Abstract
The Joint Replenishment Problem (JRP) is a fundamental optimization problem in supply-chain management, concerned with optimizing the flow of goods over time from a supplier to retailers. Over time, in response to demands at the retailers, the supplier sends shipments, via a warehouse, to the retailers. The objective is to schedule shipments to minimize the sum of shipping costs and retailers’ waiting costs.
We study the approximability of JRP with deadlines, where instead of waiting costs the retailers impose strict deadlines. We study the integrality gap of the standard linear-program (LP) relaxation, giving a lower bound of 1.207, and an upper bound and approximation ratio of 1.574. The best previous upper bound and approximation ratio was 1.667; no lower bound was previously published. For the special case when all demand periods are of equal length we give an upper bound of 1.5, a lower bound of 1.2, and show APX-hardness.
Full version available at [4]. Research supported by MNiSW grant number N N206 368839 (2010-2013); NSF grants CCF-1217314, CCF-1117954, OISE-1157129; EPSRC grants EP/J021814/1 and EP/D063191/1; FP7 Marie Curie Career Integration Grant; and Royal Society Wolfson Research Merit Award.
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Bienkowski, M. et al. (2013). Approximation Algorithms for the Joint Replenishment Problem with Deadlines. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_12
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DOI: https://doi.org/10.1007/978-3-642-39206-1_12
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