A binary branch and bound algorithm to minimize maximum scheduling cost

This paper examines a single machine scheduling problem of minimizing the maximum scheduling cost that is nondecreasing with job completion time. Job release dates and precedence constraints are considered. We assume that each job can be processed exactly once without preemption. This is a classical scheduling problem, and is specifically useful in the scheduling of medical treatments. We develop a simple branch and bound algorithm to solve the scheduling problem optimally. A binary branching technique is developed. We use a preemptive solution approach to locate a lower bound, and design a simple heuristic to find an upper bound. Our algorithm is easy to implement and finds optimal schedules in one CPU minute for almost all instances tested, with up to 1000 jobs.

► Minimizes maximum scheduling cost, with release dates and precedence constraints.
► Applicable in scheduling of medical treatments.
► Develops an easy-to-implement branch and bound algorithm.
► Optimally solves almost all random instances with up to 1000 jobs in one CPU minute.