Multi-stage Inventory Systems Research Articles

Robust optimization of uncertain multistage inventory systems with inexact data in decision rules

In production-inventory problems customer demand is often subject to uncertainty. Therefore, it is challenging to design production plans that satisfy both demand and a set of constraints on e.g. production capacity and required inventory levels. Adjustable robust optimization (ARO) is a technique to solve these dynamic (multistage) production-inventory problems. In ARO, the decision in each stage is a function of the data on the realizations of the uncertain demand gathered from the previous periods. These data, however, are often inaccurate; there is much evidence in the information management literature that data quality in inventory systems is often poor. Reliance on data “as is” may then lead to poor performance of “data-driven” methods such as ARO. In this paper, we remedy this weakness of ARO by introducing a model that treats past data itself as an uncertain model parameter. We show that computational tractability of the robust counterparts associated with this extension of ARO is still maintained. The benefits of the new model are demonstrated by a numerical test case of a well-studied production-inventory problem. Our approach is also applicable to other ARO models outside the realm of production-inventory planning.

The value of real time yield information in multi-stage inventory systems – Exact and heuristic approaches

We consider a random yield inventory system, where a company has access to real time information about the actual yield realizations. To contribute to a better understanding of the value of this information, we develop a mathematical model of the inventory system and derive structural properties. We build on these properties to develop an optimal solution approach that can be used to solve small to medium sized problems. To solve large problems, we develop two heuristics. We conduct numerical experiments to test the performances of our approaches and to identify conditions under which real time yield information is particularly beneficial. Our research provides the approaches that are necessary to implement inventory control policies that utilize real time yield information. The results can also be used to estimate the cost savings that can be achieved by using real time yield information. The cost savings can then be compared against the required investments to decide if such an investment is profitable.

Approximate queueing models for capacitated multi-stage inventory systems under base-stock control

A queueing analysis is presented for base-stock controlled multi-stage production-inventory systems with capacity constraints. The exact queueing model is approximated by replacing some state-dependent conditional probabilities (that are used to express the transition rates) by constants. Two recursive algorithms (each with several variants) are developed for analysis of the steady-state performance. It is analytically shown that one of these algorithms is equivalent to the existing approximations given in the literature. The system studied here is more general than the systems studied in the literature. The numerical investigation for three-stage systems shows that the proposed approximations work well to estimate the relevant performance measures.

The lot sizing problem: A tertiary study

This paper provides a survey of literature reviews in the area of lot sizing. Its intention is to show which streams of research emerged from Harris' seminal lot size model, and which major achievements have been accomplished in the respective areas. We first develop the methodology of this review and then descriptively analyze the sample. Subsequently, a content-related classification scheme for lot sizing models is developed, and the reviews contained in our sample are discussed in light of this classification scheme. Our analysis shows that various extensions of Harris' lot size model were developed over the years, such as lot sizing models that include multi-stage inventory systems, incentives, or productivity issues. The aims of our tertiary study are the following: firstly, it helps primary researchers to position their own work in the literature, to reproduce the development of different types of lot sizing problems, and to find starting points if they intend to work in a new research direction. Secondly, the study identifies several topics that offer opportunities for future secondary research.

Technical Note—A Note on the Structure of Joint Inventory-Pricing Control with Leadtimes

We consider a joint inventory-pricing control problem for a periodic-review, single-stage inventory system with a positive order leadtime and a linear order cost. Demands in consecutive periods are independent, but their distributions depend on the price in accordance with a stochastic demand function of additive form. Pricing and ordering decisions are made simultaneously at the beginning of each period. The objective is to maximize the total expected discounted profit over a finite horizon. We partially characterize the structure of the optimal joint ordering and pricing policies. We also show that our structural analysis can be extended to a multistage (or serial) inventory system with constant or stochastic leadtimes and an assemble-to-order system with price-sensitive demand.

Research on Multi-Stage Inventory Model by Markov Decision Process

Abstract This paper researched multi-stage inventory system and established limited inventory Markov model, on the other hand it induced DP algorithm of limited inventory Markov model. The results proved that the reorder point of multi-stage inventory system can guarantee demand, and also allows the storage costs to a minimum level in accordance with the above model.

Contributors

Contributors

Inventory Management with an Exogenous Supply Process

We study single and multistage inventory systems with stochastic lead times. We study a class of stochastic lead time processes, which we refer to as exogenous lead times. This class of lead time processes includes as special cases all lead time models from existing literature (such as Kaplan's lead times with no order crossing or independent and identically distributed lead times with order crossing, among others) but is a substantially broader class. For a system with an exogenous lead time process, we provide a method to determine base-stock levels and to compute the cost of a given base-stock policy. The method relies on relating the cost of a base-stock policy to the cost of a threshold policy in a related single-unit, single-customer problem. This single-unit method is exact for single-stage systems and for multistage systems under certain conditions. If the conditions are not satisfied, the method obtains near-optimal base-stock levels and accurate approximations of cost for multistage systems.

AN ANALYTIC FRAMEWORK FOR GENERIC INVENTORY QUEUEING SYSTEMS

ABSTRACT In this study, we propose an analytic framework for evaluating capacitated, unreliable multi-echelon, multi-stage inventory queueing systems. There are two main characteristics in our analysis. First, we consider a complex material flow structure with multiple suppliers and multiple retailers. Second, we use general distributions in the servicing processes. Based on convolution and matrix analytic approaches, we develop respective approximation models, which are applicable for either a single-product or a multi-product setting. With simulated results the two solution methods are compared in terms of computation efficiency and accuracy and managerial implications are provided. Finally, we use our model on numerical analysis of supplier selection problems. Our findings consist with the literature on the benefit of ordering at multiple suppliers to reduce waiting time. Under different parameter settings our model provides the scale of the benefit and the optimal setting of the number of suppliers.

Setting safety stocks in multi-stage inventory systems under rolling horizon mathematical programming models

This paper considers the problem of determining safety stocks in multi-item multi-stage inventory systems that face demand uncertainties. Safety stocks are necessary to make the supply chain, which is driven by forecasts of customer orders, responsive to (demand) uncertainties and to achieve predefined target service levels. Although there exists a large body of literature on determining safety stock levels, this literature does not provide an effective methodology that can address complex multi-constrained supply chains. In this paper, the problem of determining safety stocks is addressed by a simulation based approach, where the simulation studies are based on solving the supply chain planning problem (formulated as a mathematical programming model) in a rolling horizon setting. To demonstrate the utility of the proposed approach, an application of the approach at Organon, a worldwide operating biopharmaceutical company, will be discussed.

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

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.

Reactive logistics in a JIT environment

In order to realize reactive logistics in a JIT (just-in-time) environment, this paper proposes a reactive logistics system for multi-stage production, inventory and transportation systems with unstable changes in product demand. The lot size and transportation time are considered as the parameters of the transportation process. A mathematical model of the ordering system for production and transportation processes is developed, and the relationship among the lot size, transportation time, buffer size and performance measures of the system is analysed under stable changes in product demand. Based on the relationship, a reactive controller of buffer is proposed and incorporated into the ordering system. The performance of the proposed system is investigated using simulation experiments, and the results show the effectiveness of the proposed system.

Safety stocks in multi-stage inventory systems under different service measures

In this paper, we treat the problem of determining safety stocks in multi-stage inventory systems with normally distributed demands. The system follows a periodic review base-stock control policy. Assuming that every stockpoint satisfies a service level constraint and that no internal delays occur, we formulate the optimization problem for a general inventory system and derive properties of the optimal policy, which depend on the structure of the multi-stage system and the service measure used. Considering stockout occurrence related service levels, we find that the safety stock coverage times can only obtain values resulting from the extreme points of the solution set. Service levels representing size and duration of stockouts need less protection and are connected with problem reduction properties. The analysis of the reduced problems leads to similar extreme point properties as for stockout occurrence related service.

Corrected Diffusion Approximations for a Multistage Production-Inventory System

We analyze a multistage inventory system with limited production capacity facing stochastic demands. Each node follows a periodic-review base-stock policy for echelon inventory: in each period, each node attempts to produce enough material to restore cumulative down-stream inventory to a fixed target level. We develop approximations to the key measures of interest (average inventories, average backorders, and service levels) by simultaneously letting the mean demand approach the system's bottleneck capacity and letting the base-stock level for finished goods increase without bound. Using a method of Siegmund, we thus obtain diffusion limits with higher-order correction terms. A numerical example suggests that the correction terms can substantially improve the accuracy of the approximations.

A modeling approach to a JIT-based ordering system

In this paper, we consider a multi-stage multi-product production, inventory and transpor-tation system and develop a mathematical model for a pull type ordering system based on the concept of a Just-In-Time (JIT) production system. Our model considers a manufacturing system in which the setup action is improved and can deal with the number of setups required. We also propose two approximate solution procedures to rapidly obtain a suboptimal solution of the formulated integer programming problem using a mathematical programming modeling language. The approximate procedures are realized utilizing post-optimal analysis which can be performed by the modeling language. Finally, we show a numerical example of the model applied to an actual manufacturing system of an automo-bile parts manufacturer in order to verify the effectiveness of the approximate procedures and to clarify the applicability of our modeling approach.

On multi-stage production/inventory systems under stochastic demand

This paper was presented at the 1992 Conference of the International Society of Inventory Research in Budapest, as a tribute to professor Andrew C. Clark for his inspiring work on multi-echelon inventory models both in theory and practice. It reviews and extends the work of the authors on periodic review serial and convergent multi-echelon systems under stochastic stationary demand. In particular, we highlight the structure of echelon cost functions which play a central role in the derivation of the decomposition results and the optimality of base stock policies. The resulting optimal base stock policy is then compared with an MRP system in terms of cost effectiveness, given a predefined target customer service level. Another extension concerns an at first glance rather different problem; it is shown that the problem of setting safety leadtimes in a multi-stage production-to-order system with stochastic lead times leads to similar decomposition structures as those derived for multi-stage inventory systems. Finally, a discussion on possible extensions to capacitated models, models with uncertainty in both demand and production lead time as well as models with an aborescent structure concludes the paper.

Safety stock optimization in multi-stage inventory systems

Determining appropriate safety stocks in stochastic multi-state production/distribution systems is a very difficult task. Approaches for optimal determination of safety stocks regarding cost objectives and service level restrictions which are suitable for practical applications can only be found for a very limited class of multi-stage inventory problems like problems of strictly serial structure or special two-stage production/distribution systems.In this paper a procedure for determining the optimal size and distribution of safety stocks in a general serial or divergent production/distribution process ruled by a base-stock control policy is presented. This approach especially allows for taking into account the impact of end-item demand correlation on distribution and size of safety stocks by using risk-pooling effects in divergent systems.A powerful dynamic programming algorithm for solving the safety stock optimization problem is developed, and impacts of problem parameter variations on the optimal solution are discussed.

KBLS: A prototype knowledge-based system for the selection of lot-sizing models

Research in experimental simulation of multi-stage inventory systems shows that a poor choice of lot-sizing heuristics has a significant degree of cost penalty and schedule instability. A realistic approach to a multi-stage system is to choose a suitable technique for a certain special circumstance rather than trying for a single best heuristic covering all cases. To avoid serious cost penalties and high schedule instability caused by inferior techniques, knowledge-based system technology could help practitioners to make a sensible choice of heuristics. In this paper, we develop a prototype knowledge-based system whose aim is to provide an acceptable lot-size schedule in a limited time which would hopefully lead to a good master production schedule.

Feedback method of production ordering system in multi-stage production and inventory systems

Abstract This paper deals with the problem of developing a production ordering system which maintains high reliability and productivity of multi-stage production and inventory systems with capacity-constraint and machine breakdown. In this paper, two ‘push type’ production ordering systems (Matsuura and Soshiroda 1981) are proposed according to information feedback methods. The influence of forecasting error, the difference between forecasted demands, down-time, and the backlog caused by the restriction of production capacity, upon the production and inventory levels is analysed by each production ordering system. The results indicate that, in designing an effective production ordering system, a feedback method must be chosen according to the conditions of the average loading ratio, the down-time, and the autocorrelation coefficient of demand.

Multistage integrated-production inventory systems with service time

In this paper an attempt has been made to develop a model for a multilevel integrated production-inventory system, where service times are available at each of the stock points. An ‘ order upto ’ policy is adopted, so that the replenishment order quantity at the beginning of any period is adjusted by the total ‘ inventory discrepancy ’. The total cost of the system consists of inventory carrying costs at the various stock points, and the cost of failure to meet the demands experienced at the end-item stock points. The service time for satisfying the demands for the end product shall be assumed to be exogenously determined. The service times made available at the various intermediate level stock points, including the stock point of raw materials, shall be endogenous variables. The outputs of the model would be to determine whether it is economical to maintain a particular stock point, the economical quantities of stocks to be maintained at permanent stock points, the reliability of the system, and the most...