective is to minimize setup, inventory holding and back-order costs as well as mean flow time through the system. The solution approach consists of the phases `Bottleneck planning', `Schedule roll-out' and `Product-to-slot assignment'. The approach is bottleneck-oriented. A human planner is usually aware which production stage constitutes the bottleneck. If this is not the case, the bottleneck stage has to be determined beforehand. The first phase of the solution approach solves a single stage lot-sizing and scheduling problem on the bottleneck stage. Products are aggregated to product families. The suggested solution procedure is based on a new `heuristic' model formulation that uses integer variables in contrast to binary variables as employed by standard formulations. This makes it possible to solve the model to optimality or near-optimality using standard algorithms that are embedded in commercial software packages (e.g. CPLEX). The second phase generates a product family plan on all production stages. Thus, it keeps the aggregation level of product families, but explicitly includes the non-bottlenecks stages. It assigns a production time and a machine to each product family unit, which means that it solves a multi-stage scheduling and batching problem. The basic idea of the solution procedure is to establish the same product family throughput on all stages. In this way, each preceding stage supplies the intermediate products just in time for the subsequent stage. Thus, the products do not have to wait between stages and the flow time as well as the inventory volumes of intermediate products are minimized. The third phase considers the individual products and calculates the final schedule, which consists of exact production times and machine assignments for every product unit on all stages. The problem is to determine how many and which machines to set up and when to produce the individual product units. Two nested Genetic Algorithms are employed to solve the problem. The solution procedures can be embedded into hierarchical production planning systems. The presented solution approach seems very well suited for a rolling planning horizon, since the top-level phase is based on a period-by-period procedure.
scientific article; zbMATH DE number 2104446