Lost-sales inventory theory : A review

Mixture inventory model involving variable lead time with a service level constraint

https://isiarticles.com/bundles/Article/pre/pdf/22640.pdf

An extended newsboy problem with shortage-level constraints

https://pure.tue.nl/ws/files/121040626/wp_336.pdf

Determination of safety stocks in a lost sales inventory system with periodic review, positive lead-time, lot-sizing and a target fill rate

In this paper, we present a systematic overview of possible relations between cost and service models for fairly general single- and multi-stage inventory systems. In particular, we relate various types of penalty costs in pure cost models to equivalent types of service measures in service models. We show how an optimal policy for a service model may be obtained from cost-optimal policies in a related pure cost model. Pure cost models have been studied extensively in the literature. By our results it seems possible to transform many of the known optimal solutions for pure cost models to service models, which are more appropriate from a practical point of view. A number of examples are discussed to show the generality and the possibly far reaching consequences of the results.

On the relation between cost and service models for general inventory systems

In a practical situation it is often difficult to determine the value of the shortage costs for use in in ventory-control systems. However, in cost-minimization problems including service-level constraints, shortage costs are implicitly prevailing. With the purpose of exploring these relations, a continuous review (Q, r) stock-control system is considered, where the order points and lot sizes are computed simultaneously. Instead of explicitly expressing the shortage cost in the objective function, it is taken into consideration through a service-level constraint. The shadow price of this constraint can in some sense be interpreted as the shortage cost corresponding to the requested service level. By changing the value of the service level, interesting relations between shortage costs and service levels can be viewed for different sets of other inventory parameters. In order to investigate the sensitivity for probabilistic variations in the input data, two different probability distributions are used to describe the lead-time demand.

Optimal Inventory Policies with Service-Level Constraints

An operational research project at the Oskarshamn plant of Saab Scania AB Truckdivision Sweden is reported. The decision problem concerns the product mix of sheet metal purchased. A mathematical model that approximates the real-world problem is derived, the solution of which includes a p-median problem. This optimization problem is solved using Lagrangean relaxation and a subgradient optimization procedure. Numerical results for problems of real-world size and structure are reported and indicate satisfactory efficiency.

Örjan Jonsson

Papers

Optimal Inventory Policies with Service-Level Constraints

A Heuristic for Purchasing of Sheet Metal Decisions Based on Mathematical Programming