Optimising reorder intervals and order-up-to levels in guaranteed service supply chains

A.S. Eruguz, Z. Jemai, E. Sahin

Research output: Contribution to journalArticleAcademicpeer-review

19 Citations (Scopus)
408 Downloads (Pure)


We consider the problem of determining the optimal reorder intervals R and order-up-to levels S in a multi-echelon supply chain system where all echelons are assumed to have fixed ordering costs and to operate with a (R, S) policy with stationary nested power-of-two reorder intervals. By using the guaranteed service approach to model the multi-echelon system facing a stochastic demand, we formulate the problem as a deterministic optimisation model in order to simultaneously determine the optimal R and S parameters as well as the guaranteed service times. The model is a non-linear integer programming (NLIP) problem with a non-convex and non-concave objective function including rational and square root terms. Then, we propose a sequential optimisation procedure (SOP) to obtain near-optimal solutions with reasonable computational time. The numerical study demonstrates that for a general acyclic multi-echelon system with randomly generated parameters, the SOP is able to obtain near-optimal solutions of about 0.46% optimality gap in average in a few seconds. Moreover, we propose an improved direct approach using a global optimiser, bounding the decision variables in the NLIP model and considering the SOP solution as an initial solution. Numerical examples illustrate that this reduces significantly the computational time.
Original languageEnglish
Pages (from-to)149-164
JournalInternational Journal of Production Research
Issue number1
Publication statusPublished - 2014


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