Approximate evaluation of multi-location inventory models with lateral transshipments and hold back levels (original) (raw)
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A multi-location continuous review (Q, R) inventory model with emergency transhipments
Previous studies on multi-location inventory systems with transshipments have focused mainly on periodic review systems with no fixed ordering cost. Since continuous review systems are also frequently used in practice, this research develops a multi-location inventory transshipment model that combines the popular order-quantity, reorder-point (Q,R) system with a third parameter, the hold-back amount, which limits the degree of sharing. The degree to which transshipments improve both Type I (no-stockout probability) and Type II (fill-rate) customer service levels can be calculated using the model. Simulation studies conducted to test the validity of the approximate analytical model indicate that it performs very well over a wide range of inputs. From a managerial viewpoint, the model indicates that as the number of transshipping locations increases, partial pooling provides almost the same benefits as complete pooling. transshipment decisions are made before the realization of demand. Das (1975) extends Gross (1963) by allowing transshipments in the middle of each period. Krishnan and Rao (1965) develop a two-location newsboy (i.e., order-up-to) model which forms the basis of many later studies. Notably, Tagaras (1989) explicitly generalizes the model of Krishnan and Rao (1965) by allowing different unit ordering, holding, penalty, and transshipment costs across locations, in a two-location setting. Tagaras and Cohen (1992) further extend this to the case of non-zero deterministic replenishment lead time by examining, along with complete pooling, a specific partial pooling policy in which one location maintains a certain inventory level (or inventory position) after transshipping to the other location. Kochel (1990) formulates a model similar to Tagaras (1989) in a multi-location framework, though he considers a net profit objective function and (stock) selling decision at the beginning of a period. Using a model similar to those of Krishnan and Rao (1965) and Tagaras (1989), Chang and Lin (1991) examine the cost function conditions that make the case with transshipments among locations more desirable than the case without them. Other authors have extended multi-location inventory models with transshipments to incorporate multi-echelon, or multi-period, aspects. However, most of their extensions were made possible by making further assumptions beyond the single-echelon, singleperiod case, especially regarding the unit cost of an activity across locations. Hoadley and Heyman (1977) consider a general case of two-echelon, multi-location model with a oneperiod order-up-to replenishment policy. Their model allows for balancing acts (purchases, dispositions, returns, normal shipments, and transshipments) at the beginning of a period and emergency acts (expedited shipments from an upper echelon and emergency transshipments from the same echelon) in the case of a stockout. Cohen, Kleindorfer, and Lee (1986) extend the approach of Hoadley and Heyman (1977) even further to the multiechelon case, with particular emphasis on low demand, high cost, high service spare parts inventory. Their model differs from most studies in that transshipments are not restricted only to the lowest echelon. Jonsson and Silver (1987) examine a two-echelon distribution system consisting of a cross-docking central warehouse supplying several branch warehouses and investigate the desirability of complete redistribution of all branch
A Multi-Location Continuous Review (Q,R) Inventory Model with Emergency Transshipments
1997
Previous studies on multi-location inventory systems with transshipments have focused mainly on periodic review systems with no fixed ordering cost. Since continuous review systems are also frequently used in practice, this research develops a multi-location inventory transshipment model that combines the popular order-quantity, reorder-point (Q,R) system with a third parameter, the hold-back amount, which limits the degree of sharing. The degree to which transshipments improve both Type I (no-stockout probability) and Type II (fill-rate) customer service levels can be calculated using the model. Simulation studies conducted to test the validity of the approximate analytical model indicate that it performs very well over a wide range of inputs. From a managerial viewpoint, the model indicates that as the number of transshipping locations increases, partial pooling provides almost the same benefits as complete pooling. 2 1. INTRODUCTION Found in both military and commercial settings...
Evaluation of a multi-item inventory system with coupled arrivals and returns
Cirp Annals-manufacturing Technology - CIRP ANN-MANUF TECHNOL, 2006
This paper deals with the analysis of a single-location, multi-item inventory model for service tools, in which coupled arrivals and coupled returns occur. We distinguish multiple Poisson demand streams. Per stream there is a given set of tools that is requested per demand. We are interested in the order fill rates, i.e., the percentage of demands for which all requested tools are delivered from stock. Requested tools that are not on stock, are delivered via an emergency channel. For the warehouse under consideration, they may be considered as lost sales. Deliv- ered tools are returned to the warehouse after a deterministic return time, that is equal for all tools. We develop two approximations for the order fill rates, which are both based on Marko- vian models. One approximation has appeared to give an underestimation in all computational tests, while the other approximation had led to an overestimation in all instances tested. Fur- thermore, the approximations are reasonably accu...
A Stochastic Inventory Policy with Limited Transportation Capacity
In this paper we consider a stochastic single-item inventory problem. A retailer keeps a single product on stock to satisfy customers stochastic demand. The retailer is replenished periodically from a supplier with ample stock. For the delivery of the product, trucks with finite capacity are available and a fixed shipping cost is charged whenever a truck is dispatched regardless of its load. Furthermore, linear holding and backorder costs are considered at the end of a review period. A replenishment policy is proposed to determine order quantities taking into account transportation capacity and aiming at minimizing total average cost. Every period an order quantity is determined based on an order-up-to logic. If the order quantity is smaller than a given threshold then the shipment is delayed. On the other hand, if the order quantity is larger than a second threshold then the initial order size is enlarged and a full truckload is shipped. An order size between these two thresholds results in no adaption of the order quantity and the order is shipped as it is. We illustrate that this proposed policy is close to the optimal policy and much better than an order-up-to policy without adaptations. Moreover, we show how to compute the cost optimal policy parameters exactly and how to compute them by relying on approximations. In a detailed numerical study, we compare the results obtained by the heuristics with those given by the exact analysis. A very good cost performance of the proposed heuristics can be observed.
Optimal Policy for a Multi-location Inventory System with a Quick Response Warehouse
2013
We study a multi-location inventory problem with a so-called quick response warehouse. In case of a stock-out at a local warehouse, the demand might be satis ed by a stock transfer from the quick response warehouse. We derive the optimal policy for when to accept and when to reject such a demand at the quick response warehouse. We also derive conditions under which it is always optimal to accept these demands. Furthermore, we conduct a numerical study and consider model variations. Published in: Operations Research Letters, Volume 41, Issue 3, May 2013, Pages 305–310, see doi:10.1016/j.orl.2013.03.002
A new approximate evaluation method for two-echelon inventory systems with emergency shipments
Annals of Operations Research, 2013
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Annals of Operations Research, 2015
Supply contracts are designed to minimize inventory costs or to hedge against undesirable events (e.g., shortages) in the face of demand or supply uncertainty. In particular, replenishment terms stipulated by supply contracts need to be optimized with respect to overall costs, profits, service levels, etc. In this paper, we shall be primarily interested in minimizing an inventory cost function with respect to a constant replenishment rate. Consider a single-product inventory system under continuous review with constant replenishment and compound Poisson demands subject to lost-sales. The system incurs inventory carrying costs and lost-sales penalties, where the carrying cost is a linear function of on-hand inventory and a lost-sales penalty is incurred per lost sale occurrence as a function of lost-sale size. We first derive an integro-differential equation for the expected cumulative cost until and including the first lost-sale occurrence. From this equation, we obtain a closed form expression for the time-average inventory cost, and provide an algorithm for a numerical computation of the optimal replenishment rate that minimizes the aforementioned time-average cost function. In particular, we consider two special cases of lost-sales penalty functions: constant penalty and loss-proportional penalty. We further consider special demand size distributions, such as constant, uniform and Gamma, and take advantage of their functional form to further simplify the optimization algorithm. In particular, for the special case of exponential demand sizes,
In this paper we extend earlier work that analyzes a single echelon single item base-stock inventory system where Demand is modeled as a compound Poisson process and the lead-time is stochastic. The extension consists in considering a cost oriented system where unfilled demands are lost. The case of partial lost sales is assumed. We first model the inventory system as a Makovian M/G/∞ queue then we propose a method to calculate numerically the optimal base-stock level. A preliminary numerical investigation is also conducted to show the performance of our solution.
Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies
We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to Poisson process and upon arrival of a catastrophe all inventory in the system is instantly destroyed. But consumer customers in the system (in the server or in the buffer) continue still waiting for the replenishment of the stock. The arrivals of the consumer customers follow a Markovian Arrival Process (MAP) and they can be queued in an infinite buffer. Service time of a consumer customer follows a phase-type distribution. The system receives negative customers whose have Poisson flows to service facility and upon arrival of a negative customer one consumer customer is pushed out from the system, if any. One of two replenishment policies can be used in the system: either (s,S) or (s,Q). If upon arrival of the consumer customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or join the queue (backorder sa...
Centralized inventory control in a two-level distribution system with Poisson demand
Naval Research Logistics, 2002
This paper introduces a new replenishment policy for inventory control in a two-level distribution system consisting of one central warehouse and an arbitrary number of nonidentical retailers. The new policy is designed to control the replenishment process at the central warehouse, using centralized information regarding the inventory positions and demand processes of all installations in the system. The retailers on the other hand are assumed to use continuous review (R, Q) policies. A technique for exact evaluation of the expected inventory holding and backorder costs for the system is presented. Numerical results indicate that there are cases when considerable savings can be made by using the new (␣ 0 , Q 0) policy instead of a traditional echelon-or installation-stock (R, Q) policy.