Multi-echelon Inventory Systems Research Articles

Multi Objective Optimization Model for Collaborative Multi{Echelon Inventory Control in Supply Chain

The use of single objective model in which only the cost is considered in multi-echelon inventory systems does not suffice to raise the total performance of a supply chain. In this paper, we propose an optimization model in which the cost, elapsing time and the demand satisfaction rate are considered in a combined way. For the case where the capacity and supply are limited under the condition of multi classes, random demand and complex link relationships, a two-level solution algorithm is presented. This algorithm enables us to find out the optimal strategy of sites and at the same time deal with the logistic structure using a evolutionary multi objective optimization method and simulation approach. Numerical examples were designed to demonstrate the validity of the algorithm, and the results show that the multi objective optimization model can significantly improve the total performance of supply chains.

Simulation-based optimisation of multi-echelon inventory systems

Multi-location inventory models are one of the most widely investigated fields in mathematical inventory theory, but the analytically tractable models suffer from various restrictive assumptions. To overcome these restrictions simulation can be used. However, simulation is not an optimisation approach. Therefore, we propose the simulation optimisation approach where a simulator is combined with an appropriate optimisation tool.In the present paper, we show that simulation optimisation successfully can be applied to define optimal policies in very general multi-echelon inventory systems. A numerical example shows the usability of our approach.

Leveraging information in multi-echelon inventory systems

Decision-making in multi-echelon inventory systems is often facilitated by the availability of information. In this paper, we examine the effect of utilising demand information in a one-warehouse two-retailer system operating under periodic-review. A common and fixed replenishment interval is assumed for all stages. The lead times are deterministic, and are small compared to the replenishment interval. The warehouse does not maintain any cycle stock, i.e., as soon as replenishment arrives at the warehouse, retailers’ demands are fulfilled from the available stock. In the event of a shortage at the warehouse, two cases have been considered––emergency shipment and allocation. For both the cases, expected total cost (ETC) models have been developed, and it has been shown through numerical examples that the optimal ETC in the presence of demand information is always lower than that in the absence of demand information. It is also noted that the order-up-to level at the warehouse has to be dynamic to reap the benefits of availability of demand information.

Optimal Policies and Approximations for a Serial Multiechelon Inventory System with Time-Correlated Demand

Since Clark and Scarf's pioneering work, most advances in multiechelon inventory systems have been based on demand processes that are time independent. This paper revisits the serial multiechelon inventory system of Clark and Scarf and develops three key results. First, we provide a simple lower-bound approximation to the optimal echelon inventory levels and an upper bound to the total system cost for the basic model of Clark and Scarf. Second, we show that the structure of the optimal stocking policy of Clark and Scarf holds under time-correlated demand processes using a Martingale model of forecast evolution. Third, we extend the approximation to the time-correlated demand process and study, in particular for an autoregressive demand model, the impact of lead times and autocorrelation on the performance of the serial inventory system.

A robustness study of a multi-echelon inventory model via simulation

This paper examines the robustness of a standard model of multi-echelon inventory systems, specifically the models discussed in Axsäter (Oper. Res. 48(5) (2000) 686). A simulation model was developed to explore the model's ability to predict system performance for a two-echelon one-warehouse, multiple retailer system using ( R, Q) inventory policies under conditions that violate the model's fundamental modeling assumptions. In particular, the impact of non-stationary demand on this stationary demand inventory model was examined. The model performs well at the low demand and large retailer order batch size situations, but our testing of the model indicated that care must be taken when applying this model to situations that violate its fundamental assumption. These results should help practitioners to better understand the assumptions of these models and to determine when or when not to apply these models in practice.

Example of a mode of forming control decisions in multiechelon inventory systems of maintainable parts

This article considers one possible mode of forming control decisions in multiechelon inventory systems of maintainable parts. The suggested procedure consists of: determining the values of the characteristics of inventory system functioning, forming decision tables, forming a model of multiatribute decision making and ranking variants of repaired parts distribution. The control decision forming procedure is based on the modeling and simulation methods as well as on the shosen methods of multicriteria analysis, thus introducing science - based decision - making into the process of complex multiechelon inventory system control.

Stationary Policies in Multiechelon Inventory Systems with Deterministic Demand and Backlogging

A stationary policy conducts replenishment activities—the placement and fulfillment of orders—in a stationary fashion. That is, each facility receives a constant batch (facility specific) in equal time intervals (facility specific) under a stationary policy. Although the advantages of stationary policies are clear (i.e., smooth operations), they represent a restriction in policy selection. This paper investigates how costly this restriction can be. For two multiechelon systems (serial and distribution) with deterministic demand and backlogging, we show that stationary policies are 70%-effective. This bound is tight in the sense that an example exists where the bound is reached. On the other hand, the average effectiveness of stationary policies is very high. In a set of 1,000 randomly generated numerical examples, we observed that the average effectiveness was 99%, and the standard deviation was 1.5%. The numerical examples also suggest that the performance of stationary policies deteriorates in systems where the setup cost decreases dramatically from an upstream stage to a downstream stage. Finally, a key building block of the above results is the existing lower bounds on the average costs of all feasible policies in the above systems. We provide a simpler derivation of these bounds.

Modeling Stochastic Lead Times in Multi-Echelon Systems

In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling. In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not cross and (b) prespecified means and variances of all lead times in the multiechelon system are attained.

Optimizing discrete stochastic systems using simulated annealing and simulation

The objective of this paper is to present an integrated approach of two models: simulation and optimization. This approach is used to determine the design parameters of stochastically constrained systems where the measure of performance is available only via simulation. The optimization model is solved using simulated annealing (SA) for parameter selection followed by the use of Monte Carlo simulation to evaluate the measure of performance. Based on the expected simulation output, the parameter set is either accepted or rejected. A modified rejection/acceptance criterion is presented for the proposed SA algorithm taking into consideration the stochastic system constraints. Moreover, a control variate is employed as a variance reduction technique in order to obtain an efficient estimate of performance measure. The proposed approach is tested using three real cases of the multi-echelon repairable item inventory systems (MERIIS). The results show that the proposed method is efficient in determining an optimal choice of spares and repair channels in these systems.

On the (S – 1, S) Stock Model for Renewal Demand Processes:Poisson's poison

In the standard (S – 1, S) stock model, demand follows a Poisson process. It has appeared to many stock analysts that this model causes an abundance of stock in reality. In case demand is caused by failure or is derived from another process, demand typically doesnotfollow a Poisson process. In this paper, we discuss the (S – 1, S) stock model where demand follows a renewal process and the lead time is deterministic. Moreover, we will extend this to compound renewal demand and multi-echelon inventory systems. Our goal is to show the severe influence of taking the Poisson process for granted.

Stochastic considerations of Grubbström—Molinder model of MRP, input-output and multi-echelon inventory systems

In a recent paper (Grubbström and Molinder, 1994) Grubbström and Molinder studied theoretically the dynamic relationship between MRP, input-output analysis and multi-echelon inventory systems. In this paper we upgrade this approach including in the model the uncertainty of external demand and decision theory elements. In the model we suppose that we know only the upper and lower bounds of external demand rate and, because of lack of information, that the external demand is uniformly distributed. The complete decision model for our case is considered and the advantages of this approach are demonstrated.

Service level approximations for multiechelon inventory systems

This paper develops an approximate method for predicting the service levels of a one-warehouse/ N-identical retailer system operating under ( Q, r) replenishment policy. The interarrival times of customer orders are assumed to be independent, and identically Erlang distributed. The service level of the retailer is formulated based on the convex combination of two types of events, vis. the warehouse has stock when the retailer orders, and the warehouse is out of stock when the retailer orders. The latter event gives rise to additional delay time the retailer has to wait for replenishment. Probability approximations are used to derive the distribution of the delay time. The special case of exponential interarrival times is considered. The proposed model performs relatively better than other existing heuristics when the number of orders placed at the warehouse increases.

Evaluation of base-stock policies in multiechelon inventory systems with state-dependent demands. Part II: State-dependent depot policies

Evaluation of base-stock policies in multiechelon inventory systems with state-dependent demands. Part II: State-dependent depot policies

A Multiechelon Inventory Model with Fixed Replenishment Intervals

This paper develops a new model for studying multiechelon inventory systems with stochastic demand. For the model we assume that each site in the system orders at preset times according to an order-up-to policy, that delivery times are deterministic, and that the demand processes are stochastic with independent increments. We introduce a new scheme for allocating stock in short supply, which we call virtual allocation and which permits significant tractability. We exercise the model on a set of test problems for two-echelon systems to get insight into the structure of good policies. The primary findings are that both the central warehouse (upper echelon) and the retail sites (lower echelon) should hold safety stock, but that most of the safety stock should be at the retail sites. Consequently, the central warehouse will stock out with high probability. Furthermore, we show that the virtual allocation rule is near optimal for the set of test problems.

Further theoretical considerations on the relationship between MRP, input-output analysis and multi-echelon inventory systems

In recent papers relationships between input-output analysis and material requirements planning (MRP) have been studied. A generalized input-matrix has been designed to incorporate requirements as well as production lead times by means of z-transform methodology in a discrete time model. In this paper, previous findings are generalized in different directions. On the one hand, the theory is extended to continuous time using the Laplace transform, which enables it to incorporate the possibility of batch production at finite production rates. Also conditions for the detailed coordination problem are investigated in relation to the multi-echelon lot-sizing problem.

Approximating general multi-echelon inventory systems by Poisson models

We consider a continuous review two-level inventory system with a central warehouse and a number of retailers. The demand processes at the retailers are different compound Poisson processes. We present and evaluate an approximate optimization technique, where the real demand is replaced by “equivalent” Poisson demand such that the ratio between mean and standard deviation is the same as for the real distribution. The solution of the Poisson model is then scaled back to the original problem.

Multi-Echelon vs. Single-Echelon Inventory Control Policies for Low-Demand Items

Multi-echelon inventory systems are often controlled as a network of single-echelon inventory systems for simplicity of managerial authority, organizational control, and performance monitoring. This paper explores the amount of suboptimization in such a situation, using an actual demand data set provided by other researchers. We consider low-demand, high-cost items controlled on an (S − 1, S) basis, with all warehouse stockouts met on an emergency-ordering basis. We demonstrate that the suboptimality penalty for this data set is 3% to 5% when single-echelon systems are appropriately parameterized.

Evaluation of base-stock policies in multiechelon inventory systems with state-dependent demands part I: State-independent policies

We consider a two-echelon inventory system where the exogenous demands occur only at the retailer locations, and the demand rates are functions of an underlying continuous-time Markov chain. This underlying process may represent, for example, general economic conditions, the number of active users in the system, et cetera. Each retailer location follows a base-stock policy that is independent of the process. However, the warehouse (central depot) follows a state-dependent base-stock policy. We develop a procedure to compute the exact steady-state customer-delay distribution for both the warehouse and the retailer locations.

Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (si Si) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.

Multiechelon inventory systems with lateral supply

We develop approximations to estimate the expected backorders in a multiechelon system in which lateral supply actions between bases are allowed when a backorder occurs. These approximations are easy to compute, and the average absolute error over a wide range of parameter values is less than 4% when items are depot repairable, even when bases are dissimilar. With lateral supply, backorder reductions of 30-50% are not uncommon, and a 72% reduction was observed in two cases. Lateral supply becomes more important with low demand rates. A similar approach was unsuccessful for base-repairable items. However, lateral supply has a beneficial effect only when the lateral supply time is very short, 1/4 or less of the average base repair time. Even in such cases lateral supply is unlikely to be important in an actual application, because base management can expedite repair of critical items.