A developed slope order index (SOI) for bottlenecks in projects and production lines

This paper finds a sequence of m jobs on one processor with the minimum total cost as a solution to the sequencing problem where the raw materials are either expensive to buy or carry. There have been numerous studies considering m jobs on one processor which consider various cost factors such as the total penalty cost. One of the important, but less investigated cost factors, in the previous studies, is the inventory carrying and its relevant capital costs. The inventory costs such as the holding cost and capital cost must be considered in proposing a solution to the sequencing problem. In this paper, by taking those costs into account to address the sequencing problem, a developed slope order index is computed to enable decision makers to a sufficient cost saving sequence of m jobs on one processor. This paper contributes the current knowledge by proposing a new sequencing solution in which some previously less observed costs are considered. The result of this paper can also be employed in scheduling of m jobs where there is a bottleneck and the inventories are expensive or their holding costs are considerable.