The stochastic lot sizing problem with piecewise linear concave ordering costs

• We address the stochastic lot sizing with piecewise linear concave ordering costs.
• We introduce the generalized (R,SR,S) policy and present a MIP formulation thereof.
• The generalized (R,SR,S) policy yields an optimality gap around 1%.

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,SR,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,SR,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,SR,S) policy against the cost-optimal generalized (s,S  ) policy. The results of the numerical study reveal that the (R,SR,S) policy performs very well – yielding an average optimality gap around 1%.