Optimal lot-sizing and scheduling of multistage batch plants considering multiple orders per product

FUMERO, YANINA; MONTAGNA, JORGE MARCELO; CORSANO, GABRIELA

5th International Conference on Engineering Optimization

Conferencia; EngOpt 2016, 5th International Conference on Engineering Optimization; 2016

COPPE/UFRJ

In the process industry, batch production systems provide greater flexibility since a large number of products can be elaborated using the same equipment. In these facilities, products compete for the use of the resources required for manufacturing, such as processing equipment, storage tanks, utilities, raw materials, etc. and consequently the production scheduling plays a crucial role in this type of industries. Several modeling approaches and solution strategies for the scheduling problem of batch facilities have been addressed in the last decades, however the mathematical programming has become one of the most widely explored methods for solving this problem.Batch scheduling is a highly combinatorial problem involving two issues: the lot-sizing or batching problem, which defines the set of batches to be scheduled and their sizes, and the short-term scheduling problem, which determines the assignment, sequencing and timing of the selected batches. In sequential production environments, for complexity reasons, the whole problem has been traditionally solved in a hierarchical manner, where the batching is solved first to define the number and sizes of batches, and the short-term scheduling problem is later solved for determining when and where the pre-defined batches are to be produced. That is, orders are first divided into batches according to unit capacities, and then these batches are used as inputs in the scheduling problem. Although this typical sequential procedure is generally used in practice and academia, the quality of the production schedule is indeed highly dependent on the lot-sizing decisions already taken. Furthermore, in these optimization methods, a common assumption is to consider fixed processing times, irrespective of the corresponding batch sizes, which is not always valid depending on process specifications. Thus, batching and scheduling must be simultaneously considered in order to achieve appropriate and efficient solutions.In recent years, attention has been paid to the development of integrated optimization models for simultaneously solving both problems. In the literature, a few works with this approach have been presented.In this work, a mixed-integer linear programming (MILP) formulation for the simultaneous batching and scheduling in multistage multiproduct batch plants with nonidentical parallel units is proposed. The slot-based model considers multiple orders per product with different due dates, variable processing times, zero-wait (ZW) transfer policy, and sequence-dependent changeover times. An order may be fulfilled by one or more batches, therefore, an appropriate number of batches must be proposed for each order with the purpose of ensuring optimality of the solution. The goal problem is to determine (a) the number and size of batches for each customer order, (b) the assignment of batches and their sequence on each unit, and (c) the timing of selected batches. The model is flexible to accommodate different objective functions, such as earliness, makespan, and processing costs. Different examples are presented in order to highlight the application and performance of the proposed algorithm.