(90c) Optimal Periodic Scheduling Of A Pharmaceutical Plant

Enterprise-wide Optimization (EWO) has become a major goal in the chemical, petroleum and pharmaceutical industries due to the increasing pressures of remaining competitive in the global marketplace (Grossmann, AIChE Journal 2005, 51, 1846). A major focus in EWO is the optimal operation of manufacturing facilities, where scheduling plays an important part. For companies to respond to market requirements quickly, they have to rely on increasingly more flexible plants and on an optimal management of equipment resources. Allocating too many equipments to the production of a particular product may lower its makespan but might also make it impossible for the plant to accept other orders for that same time window, thus facing the risk of missing out on important business opportunities.

The problem considered in this paper comes from a Portuguese pharmaceutical plant. Given are a large set of equipment items that perform different functions (e.g. reactor, filter) and are further characterized by construction material (e.g. stainless steel, hastelloy) and capacity, and are employed for the production of a pre-determined amount of a single product. The synthesis of the product involves a few intermediates, each with its own sequence of processing steps, where each task has a fixed duration and requires the use of one or more vessels of a particular material. Changeovers increase the complexity of the problem since they are required every time an intermediate/product is changed and their duration is of the same order of magnitude of processing tasks. Several product batches are needed to fulfill the demands so a periodic mode of operation is considered.

The problem is tackled with a Resource-Task Network (RTN) discrete-time formulation and a decomposition method is used to overcome the prohibitively large problem size resulting from the multiple combinations of distributing the equipments over the processing tasks. The MILP-based solution procedure finds the optimal schedule in terms of one intermediate at a time and in this respect is similar to the procedure of Roslöf et al. 2001 (Comput. Chem. Eng. 25, 821). In this way, a considerable reduction in the number of tasks is achieved, since only processing tasks of the product under consideration and changeover tasks to/from that same product are considered at each step. The objective function is the total cost minimization, which includes equipment selection cost as well as the operation cost that is proportional to the cycle time. The tradeoff is between the cycle time duration and the number of equipments: the shorter the cycle time the higher the number of equipments and hence the cost. Since we are dealing with a discrete-time formulation the cycle time is fixed, so finding the optimal cycle time requires applying the solution procedure iteratively.

The results have shown that the method is very efficient, since it can find the optimal periodic schedule in a few minutes of computational time and thus meeting one of the requirements of the plant manager. Furthermore, as a part of the solution procedure, it provides close to the optimum solutions using different cycle times that may be more convenient to implement than other features, assumed at this stage, to be less relevant and therefore not included in the objective function.