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

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

Transshipments in a divergent two-echelon network using the consistent appropiate share rationing policy

Consider a two-echelon inventory system consisting of a central depot (CD) and a number of retailers. Only the retailers face customer demand. The CD is allowed to hold stock. In all stockpoints, the echelon inventory position is periodically raised to certain order-up-to-Ievels. At the central depot, incoming stock is allocated by using the consistent appropriate share rationing (CAS) policy. When the orders arrive at the retailers, an instantaneous rebalancing of the total net stock of the retailers takes place, so as to maintain all end-stockpoint inventory at a balanced position. This rebalancing is realized by the transshipment of stock, assuming that the time to transship stock from one retailer to another is negligible compared to the lead time between CD and a retailer. The objective of this analysis is the determination of all the control parameters (integral order-up-to-Ievel, parameters of allocation policy at the CD and of the rebalancing policy at the retailer), so that the desired (different) service levels are achieved at the retailers at minimal expected total costs. Exact expressions are developed to determine these parameters. However, we will use some heuristics to actually compute these parameters, because of the intractability of the exact expressions. All analytical results are validated by Monte-Carlo simulation. The model developed will be compared with the same model without periodic, instantaneous rebalancing at the retailer. This yields insight into the conditions under which transshipment could be useful

Computational results for the control of a divergent N-echelon inventory system

Consider a divergent multi-echelon inventory system, e.g., a distribution system or a production system. At every facility in the system orders are placed (or production is initiated) periodically. The order arrives after a fixed lead time. At the end of each period linear costs are incurred at each facility for holding inventory. Also, linear penalty costs are incurred at the most downstream facilities for backorders. The objective is to minimize the expected holding and penalty costs per period. Within a class ofpractically useful policies the decomposition result is used to develop an algorithm which determines the control parameters of a near cost-optimal replenishment policy. A simulation study of a divergent 3-echelon system reveals that this algorithm performs well

Cost-effective control policies for multi-echelon distribution systems

In this paper we consider a divergent multi-echelon inventory system, e.g., a distribution system or a production system. At every stockpoint orders are placed periodically. The order arrives after a fixed lead time. At the end of each period linear costs may be incurred at each stockpoint for holding inventory. Also, linear penalty costs are incurred at the most downstream facilities for backorders. The objective is to minimise the expected holding and penalty costs per period. Diks & De Kok [1996a] developed a decomposition algorithm in order to determine the control parameters of a near cost-optimal replenishment policy. Since this algorithm cannot be applied on divergent multi-echelon systems in which at some stockpoints no value is added to the product (e.g. major parts of distribution systems), we developed an extension of the algorithm in order to deal with these systems as well. A simulation study of a divergent 3-echelon system reveals that this extended algorithm performs well. Keywords: Inventory, Allocation, Logistics

Optimal control of a divergent N-echelon inventory system

Consider a divergent multi-echelon inventory system, e.g. a distribution system or a production system. At every facility in the system orders are placed (or production is initiated) periodically. The order arrives after a fixed lead time. At the end of each period linear costs are incurred at each facility for holding inventory. Also, linear penalty costs are incurred at the most downstream facilities for backorders. The objective is to minimize the expected holding and penalty costs per period. We prove that under the balance assumption it is cost-optimal to control every facility by an order-up-to-policy. The optimal replenishment policy, i.e., the order-up-to-level and the rationing functions at each facility, can be determined by decomposition of the system. This decomposition result reduces complex multi-dimensional control problems to 'simple' one-dimensional problems, which closely resemble the classical newsboy problem achieving a proper trade-off between the consequences of too much stock and too little inventory. Keywords: multi-echelon, optimal control, inventory, allocation, rationing, divergent

Allocation policies 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, Lagodimos & Seidel, 1994; Verrijdt & De Kok, 1996]) performs good as well. Keywords: Multi-echelon, inventory, allocation, rationing, divergent