Scheduling with arranged multi-purpose machines
by Mourad Boudhar, Hamza Tchikou
International Journal of Operational Research (IJOR), Vol. 8, No. 3, 2010

Abstract: In the present study, we consider a special case of multi-purpose machines (MPMs) in which there is a linear order given for the machines. In addition, for each job J_i(1≤i≤n), a 'first permissible' machine h_i (1≤h(i)≤m) is given on which it can be processed. Thus, machines M_hi,…, M_m are capable of processing job J_i while machines M₁,…, M_hi−1 cannot process job J_i. Each job J_i requires a time p_i and the goal is to minimise the makespan. We prove the NP-hardness of the general problem and present some polynomial sub-problems. Heuristics with an exact algorithm of branch and bound type are also presented with numerical experimentations.

Online publication date: Fri, 04-Jun-2010

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