Combinatorial design of a minimum cost transfer line

The problem of equipment selection for a production line is considered. Each piece of equipment, also called unit or block, performs a set of operations. All necessary operations of the line and all available blocks with their costs are known. The difficulty is to choose the most appropriate blocks and group them into (work)stations. There are some constraints that restrict the assignment of different blocks to the same station. Two combinatorial approaches for solving this problem are suggested. Both are based on a novel concept of locally feasible stations. The first approach combinatorially enumerates all feasible solutions, and the second reduces the problem to search for a maximum weight clique. A boolean linear program based on a set packing formulation is presented. Computer experiments with benchmark data are described. Their results show that the set packing model is competitive and can be used to solve real-life problems.