In part 1 of this series, it was seen how minimum run length constraints may complicate conventional multiperiod models. For short-term scheduling, these constraints, along with sequencing issues, become even more critical, and part 2 explores the application of continuous time formulations to this class of problems. Two mixed-integer linear programming (MIP) formulations are presented for the detailed short-term scheduling of a single-stage multiproduct facility with multiple parallel semicontinuous processors. Given a set of due dates, demands for products at these dates, and several operational and topological constraints, it is desired to determine the start and end times of individual product campaigns and machine assignments to minimize the inventory, transition, and shortage costs. The key feature of these formulations is that they can accommodate prespecified discrete time events such as due dates while employing a continuous representation of time. In addition to regular production, various outages such as tests and maintenance can be scheduled and a variety of transitions between operations can be accommodated. For purposes of illustration, a (relatively) small real plant scheduling problem is solved.

In this two-part series of papers, production planning and scheduling models are developed for the case of semicontinuous processes which are assumed to comprise several facilities in distinct geographical locations, each potentially containing multiple parallel units. The models developed are deterministic in nature and are formulated as mixed-integer linear programs (MIP's). Part 1 deals with multiperiod midterm planning models where sourcing considerations are important, given that products can be manufactured at several facilities, often on different continents. Optimal allocation of assets to production tasks in order to satisfy the fluctuating demands of the global marketplace over an extended horizon is the main goal in this kind of model. Plan performance is assessed relative to an objective function involving maximization of earnings and minimization of production, inventory, and transportation costs. In these types of models, the actual timing and sequencing of production campaigns is not determined. For this purpose, part 2 discusses the application of two novel short-term scheduling formulations to a single-stage, multiproduct, multiprocessor facility. The goal is to minimize the production, inventory, and transition costs for a single facility. These are continuous time formulations in the sense that they allow production events to occur at any point over the scheduling horizon while retaining the ability to assess costs at discrete points in time, as in the classic multiperiod formulations. Thus, they overcome the restrictions imposed by the use of time boundaries in multiperiod models. For purposes of illustration, a limited number of examples are presented which are modifications of real industrial problems.

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