Dynamic capacitated lot sizing with random demand and dynamic safety stocks

Abstract

Suggested Citation: Helber, Stefan; Sahling, Florian; Schimmelpfeng, Katja (2011) AbstractWe present a stochastic version of the single-level, multi-product dynamic lotsizing problem subject to a capacity constraint. A production schedule has to be determined for random demand so that expected costs are minimized and a constraint based on a new backlog-oriented δ-service-level measure is met. This leads to a non-linear model that is approximated by two different linear models. In the first approximation, a scenario approach based on random samples is used. In the second approximation model, the expected values of physical inventory and backlog as functions of the cumulated production are approximated by piecewise linear functions. Both models can be solved to determine efficient, robust and stable production schedules in the presence of uncertain and dynamic demand. They lead to dynamic safety stocks that are endogenously coordinated with the production quantities. A numerical analysis based on a set of (artificial) problem instances is used to evaluate the relative performance of the two different approximation approaches. We furthermore show under which conditions precise demand forecasts are particularly useful from a production-scheduling perspective.

Fix‐and‐Optimize and Variable Neighborhood Search Approaches for Stochastic Multi‐Item Capacitated Lot‐Sizing Problems

“…This method is novel and can balance the approximated accuracy and computational times. This method can also be extended to other cases such as the lot-sizing problems with substitutions (see [18]) and safety stocks (see [29]). …”

A novel fuzzy stochastic multi-objective linear programming for multi-level capacitated lot-sizing problem: a real case study of a furniture company

“…[32] addressed stochastic lot-sizing problem with controllable processing times which can be beneficial to cope with demand uncertainty. [33] presented a non-linear mixed integer stochastic model for a single-level multi-product CLSP with random demand and dynamic safety stocks. To find efficient and stable schedules, the model is approximated by two linear models.…”

Stochastic lot sizing problem with controllable processing times

“…Tempelmeier [33] proposed a heuristic approach to solve the multi-item capacitated stochastic lot-sizing problem under fill rate constraint. Helber et al [10] consider the multi-item stochastic capacitated lot sizing problem under a new service level measure, called as δ-service-level. This service level reflects both the size of the backorders and waiting time of the customers and can be defined as the expected percentage of the maximum possible demand-weighted waiting time that a customer is protected against.…”

“…There are studies in the literature that consider the lot sizing problem with subcontracting (or outsourcing) [3,10,18] or capacity acquisition (or expansion) [1,17,22]. However, in all these studies costs of these options are assumed as linear or concave.…”