A MILP model for the simultaneous batching and scheduling of multi-site batch facilities

MONTAGNA, JORGE M.; ACKERMANN, SERGIO; MONTAGNA, JORGE M.; ACKERMANN, SERGIO; FUMERO, YANINA; FUMERO, YANINA

Barcelona

Congreso; 10th World Congress of Chemical Engineering; 2017

EFCE Spain Group

When dealing with multi-site multiproduct production environments, solving the scheduling problem on each plant separately will not lead, in general, to reach the optimal solution. Since each production facility can produce several products, deciding on which plant to process each order is an important part of the problem, and then, an integrated optimization over all facilities is required.On the other hand, because plants are multistage with nonidentical parallel units in each stage, the simultaneous batching and scheduling is convenient, instead of following the traditional path of solving decoupled problems in a hierarchical manner. Usually, in this type of facilities, the batching decisions are solved first to define the number and sizes of batches according to the size of orders and units capacity, and then these batches are used as inputs to solve later the short-term scheduling problem for determining where, how and when the pre-defined batches must be produced. With this classical approach, the quality of the solution is highly dependent of the batching decisions already taken; even more, when nonidentical parallel units at each stage and multi-site facilities are considered, this option will not often reach profitable and efficient solutions.In this work, a mixed-integer linear programming (MILP) model for the simultaneous batching and scheduling for multi-site multiproduct batch facilities with nonidentical parallel units is proposed.The problem consists of determining in which plant of the multi-site facilities must be processed each order, 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, taking into account different time-based objectives: makespan, total earliness and total lateness. The proposed mathematical model considers multiple orders per product with different due dates, zero-wait transfer policy and sequence-dependent changeover times. An order must be entirely processed in a plant and may be fulfilled by one or more batches. Several examples are presented to show the application and performance of the proposed model.