The stochastic lot sizing problem with piecewise linear concave ordering costs. (January 2016) - Tunc, Huseyin; Kilic, Onur A.; Tarim, S. Armagan; Eksioglu, Burak
Abstract: We address the stochastic lot sizing problem with piecewise linear concave ordering costs. The problem is very common in practice since it relates to a variety of settings involving quantity discounts, economies of scales, and use of multiple suppliers. We herein focus on implementing the ( R, S ) policy for the problem under consideration. This policy is appealing from a practical point of view because it completely eliminates the setup-oriented nervousness – a pervasive issue in inventory control. In this paper, we first introduce a generalized version of the ( R, S ) policy that accounts for piecewise linear concave ordering costs and develop a mixed integer programming formulation thereof. Then, we conduct an extensive numerical study and compare the generalized ( R, S ) policy against the cost-optimal generalized ( s, S ) policy. The results of the numerical study reveal that the ( R, S ) policy performs very well – yielding an average optimality gap around 1%. Abstract : Highlights: We address the stochastic lot sizing with piecewise linear concave ordering costs. We introduce the generalized ( R, S ) policy and present a MIP formulation thereof. The generalized ( R, S ) policy yields an optimality gap around 1%.