Selecting ingot sizes for joint production of sheet products

This paper addresses a tactical planning problem of selecting standard ingot sizes to facilitate joint processing of finished sheets in a make-to-order aluminum sheet manufacturing plant. The facility has traditionally dedicated one ingot to each item ordered but is now considering producing multiple items from each ingot to reduce excess metal and exploit economies of scale in processing costs. The effectiveness of this joint processing strategy depends on the available standard ingot sizes. We develop an integer programming model to decide ingot sizes, given the projected demand and technological/operational constraints on combining orders. The model selects a prespecified number of standard sizes and determines which combinations to use to satisfy the demand for all products. The objective is to minimize the total weight of excess metal. We describe a dual-ascent method to generate lower bounds for the problem and heuristic procedures to identify good solutions. Computational results for test problem instances based upon data from an aluminum sheet manufacturer confirm the effectiveness of the algorithm; on average, the gaps between the upper and lower bounds are about 4%. We also illustrate how the model can be used to perform sensitivity analyses.