Multi-echelon Distribution Systems Research Articles

Controlling general multi-echelon distribution supply chains with improved reorder decision policy utilizing real-time shared stock information

The objective of this paper is to introduce an improved reorder decision policy for controlling general multiechelon distribution systems utilizing shared stock information. Since traditional reorder policies sometimes show poor performances when applied to distribution systems, the order risk policy, which utilizes shared stock information more accurately, was developed for the two-echelon distribution system in the previous research. In this paper, the order risk policy is extended to general multi-echelon systems. Since the calculation of the exact order risk for general multi-echelon systems is complex, a practical approximation method is developed. Through computational experiments, the superior performance of the order risk policy, compared to the existing reorder policies, is shown and the value of shared stock information varying with the characteristics of the supply chain is analyzed.

Strategic design of distribution systems with economies of scale in transportation

We formulate and analyze a strategic design model for multi-product multi-echelon distribution systems where there are significant economies of scale in the transportation movements. The key design decisions considered are: the number and locations of distribution centers (DC's) in the system, the number and locations of consolidation centers (CC's), the inventory levels of the various products to be held at the distribution centers, and the routing of shipments (through a consolidation center or direct) between plants and distribution centers. A heuristic solution method is developed that can efficiently find near-optimal solutions. The quality of solutions to a series of test problems is evaluated---by comparison to exact solutions created by enumeration in small tests, and by comparison to lower bounds developed for larger test problems. In the problems for which exact solutions are available, the heuristic solution is within 1% of optimal. The computational procedure appears to hold substantial promise for effective solution of large distribution system design problems.

Profit models and optimisation for a multi-item-multi-echelon distribution system

A multiechelon Distribution System (DS) with multiple products is researched in this paper, where multiple manufacturers (M), one Regional Distribution Centre (RDC) (D) and multiple retailers (R) are involved facing normal distribution demand at the market. Firstly, the expected profit models are deduced for each member in this DS. Secondly, manufacturers and RDC's joint optimisation models (M-D models) and RDC and retailers' joint optimisation models (D-R models) are developed and solved to obtain the optimal Order-Up-to Levels (OULs) for different products at different stages in the DS under the constraints of 'weighted' service levels. Finally, two calculation examples are given to illustrate the solving process of OULs for the models.

Unternehmensübergreifende Optimierung der Bestellpolitik — das JELS-Modell mit einem Intermediär

In modern concepts of physical distribution the joint optimization of logistics processes among the various channel elements very often is emphasized. The focus in this area of management science, dealing with the optimization on inventory management, is on the comparison of independent optimization strategies with those of joint economic-lot-sizing. Many of these approaches are characterized by the fact that they aim at distribution systems, where buyers are served by manufacturers directly. In real life situations however, different forms of multi-echelon distribution systems are typical.

Optimal and Near-Optimal Decisions for Procurement and Allocation of a Critical Resource with a Stochastic Consumption Rate

Management of critical resources having uncertain consumption rates is perhaps the most common challenge encountered by businesses in discharging their numerous functions, e.g., inventory distribution, marketing, finance, production, personnel, etc. It involves making two key decisions optimally: (1) How much of each critical resource must be procured (replenishment quantity decision), and, having procured, (2) How much of each resource should be allocated among the competing entities (allocation decision). The finance/inventory literature thus far has addressed the allocation decision in an optimal fashion using certain ranking algorithms. However, the optimal replenishment decisions have not yet been addressed optimally except under a restrictive assumption called the allocation assumption. Using the illustration of a periodic-review, stochastic-demand, fixed-route, centralized, multi-echelon distribution system in this paper, we propose a non-ranking allocation policy that is faster than those existing in the literature and also develop an optimal replenishment algorithm that is independent of the allocation assumption. Furthermore, we allow our distribution system a greater flexibility than that allowed in the literature thus far--we explicitly permit fixed delivery routes, arbitrary demand distribution parameters, non-identical delivery leadtimes simultaneously with a positive order leadtime. The major empirical contribution of this work is to demonstrate, through an extensive simulation study, that computationally efficient heuristic, called the hybrid heuristic, performs close to optimal, even for the systems with high demand uncertainty. Intriguingly, the bottom line finding of our computational experiments is that while the probability of violation of the allocation assumption itself is very sensitive to the system demand uncertainty, it is relatively insensitive to the expected system inventory costs in the vicinity of the optimal region. We also develop hand- computable theoretical lower and upper bounds on system replenishment quantity and expected system cost per period that require a single Normal distribution table look-up.

The effect of [formula omitted] ordering policy on the supply chain

In many supply chains, the variability of orders may considerably increase relative to the variability of the buyers' demand. This variability increase is largely an effect of the ordering policy. This phenomenon, which has become known as the bullwhip effect, makes supply chain planning difficult. We consider the following three basic elements of a supply chain: the purchase orders of the individual retailers, the aggregate orders of the retailers, and the supplier's ordering/production policy. A complex multi-echelon distribution system can also be analyzed by combining these elements. We investigate how the (s, S) policy parameters, the demand parameters, and the cost coefficients influence the variability of the orders by using approximations to the exact quantitative models. The accuracy of the approximations is acceptable in most cases of practical importance. We show how demand correlation can decrease the variability of aggregate orders, and how autocorrelation in buyer's orders can smooth the supplier's ordering policy. However, these variability reductions are usually not considerable. Small frequent orders can reduce the effect of high variability and the resulting uncertainty.

Probabilistic Analyses and Algorithms for Three-Level Distribution Systems

We consider the problem of integrating inventory control and vehicle routing into a cost-effective strategy for a distribution system consisting of a single outside vendor, a fixed number of warehouses and many geographically dispersed retailers. Each retailer faces a constant, retailer specific, demand rate and inventory holding cost is charged at the retailers and the warehouses. We show that, in an effective strategy which minimizes the asymptotic long run average cost, each warehouse receives fully loaded trucks from the vendor but never holds inventory. That is, each warehouse serves only as a coordinator of the frequency, time and sizes of deliveries to the retailers. This insight is used to construct an inventory control policy and vehicle routing strategy for multi-echelon distribution systems. Computational results are also reported.

Efficient inventory management in multi-echelon distribution systems

In this paper, an improved DRP method to schedule multi-echelon distribution network is proposed such that order-quantities and order points are dynamically obtained to meet the demand in just in time concept and minimize the out-of-stock probability. The order scheduling method reflects the dynamic characteristics of inventory level changes in the regional distribution centers and the central distribution center. The experiment has been done with various demand distributions, forecast error distributions and lead times. The proposed method was compared with the traditional DRP-based scheduling methods which use different lot-sizing and order point decision techniques. From the result, it is found that the proposed heuristic method yields preferable lot-sizing schedules.

Supply rationing in multi-echelon divergent systems

In this paper we determine a simple inventory control rule for multi-echelon distribution systems under periodic review without lot sizing. The primary focus is the two-echelon model with a stockless central depot, but several extensions (>2 echelons, central stock allowed) are discussed as well. The, control rule consists of two parameter sets: a set of rationing fractions at the central depot with the purpose to minimize inventory imbalance, and a set of order-up-to levels for the local stockpoints with the purpose to achieve a target service level (fill rate) per local stockpoint. The problem to calculate these control parameters is solved by decomposition in two subproblems. First the rationing fractions are determined such that the (approximate) expected system imbalance is minimized. Next the order-up-to levels are calculated such that the target fill rates are achieved. Numerical results show that this control rule, called Balanced Stock (BS) rationing, is accurate and more robust than the Consistent Appropriate Share (CAS) rationing polocy.

Stock allocation in general multi-echelon distribution systems with ( R, S) order-up-to-policies

In this paper we analyze stock allocation policies in general N-echelon distribution systems, where it is allowed to hold stock at all levels in the network. The goal is to achieve differentiated target customer service levels (fill rates). Various allocation rules and accompanying numerical methods that have already been developed for smaller networks are extended and compared in an extensive numerical experiment. We conclude that the extension of Balanced Stock rationing (see Van der Heijden (1996)) is the most accurate method, in particular in cases of relatively high imbalance. If the imbalance is not too high, the extension of Consistent Appropriate Share rationing (see De Kok et al., 1994; Verrijdt and De Kok, 1996) performs good as well.

Dynamic Lot Sizing for Multi-Echelon Distribution Systems with Purchasing and Transportation Price Discounts

We consider the problem of determining optimal purchasing and shipping quantities over a finite planning horizon for arborescent, multi-echelon physical distribution systems with deterministic, time-varying demands. We assume that the inventory holding cost at a given warehouse of the distribution network is a linear function of the inventory level, and that the total procurement cost (i.e., ordering, plus purchasing, plus transportation and reception costs) is a general piecewise-linear function of the quantities shipped to and from the warehouse. We formulate a mixed integer linear programming model of the problem and develop a Lagrangian relaxation-based procedure to solve it. We show computational results for problems with 12 periods, up to 15 warehouses, and 3 transportation price ranges.

Price discounting in multi-echelon distribution systems

Designing distribution systems requires two essential decisions, one strategic (i.e., the number of levels between the producer and the customer) and the other tactical (i.e., channel management policies such as trade discounts). While the modeling literature focuses on one or the other, evidence from the field indicates that the two decisions are in fact interactive. In this paper we focus on the tactical issue of price rebates, but we frame the problem in the overall context of the firm's distribution structure. We offer a theoretical analysis of a two-stage distribution system and construct an O(n log n) to optimize the producer's profit function. We then discuss in detail one potential application for the model in solving gray market conflicts.

An Analysis of Inventory Planning System Effectiveness in a Multiechelon Distribution System.

This paper presents the results of a simulation model comparing the Pull approach with Distribution Requirements Planning in a multiechelon distribution system. The regional distribution centers experienced stochastic demand and replenishment leadtimes. Factors included manufacturing capacity, lotsize magnitude, and safety stock allocation policy. Inventory investment and customer service were measured.

The use of expert systems in the design of multi-echelon production distribution systems

Strategic decision making within multi-echelon production distribution systems is a difficult task due to the complex chain structures and inherent operating uncertainties of such systems. Hence there is a need for the application of expert systems methodology in this field.

Capacitated heuristic program for multiactivity, multi-facility system designs

Abstract Multi-activity, multi-facility design systems occur in a wide variety of industrial and service applications: e.g.: regional health care centers with configurations of activities at each center, and multi-echelon inventory distribution systems. The problem in designing such systems is to determine from a candidate set of possible locations what facility locations should be opened and what types of activities should be carried out at each of the open facilities. This article presents an efficient heuristic procedure for such a problem. The heuristic procedure described can be used to solve both the uncapacitated and the capacitated problems where capacity is expressed in terms of the number of activities which can be supported by the facilities. Extensive computational experience with the heuristic is presented. The performance of the heuristic is compared against optimal solutions and the results look very encouraging.