A polynomial algorithm for lot-size scheduling of two type tasks

Authors:
Mikhail Y. Kovalyov;Marcus Pattloch;Günter Schmidt
Affiliations:
Institute of Engineering Cybernetics, National Academy of Sciences of Belarus, Surganova 6, 220012 Minsk, Belarus;DFN-Verein, Pariser Str. 44, 10707 Berlin, Germany;Universität des Saarlandes, Im Stadtwald, 66041 Saarbrücken, Germany
Venue:
Information Processing Letters
Year:
2002

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Abstract

We study the problem of scheduling unit time tasks of two types on m parallel identical machines. For each type, given numbers of tasks are required to be completed by the specified deadlines. These tasks leave the system at the deadlines. The in-process inventory capacities are given. The objective is to construct a schedule that minimizes the number of changeovers occurring between the tasks of different types. This problem arises, for instance, in the production of gear-boxes on transfer lines and in the tobacco industry. Pattloch and Schmidt [Discrete Appl. Math. 65 (1996) 409-419] give an O(mH) algorithm to solve this problem where H is the latest deadline. We present here a modification of that algorithm with O(K min{K, m}), time complexity where K is the number of deadlines.