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Modelling inter-temporal capacity transfer in an aluminium smelter

In this paper, an existing model of a multi -period nonlinear bilevel model of an aluminium smelter which allows for the transfer of stocks of raw materials throughout the planning period is extended to allow for the inter-temporal transfer of capacity. The situation arises in reality where a part of the smelter is closed for scheduled maintenance and in order to adhere to the prime directive of the aluminium smelter Management, “don't stop production", it is necessary to transfer capacity from previous months to the month in question. Capacity per se cannot be transferred, however, the stocks of needed intermediate products (i.e., partly processed materials required for the next stage of production) can be, thus allowing the plant to continue operation. In incorporating the necessary infrastructure into the existing multi period model, a number of substantial alterations were required. The most important change was the introduction of an additional variable to allow for the separation of the levels of activity of two main areas of the plant that produce the needed materials to allow smelting to take place. Numerical examples are given. Additional work on the already foreshadowed heuristic solution algorithm for the multi -period model is also highlighted.