(558b) Optimal Integration of Planning and Scheduling for Parallel Multi-Product Batch Reactors

Due to the increasing pressure for reducing costs and inventories, in order to remain competitive in the global market place, Enterprise-Wide optimization has become the ?holy grail? in process industries. Central to Enterprise-wide optimization are the activities of planning and scheduling, which deal with long and short term time scales for decisions on production targets and allocation of resources. One of the major challenges in this area is temporal integration where the aim is to coordinate decisions across very different time scales. Typically, planning models are linear and simplified representations that are used to predict production targets over several months. Also, at this level effects of changeovers are only roughly approximated as compared to the scheduling models. This however results in optimistic estimates of production which may not be realized at the scheduling level, and may yield infeasible schedules. In order to avoid infeasible schedules and guarantee consistency between production planning and scheduling levels, planning and scheduling should be effectively integrated. In this paper, we address the simultaneous integration of planning and scheduling of parallel multi-product batch reactors, a challenging problem that has been motivated by a real world application at the Dow Chemical Company. The conventional approach for managing production planning and scheduling relies on a two step process. The first step involves long range production planning (e.g. 12 months), while the second involves short term scheduling (e.g. 1-2 weeks). The goal of the production planning is to determine the production capacity for meeting given demands taking into account raw material costs and availabilities and product prices. The goal of the production scheduling on the other hand is to determine the detailed timing of production as well as cleaning tasks and the amount of materials produced on each reactor while taking into account inventory replenishment needs and inventory capacities. When determining the short term schedule, sequence dependent changeover times have a significant impact on the plant's capacity and therefore on the long range production plan. However, the production plan does not normally account for change-over times, which may result in inconsistencies between the production planning and the scheduling levels. To overcome this problem, we propose a rigorous bi-level decomposition scheme that will generate solutions that are theoretically equivalent to performing simultaneous planning and scheduling over the entire planning horizon at a reasonable computational expense. The specific problem that we address is as follows. Given is a plant that contains batch reactors that operate in parallel. The batch reactors are to be used to manufacture intermediates and final products. A subset of the final products is produced in a single reaction stage, while the remaining final products require intermediates, thus involving two reaction stages with intermediate storage. Each final product is fed to a dedicated storage tank. In order to formulate this problem we assume that we are given the products each reactor can produce, as well as the batch times and batch sizes for each product and the corresponding reactor. While the batch times and batch sizes are fixed, the number of batches of each product is a variable that is to be determined. Sequence dependent cleaning times and the total time each reactor is available in each month are given. We are also given raw material costs and availability, and storage tanks with associated capacities. Specified is a production horizon composed by certain number of time periods given by due dates to satisfy demands of several products where demands are specified as upper bounds. The problem is then to determine the optimal production plan and schedule in terms of monthly production quantities for each reactor and the sequence of batches so as to maximize the profit while satisfying production demands at the specified due dates. In order to address the above problem, we propose a novel continuous time MILP optimization model for the simultaneous planning and scheduling that is based on slot time representation that overcomes some of the major difficulties faced by the STN and RTN discrete and continuous time models. While effective for short-term scheduling, the proposed model becomes computationally expensive to solve for long planning horizons. Hence, we propose a rigorous bi-level decomposition algorithm that reduces the computational cost of the problem. The problem is decomposed into an aggregated upper level planning and a lower level planning and scheduling problem. The upper level determines the products to be produced at each time period as well as number of batches of each product, production levels and product inventories. The upper level is based on a new relaxed STN model where the detailed timing constraints and changeovers are replaced by time balances yielding a tight upper bound on the profit. The lower level is solved in the reduced space of binary variables according to the information obtained from the upper level model; therefore it yields a lower bound on the profit. The lower level determines production and inventory levels as well as detailed timing of the sequence of products and associated assignments to processing equipments and storage tanks. The procedure iterates until the difference between the upper and lower bound is less than a specified tolerance. To expedite the search we add logic cuts that arise from the structure of the problem which help reduce the feasible search space for the binary variables and tighten the gap between the solutions of the two levels. The proposed decomposition scheme ensures consistency between the two levels and optimality within a specified tolerance. Application of the proposed solution approach is illustrated with several examples which show that the aggregated upper level model yields very tight bounds, while the slot based scheduling model can be solved very effectively with constraints supplied by the aggregate model.