Optimal sequencing of tasks in an aluminium smelter casthouse

This paper examines the problem of determining the sequence in which to cast aluminium ingots such that setup times are minimized. The aluminium ingots are of different size and consist of different alloys; this poses constraints on the allowable ordering of casting jobs. The sequencing problem can be formulated as an asymmetric traveling salesman problem with additional constraints. Two different methods are used to formulate and solve this problem, a genetic algorithm (GA) and an integer programming approach (IP). A new method for detecting sub-tours in the IP formulation is set forth and used. Both the GA and IP approach are implemented in a software tool that is being used in the aluminium production industry. The results show that even though the integer programming formulation can be used to solve the problem to optimality, the size of the problem is a limiting factor for practical implementation. Therefore, the genetic algorithm is used in the industrial implementation with good results.