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Unformatted text preview: Scheduling of batch plants-Deterministic Model Problem definition The scheduling problem of a multiproduct batch plant under product demand uncertainty is solved to obtain a scheduling policy such that the expected profit is maximised. The production lines, a set of products to be produced with their given recipes, the time horizon, the economic data and the distribution probabilities associated to the uncertain parameters are given. The scheduling policy involves the number of batches to be produced of each product, the detailed sequence and the starting and final times of each operation performed. The following assumptions have been made: One production line with assigned equipment units is considered. This assumption can be easily relaxed. The zero wait transfer policy is adopted. Under this policy, an intermediate product must be immediately transferred to the next processing step just after its production. Neither intermediate storage nor waiting times in the processing units are available. This assumption could be easily modified to consider other transfer policies. The scheduling policy is addressed for a time horizon of one month. Fixed inventory and penalisation costs are adopted for each product. Deterministic model The deterministic model, with serves as starting point for the proposed stochastic approach, is formulated as a MILP problem based on a batch slot concept. With this formulation, the time horizon is viewed as a sequence of batches, each of which will be assigned to one particular product. The decision variables involve the number of batches to be produced along with the sequence and the starting and finishing operation times. The proposed mathematical model is as follows: Objective function The objective function (E.1) maximises the profit value (P) taking into account the sales of each product, the inventory costs associated to the amount of product produced but not delivered, and a penalisation cost for production shortfalls. The last term incorporated on the right hand side of the equation is a timing term, which assures that the operations will start as soon as possible. the operations will start as soon as possible....
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- Spring '11