Note: Approximation of the k-batch consolidation problem

Authors:
Sung-Pil Hong;Myoung-Ju Park;Soo Y. Chang
Affiliations:
Department of Industrial Engineering, Seoul National University, San 56-1 Shilim-Dong, Kwanahk Gu, Seoul, 151-742, Republic of Korea;Department of Industrial Engineering, Seoul National University, San 56-1 Shilim-Dong, Kwanahk Gu, Seoul, 151-742, Republic of Korea;Department of Industrial and Management Engineering, Pohang University of Science and Technology, San 31 Hyoja-Dong, Pohang, Kyungbook, 790-784, Republic of Korea
Venue:
Theoretical Computer Science
Year:
2009

Citing 7
Cited 1

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Abstract

We consider a problem of minimizing the number of batches of afixed capacity processing the orders of various sizes on a finiteset of items. This batch consolidation problem is motivated by theproduction system typical in raw material industries in whichmultiple items can be processed in the same batch if they sharesufficiently close production parameters. If the number of itemsprocessed in a batch is restricted to being up to some fixedinteger k, the problem is referred to as the k-batchconsolidation problem. We will show that the k-batchconsolidation problem admits an approximation whose factor is twicethat of the k-set cover problem. In particular, this impliesan upper bound on the approximation factor,2Hk-1, whereHk=1+½+...+1/k.