Sven Axsäter

Simple solution procedures for a class of two-echelon inventory problems

We consider an inventory system with one warehouse and N retailers. Lead times are constant and the retailers face independent Poisson demand. Replenishments are one-for-one. We provide simple recursive procedures for determining the holding and shortage costs of different control policies.

Exact and approximate evaluation of batch-ordering policies for two-level inventory systems

We consider a two-level inventory system with one warehouse and N identical retailers. Lead times (transportation times) are constant and the retailers face independent Poisson demand. In a previous paper, we derived a recursive procedure for determining the policy costs for an average item in case of one-for-one replenishment policies. In this paper, we show how these results can be used for the exact or approximate evaluation of more general policies where both the retailers and the warehouse order in batches. We compare our methods to the method recently suggested by A. Svoronos and P. Zipkin.

A New Decision Rule for Lateral Transshipments in Inventory Systems

This paper deals with a single-echelon inventory system consisting of a number of parallel local warehouses facing compound Poisson demand. There are standard holding and backorder costs as well as ordering costs at all warehouses. Normally, the warehouses replenish from an outside supplier. However, lateral transshipments between the warehouses are also possible. Such transshipments take no time but incur additional costs. When a demand occurs at a warehouse, the question is whether the whole demand or part of it should be covered by a lateral transshipment from another warehouse. Given a set of alternative decisions, our decision rule minimizes the expected costs under the assumption that no further transshipments will take place. This rule is then used repeatedly as a heuristic. A simulation study illustrates how the suggested technique performs under different conditions.

Exact Analysis of Continuous Review (R,Q) Policies in Two-Echelon Inventory Systems with Compound Poisson Demand

We consider a two-level inventory system with one central warehouse andN retailers. All installations apply different continuous review installation stock ( R,Q) policies. The retailers face independent compound Poisson demand processes. Transportation times are constant. We present a method for exact evaluation of control policies that provides the complete probability distributions of the retailer inventory levels.

Control Theory Concepts in Production and Inventory Control

The use of efficient production and inventory control systems is of great importance for industry. Therefore this area could be expected to provide many fruitful applications of control theory techniques. However, control theory has traditionally been aimed at applications in other fields, and results have only limited applicability in production and inventory control. This paper gives an overview of earlier research concerning control theory applications in production and inventory control. Areas given special emphasis are those in which control theory seems to have a stronger potential of practical application.

Supply Chain Operations: Serial and Distribution Inventory Systems

Publisher Summary This chapter reviews the models and techniques used for the analysis of serial and distribution inventory systems with stochastic demands. It discusses optimization of reorder points and compares different common ordering systems. The batch quantities are assumed to be known. They may, for example, be predetermined in a deterministic model. Results for single-echelon models indicate that this gives a very good approximation. The chapter compares and discusses different ordering policies that are common in connection with multi-echelon inventory control. The chapter presents the evaluation and optimization of serial inventory systems. Models for evaluation and optimization of order-up-to-S policies in distribution systems are treated. In addition, general batch-ordering policies in distribution systems are discussed. The chapter also discusses an infinite horizon version of the Clark–Scarf model, which is then generalized to batch-ordering policies.

Aggregation of Product Data for Hierarchical Production Planning

When applying an aggregate view to production planning, the production system is given a hierarchical structure. The problem description at the upper level which is less detailed concerns product groups and machine groups rather than individual products and machines. This means that product structures and capacity requirements also must be expressed in terms of product groups and machine groups. In this paper it is shown under what conditions a perfect aggregation of product data can be obtained. If a perfect aggregation is not possible, our problem is to find a good approximate solution. A mathematical formulation of this approximation problem and its general solution is also given.

Evaluation of unidirectional lateral transshipments and substitutions in inventory systems

One interpretation of the model considered in this paper is a single-echelon inventory system consisting of a number of local warehouses, which normally replenish from an outside supplier. In case of a stockout at a warehouse an emergency lateral transshipment from another warehouse may be possible. However, such transshipments are only allowed in one direction, i.e., the flow structure is unidirectional. Such policies can be of interest if the warehouses have very different shortage costs. Another interpretation is substitution in an inventory system. We then instead consider different items in a single warehouse. When a demand for a low quality item cannot be met directly, the item can be replaced by another high quality item. We provide a simple and efficient approximate technique for policy evaluation in such systems. The performance of this technique is evaluated in a simulation study. Although the errors are not always negligible, the suggested method gives a good picture of how the considered lateral transshipments or substitutions affect the inventory system.

Aggregation and Disaggregation in Hierarchical Production Planning

Abstract This paper reports on a simulation study of hierarchical planning procedures, which can support a material requirements planning system. Data for this study have been obtained from a Swedish manufacturing company. The three final products considered in the simulations represent a major part of this company. An aggregate plan in terms of product groups and machine groups is derived with the aid of an aggregate model. This plan is then disaggregated by changing order release times obtained from material requirements planning, and by distributing extra capacity among individual machines. The results indicate that our methods in general perform significantly better than a comparable reference case without the supporting hierarchical planning process. In our simulation experiments we evaluate different design features, like disaggregation procedures and methods for aggregating items and machines.

Multi-stage production planning and inventory control

Some Modelling Theoretic Remarks on Multi-Stage Production Planning.- Inventory - Production and Distribution Systems.- Two-Stage Production Planning in a Dynamic Environment.- Overview of a Stock Allocation Model for a Two-Echelon Push System Having Identical Units at the Lower Echelon.- System - Based Heuristics for Multi-Echelon Distribution Systems.- A Branch and Bound Algorithm for the Multi Item Single Level Capacitated Dynamic Lotsizing Problem.- Multi-Stage Lot-Sizing.- Aggregating Items in Multi-Level Lot Sizing.- Optimal Lot-Sizing for Dynamic Assembly Systems.- Planning Component Delivery Intervals in Constrained Assembly Systems.- Multi-Stage Lot-Sizing for General Production Systems.- Practical Applications and Hierarchical Integration Problems.- Practical Application of the Echelon Approach in a System with Divergent Product Structures.- Hierarchical Production Planning: Tuning Aggregate Planning with Sequencing and Scheduling.- The Design of an Hierarchical Model for Production Planning and Scheduling.- About Authors.