The shifting bottleneck procedure for job shop scheduling
Management Science
Random number generators: good ones are hard to find
Communications of the ACM
An algorithm for solving the job-shop problem
Management Science
Note. Satisfying Due Dates in Large Job Shops
Management Science
Modelling worker fatigue and recovery in dual-resource constrained systems
Computers and Industrial Engineering
The deployment scheduling analysis tool (DSAT)
Mathematical and Computer Modelling: An International Journal
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A common industrial operation is a dual resource constrained job shop where: (a) the objective is to minimize L"m"a"x, the maximum job lateness; (b) machines are organized into groups; and (c) each worker is assigned to a specific machine group. Because this problem is NP-hard, finding optimal solutions by enumeration is impractical. This paper details a procedure to compute a lower bound on L"m"a"x that will be used in follow-up work to effectively evaluate the absolute performance of heuristic solutions. Given an allocation of workers to machine groups, a lower bound on L"m"a"x is first computed for each machine group using a network-flow formulation. The lower bound on L"m"a"x for the job shop is the largest of the lower bounds for the machine groups. A search algorithm then finds a worker allocation yielding the smallest such lower bound on L"m"a"x for the job shop; and the latter quantity is our proposed lower bound on L"m"a"x. Given a worker allocation, we use the Virtual Factory (a heuristic scheduler developed by Hodgson et al. in 1998) to generate a schedule. Experiments with a wide variety of job shops indicated that the proposed lower bound on L"m"a"x could often be achieved by a Virtual Factory schedule based on the worker allocation yielding this lower bound. However, there were problem instances for which other worker allocations enabled the Virtual Factory to generate better schedules. Follow-up work provides optimality criteria, and heuristics to find improved allocations if these criteria are not satisfied.