Tradeoff between setup times and carrying costs for finished items

This paper considers a multiple job class problem with bi-criteria. One criterion is to minimize the total setup time, which is equivalent to minimizing the makespan. The other criterion is to minimize sum of the ranges of the customer orders, where the range of a customer order refers to the difference between the maximum and minimum completion times of jobs in the same customer order. The latter criterion can be regarded as a measure of carrying costs for finished goods waiting to be shipped along with other unfinished items for the same customer. A branch-and-bound algorithm is developed to generate all the efficient schedules. Computational results are provided for small and medium sized problems.