A Global Chance-Constraint for Stochastic Inventory Systems Under Service Level Constraints

Abstract

We consider a class of production/inventory control problems that has a single product and a single stocking location, for which a stochastic demand with a known non-stationary probability distribution is given. Under the widely-known replenishment cycle policy the problem of computing policy parameters under service level constraints has been modeled using various techniques. Tarim and Kingsman introduced a modeling strategy that constitutes the state-of-the-art approach for solving this problem. In this paper we identify two sources of approximation in Tarim and Kingsman's model and we propose an exact stochastic constraint programming approach. We build our approach on a novel concept, global chance-constraints, which we introduce in this paper. Solutions provided by our exact approach are employed to analyze the accuracy of the model developed by Tarim and Kingsman.

Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

“…We performed tests using four different ordering cost values a ∈ {40, 80, 160, 320} and two different σ t /d t ∈ {1/3, 1/6}. The planning horizon length takes even values in the range [24,50] when the ordering cost is 40 or 80 and [14,24] when the ordering cost is 160 or 320. The holding cost used in these tests is h = 1 per unit per period.…”

“…Empirical results showed that such a model is unable to solve large instances, but Tarim and Smith [23] introduced a more compact and efficient Constraint Programming (CP) formulation of the same problem that showed a significant computational improvement over the MIP formulation. A stochastic constraint programming [22] approach for computing (R n , S n ) policy parameters is proposed in [14]. In this work the authors drop the mild assumptions originally introduced by Tarim and Kingsman and compute optimal (R n , S n ) policy parameters.…”

A Forecast-based Inventory Control Policy for an Item with Non-stationary Demand

“…, Zipkin(1989), Lovejoy(1990), Morton and Pentico(1995), Iida(2002), Tarim and Kingsman (2004), Levi et al(2007), Rossi et al(2008), Guan and Liu(2010) 두 번째 분류의 연구들은 비정상 수요에서 구매자 관점의 재고관리 정책에 관한 연구이다. Sethi and Cheng(1997) (1)   기 수요를 예측한다.…”

Flow-Based Combinatorial Chance Constraints

“…More recently, scenario-based stochastic constraint programming [25], and cost-based filtering for stochastic constraint programming [24,26] have been proposed. Lastly, the concept of global chance constraints that was introduced by Rossi et al [23] is of particular interest to our work.…”