Short-term scheduling of multiproduct batch plants under limited resource capacity

In multiproduct batch plants, the processing tasks required to complete the production of different items share manufacturing resources such as raw materials, intermediates, manpower, equipment and utilities (steam, electricity, cooling water, etc). Such resources are usually available by limited amounts that cannot be exceeded at any time of the scheduling period. This type of restriction is computationally costly when a continuous-time representation is applied to model the short-term scheduling of multiproduct batch plants. To meet such constraints, it becomes important to monitor the resource requirement profile over the entire planning horizon to exclude from the problem feasible space those schedules exceeding at least one of the resource capacities. Most of current continuous-time based methodologies ignore the resource capacity constraints. Manufacturing resources are usually classified into two major groups: renewable and nonrenewable resources. A renewable resource like units or manpower becomes again available for use after ending the processing task to which is currently assigned. Schedules involving the execution of simultaneous tasks featuring a total resource requirement larger than the available capacity is to be discarded by a proper problem representation. To this end, 0-1 decision variables and additional constraints have been defined to forbid running simultaneous processing tasks if, by doing that, some shortage in a resource capacity arises. A typical case in industry is the number of production lines running in parallel being constrained by the labor capacity. Among non-renewable resources, finite initial inventories and especially the reception of open orders of raw materials and intermediates during the period to be scheduled are challenging real-world capacity constraints to be considered by the proposed mathematical formulation. In this paper, it has been developed a new MILP mathematical formulation for the short-term scheduling of multiproduct batch plants subject to resource capacity constraints usually encountered in the manufacturing industry. The proposed model has been solved by using the modeling system GAMS and the solver OSL (IBM, 1991). A significant number of examples involving up to 15 jobs and limited availability of raw materials, utilities and manpower have been successfully solved. Results show an important reduction in the number of variables with regards to current continuous-time approaches and a good computational efficiency.