In recent years, many companies have shifted from single-site production to more complex manufacturing environments involving multiple multiproduct facilities. At the operational level, the scheduling posed on each individual facility does not lead to efficient use of resources and consequently an optimal production management over the whole production system cannot be achieved. In this context, a multisite production scheduling framework is fundamental to respond appropriately to the market requirements. In this work, a mixed-integer linear programming (MILP) model for the simultaneous batching and scheduling of multisite multiproduct batch plants with nonidentical parallel units is proposed. Given a set of manufacturing sites with unit capacities and structure known and multiple orders with associated release and due dates, the proposed approach determines the plant where each customer order must be processed, the number and sizes of batches to satisfy each order, the assignment of these batches to units, as well as the sequencing and timing of batches on each unit of the plant that processes them, in order to minimize the global makespan related to the whole production system. The application and performance of the proposed model are highlighted through numerical examples.

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The large number of studies addressing the scheduling problem in multiproduct batch plants with different units operating in parallel and out of phase at each stage highlights its importance in achieveing their efficient operation, as well as the difficulty and the number of variants that may arise in solving this problem. Scheduling is usually solved in a simplified way, considering as data the number and size of the required batches to satisfy the demand. More recently, models have been developed that simultaneously solve the batching, that is, determine the number and size of batches, and scheduling problems, generally achieving better solutions. However, these models are of great computational complexity due to their combinatorial nature, and, therefore, the development of efficient models that allow addressing large problems remains a great challenge. This work presents a new approach, where production paths are defined that allows obtaining the solution in short computation times. Then, a novel discrete-time mixed-integer linear formulation (MILP) for the simultaneous resolution of batching and scheduling in a multistage batch plant is presented and its performance is considered in detail.

In multisite production environments, the appropriate management of production resources is an activity of fundamental relevance to optimally respond to market demands. In particular, each production facility can operate with different policies according to its objectives, prioritizing the quality and standardization of the product, customer service, or the overall efficiency of the system; goals which must be taken into account when planning the production of the entire complex. At the operational level, in order to achieve an efficient operation of the production system, the integrated problem of batching and scheduling must be solved over all facilities, instead of doing it for each plant separately, as has been usual so far. Then, this paper proposes a mixed-integer linear programming model for the multisite batching and scheduling problems, where different operational policies are considered for multiple batch plants. Through two examples, the impact of policies on the decision-making process is shown.

El scheduling de la producción tiene un rol fundamental para lograr la operación eficiente de una planta batch multiproducto. La dificultad del problema y número de variantes que se pueden presentar ha hecho del mismo un área de constante investigación y desarrollo de modelos y estrategias de resolución. Usualmente el scheduling ha sido resuelto de manera simplificada, teniendo como datos el número y tamaño de batches (o lotes) necesarios para satisfacer la demanda. Sin embargo, la resolución simultánea del batching y scheduling lleva en general a la obtención de mejores soluciones. Los modelos desarrollados hasta el momento para abordar dichos problemas de manera simultánea son de una gran complejidad computacional, debido a su naturaleza combinatoria, por lo que lograr el desarrollo de modelos eficientes que permitan abordar problemas de gran tamaño continúa siendo un desafío. En este trabajo se presenta un novedoso modelo de programación mixta entera lineal (MILP) para la resolución simultánea del batching y scheduling en una planta batch multietapa, con unidades distintas operando en paralelo y fuera de fase en cada etapa.