Two machine mixed shop scheduling problem with controllable machine speeds

This paper considers a scheduling problem in which the objective is to determine an optimal machine speed pair and an optimal schedule. There are two machines A, B and n jobs each of which consists of two operations. One operation is to be processed on machine A and the other on machine B. All jobs are open shop type, i.e., processing order of two operations is not specified and so processing of each job can be started on either machine. Of course each machine processes at most on!! job and each job is processed on at most one machine, simultaneously. Further it is assumed that speeds of machines A, B are controllable. In the situation, the total sum of costs associated with the maximum completion time and machine speeds is to be minimized. The problem is a generalization of two machine open shop problem in a sense that machine speeds are not fIXed but variables. This paper proposes an O(n log n) algorithm which fmds an optimal speed of each machine and optimal schedule.