Solving the Two-Stage Hybrid Flow Shop Problem by a Branch-and-bound Algorithm
نویسندگان
چکیده
A set J of n jobs has to be scheduled in a manufacturing system with two stages (machining centers) Z1 and Z2. Each stage Zi (i = 1, 2) has mi identical machines in parallel (with max(m1, m2) ≥ 2). Each job j (j = 1, ..., n) has to be processed first for aj units of time by one machine of Z1, and then for bj units of time by one machine of Z2. These operations must be processed without preemption. Moreover, a job cannot be processed by more than one machine at the same time and each machine processes at most one job at one time. All processing times are assumed to be deterministic and integer and all machines are ready from time zero onwards. The objective is to construct a schedule for which the maximum completion time, or makespan, is minimized. This problem, denoted by F2(P ) ||Cmax, is strongly NP-hard.
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