Minimization of earliness, tardiness and due date penalties on uniform parallel machines with identical jobs

Authors:
Inna G. Drobouchevitch;Jeffrey B. Sidney
Affiliations:
Korea University Business School, Anam-dong, Seongbuk-gu, Seoul 136-701, Republic of Korea;Telfer School of Management, The University of Ottawa, Ottawa, Canada K1N 6N5
Venue:
Computers and Operations Research
Year:
2012

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Abstract

We consider a problem of scheduling n identical nonpreemptive jobs with a common due date on m uniform parallel machines. The objective is to determine an optimal value of the due date and an optimal allocation of jobs onto machines so as to minimize a total cost function, which is the function of earliness, tardiness and due date values. For the problem under study, we establish a set of properties of an optimal solution and suggest a two-phase algorithm to tackle the problem. First, we limit the number of due dates one needs to consider in pursuit of optimality. Next, we provide a polynomial-time algorithm to build an optimal schedule for a fixed due date. The key result is an O(m^2logm) algorithm that solves the main problem to optimality. Scope and purpose: To extend the existing research on cost minimization with earliness, tardiness and due date penalties to the case of uniform parallel machines.