A branch and bound algorithm for minimizing total completion time on a single batch machine with incompatible job families and dynamic arrivals

Authors:
Shiqing Yao;Zhibin Jiang;Na Li
Affiliations:
Department of Industrial Engineering & Logistics Management, Shanghai Jiao Tong University, Shanghai, China;Department of Industrial Engineering & Logistics Management, Shanghai Jiao Tong University, Shanghai, China;Department of Industrial Engineering & Logistics Management, Shanghai Jiao Tong University, Shanghai, China
Venue:
Computers and Operations Research
Year:
2012

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Abstract

In this paper, we consider a single batch machine scheduling problem with incompatible job families and dynamic job arrivals. The objective is to minimize the total completion time. This problem is known to be strongly NP-hard. We present several dominance properties and two types of lower bounds, which are incorporated to construct a basic branch and bound algorithm. Furthermore, according to the characteristics of dynamic job arrivals, a decomposed branch and bound algorithm is proposed to improve the efficiency. The proposed algorithms are tested on a large set of randomly generated problem instances.