Single-machine scheduling with trade-off between number of tardy jobs and resource allocation

doi:10.1016/S0167-6377(96)00035-1

Operations Research Letters

Volume 19, Issue 5, November 1996, Pages 237-242

https://doi.org/10.1016/S0167-6377(96)00035-1 Get rights and content

Abstract

We consider a single-machine scheduling problem in which job processing times are controllable through the allocation of a limited resource. The amount of resource consumption of a job is assumed to be linearly related to the job processing time. The performance criteria are the total resource consumption and the number of tardy jobs. Our objective is to construct the trade-off curve between the total amount of resource consumed and the number of tardy jobs. An NP-hardness proof is presented for the problem of minimizing the total amount of allocated resource subject to a limited number of tardy jobs. A pseudo-polynomial-time dynamic programming algorithm is proposed for constructing the trade-off curve. This dynamic program can be generalized to the case where the job processing time is a decreasing function of the amount of allocated resource.

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Thus, to solve such problems, we will express them in the context of scheduling theory and propose solution algorithms. Namely, the decreasing efficiency of the pickling bath can be modeled by a technique called the “aging effect” approach (see [4–9]), whereas the prevention of this negative phenomenon by heating up the bath (using electrical energy or gas) or by agitation of the pickling bath (using electrical energy as well) can be modeled by resource allocation models (see [10–14]). The quoted example is not isolated, since similar problems can be found in many other manufacturing systems, in which, for instance, tiredness of human workers (e.g. [15,16]) and tool wear of lathe machines (e.g. [17]) affects the production output.
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¹: Supported in part by the Hong Kong Polytechnic University under grant number 351-193-A3-014.

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Single-machine scheduling with trade-off between number of tardy jobs and resource allocation

Abstract

European J. Oper. Res.

Single machine scheduling with controllable processing times and number of jobs tardy

Oper. Res.

Computers and Intractability: A Guide to the Theory of NP-Completeness