Constraint programming for stochastic inventory systems under shortage cost

Abstract

One of the most important policies adopted in inventory control is the replenishment cycle policy. Such a policy provides an effective means of damping planning instability and coping with demand uncertainty. In this paper we develop a constraint programming approach able to compute optimal replenishment cycle policy parameters under non-stationary stochastic demand, ordering, holding and shortage costs. We show how in our model it is possible to exploit the convexity of the cost-function during the search to dynamically compute bounds and perform cost-based filtering. Our computational experience show the effectiveness of our approach. Furthermore, we use the optimal solutions to analyze the quality of the solutions provided by an existing approximate mixed integer programming approach that exploits a piecewise linear approximation for the cost function.

Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing

“…The model presented can be used to compute an upper bound for E[TP] -note that underestimating buffer stocks, i.e.Ĩ lb t leads to lower holding costs and to an overestimation of the expected order quantity and associated margins mQ t in the objective function. If we aim to compute a lower bound instead, all occurrences of I lb t should be replaced byĨ ub t and constraints (22) should be replaced by constraints (23). Other MILP formulations under β cyc and β service levels are obtained in a similar fashion, since only the service level constraints of the model are affected by this change.…”

The stochastic lot sizing problem with piecewise linear concave ordering costs

“…However, following earlier results, we regard such occurrences as rare events and ignore the associated costs (see e.g. Rossi et al, 2012).…”

“…This strategy has recently been subject to a detailed scrutiny due to its practical relevance, and applied to a variety of inventory control problems (see e.g. Bookbinder & Tan, 1988;Tarim & Kingsman, 2004Rossi et al, 2012). All of these studies have analyzed the (R, S) policy under the assumption that ordering cost is comprised of a fixed and a linear component.…”

Application of stochastic programming to reduce uncertainty in quality-based supply planning of slaughterhouses

“…Future works may investigate more accurate and structured reliability measures, such as those discussed in Tarim et al [18], in place of the chance constraints discussed in the current model. Another interesting strategy might be to penalize shortages, following Rossi et al [16]. The model is currently positioned at an operational/tactical level.…”