Two-echelon spare parts inventory system subject to a service constraint

In this paper, we consider a spare parts inventory problem faced by a manufacturer of electronic machines with expensive parts that are located at various customer locations. The parts fail infrequently according to a Poisson process. To serve customers when a failure occurs, the manufacturer operates a central warehouse and many field depots that stock spare parts. The central warehouse acts as a repair facility and replenishes stock at the field depots. There is a centralized decision-maker who manages the inventory in both the central warehouse and the field depots. We develop a continuous review, base stock policy for this two-echelon, multi-item spare parts inventory system. We formulate a model to minimize the system-wide inventory cost subject to a response time constraint at each field depot. We present an efficient heuristic algorithm and study its computational effectiveness.     

Efficient heuristics for two-echelon spare parts inventory systems with an aggregate mean waiting time constraint per local warehouse

This paper presents solution procedures for determining close- to-optimal base stock policies in a multi-item two-echelon spare parts inventory system. The system consists of a central warehouse and multiple local warehouses, and there is a target for the aggregate mean waiting time per local warehouse. We develop four different heuristics and derive a lower bound on the optimal total cost. The effectiveness of each heuristic is assessed by the relative gap between the heuristic’s total cost and the lower bound. The results of the computational experiments show that a greedy procedure performs most satisfactorily. It is accurate as indicated by relatively small gaps, easy to implement, and the computational requirements are limited. Its computational efficiency can be increased by using Graves’ approximate evaluation method instead of an exact evaluation method, while the results remain accurate. That results in a feasible algorithm for real-life cases with many items and local warehouses.     

Managing two-stage serial inventory systems under demand and supply uncertainty and customer service level requirements

We consider a two-echelon serial inventory system with demand and supply uncertainty, non-zero lead times for component procurement and end-product assembly, and a minimum customer service level requirement. We present two supply models which incorporate both quantity and timing uncertainty; these models correspond to current and proposed supply environments. Assuming that installation base-stock ordering policies are followed and that the demand distribution is quasi-concave, we show that the chance-constrained problem of determining optimal base-stock levels which minimize the total inventory investment (cost-weighted stock levels) subject to a service constraint is a convex programming problem. We characterize the relation between the optimal base-stock levels of the component and the end-product. We also illustrate how an optimal internal (component) service level can be computed, which permits decomposition of the two-stage serial system into two coordinated single-echelon systems. Computational experiments illustrate insights on the effects of supply uncertainty and other problem parameters on stock-positioning in a two-echelon serial system. In particular, we evaluate the benefits of switching from one supply environment to another.     

A Bound Heuristic Technique for Solving DRAMA Spares Optimizations

1IntroductionTodaythePublicrequiresthatallcomplexellgilleering,suchasatomicPOwerplants,airCrafl,automobilesandcomputer,etc.,behighlyreliable.Generally,tilesystemsarerepairableinventorysystemsthatarecomposedofitemswhicharerepairedalldretUrnedtouseratherthandiscarded.TherepairableinventoryProblemistypicallyconcernedwilhtheoptimalstockingofpartsatbases(orforwardlocations)andacentereddelx)t1'llcilitywhichrepairedunitsreturnedfromthehaseswhileprovidingsomePredeterminedlevelofservice.Themathemati…     

Policy and cost approximations of two-echelon distribution systems with a procurement cost at the higher echelon

This paper investigates a two-echelon (warehouse-retailer) inventory system with stochastic demand and a pull system of inventory allocation. We assume that ordering costs are charged at the warehouse for procuring the item from a supplier. However, the internal costs of ordering the item from the warehouse by the retailers are considered negligible. For this problem, the lower echelon uses a single critical number, an order-up-to-level policy, whereas a (s, S) inventory system is followed at the upper echelon. We develop a cost model for this problem and provide a simple algorithm for estimating the optimal policy. Simulation is used to test the accuracy of the model.     

需求受相关性影响的设备备件库存优化

备件多级库存模型通常基于备件需求相互独立的假设，但随着库存系统层次的增加以及协同管理方式的应用，备件需求的相关性将显著影响库存优化决策。针对需求具有相关性的备件库存问题，以服务响应时间为约束条件，以库存成本及缺货成本最小化为目标建立备件两级库存决策模型。引入Nataf概率变换法，利用已知的备件需求边缘概率密度函数构造满足特定相关性条件的随机需求样本，并将蒙特卡洛仿真与遗传算法相结合求解最优库存分配方案。仿真算例证明，设备备件库存的最优决策随着需求相关性系数的增大而发生变化，根据需求相关性的变化适当地调整库存决策，有利于降低备件库存系统总成本，提高库存系统对顾客需求的响应能力。     

The trans-shipment problem in a two-echelon,multi-location inventory system with lost sales

In this paper, we address a two-echelon, multi-location pooling inventory system that consists of an outside supplier, a warehouse and two retailers. To control their inventories, both warehouse and retailers use (R,?s,?S) policy. The retailers face stochastic customer demands for a single product and the warehouse receives only the replenishment orders of retailers. In case of stock-out at retailers, emergency trans-shipments are used to satisfy the unmet demand at one retailer with the surplus from the other retailer. When the stock is insufficient at the warehouse, we propose two rationing policies to allocate on-hand stock between retailers. The demand that cannot be satisfied neither by stock on-hand nor by trans-shipment from retailers is considered lost. Our work has two objectives. First, we propose an inventory model based on three components: the optimisation inventory model, the trans-shipment policy and the rationing policies for determining the best values of (s,?S) at each location that minimise total system cost. Second, we validate this model via an empirical simulation study that allows us to identify the influential parameters on trans-shipment benefits.     

A framework for decentralized multi-echelon inventory control

We provide a cost structure that can be used for decentralized control of a multi-echelon inventory system with a central warehouse and a number of retailers. This cost structure means that the warehouse, in addition to its local costs, pays a penalty cost for a delay at the warehouse to the retailer facing the delay. A basic assumption is that each installation starts with an initial policy concerning e.g., inventory control and transportation. The installations then play a Stackelberg game with the warehouse being [he leader. By minimizing its local costs according to the suggested cost structure, an installation can reduce its costs. The total system costs are then reduced by the same amount. No installation needs to face higher costs due to policy changes at other installations, since the cost structure satisfies a rationality constraint. If an installation applies its initial policy the local costs are the same as in the initial state, even if the other installations change their policies. If the game is played repeatedly the system will approach a Nash equilibrium but not necessarily the centralized optimal solution. As an example we consider a system with one-for-one ordering retailers.     

Analyzing the effect of inventory policies on the nonstationary performance with transfer functions

In this paper we apply transfer function methods to analyze the performance of supply chains in response to nonstationary demand and, in particular, we investigate how various inventory policies and demand forecasting parameters affect supply chain responsiveness. In a single-echelon inventory system we investigate the performance of a common base stock policy. Specifically, we describe the order and inventory trajectories using discrete transfer functions, and we derive closed-form analytical expressions for the transient behavior in response to a step change in demand. We introduce performance measures commonly used to analyze nonstationary performance and derive closed-form expressions for these measures. Next, we study the performance of a two-echelon supply chain under installation stock and echelon stock policies. We explicate the performance tradeoff in response to stationary versus nonstationary demand, and show that the transient response of orders and inventory levels can be either underdamped or overdamped depending on the exponential smoothing parameter. We show that the echelon stock policy is more responsive than the installation stock policy when both policies have similar stationary performances.     

Closed loop two-echelon repairable item systems

In this paper we consider closed loop two-echelon repairable item systems with repair facilities both at a number of local service centers (called bases) and at a central location (the depot). The goal of the system is to maintain a number of production facilities (one at each base) in optimal operational condition. Each production facility consists of a number of identical machines which may fail incidentally. Each repair facility may be considered to be a multi-server station, while any transport from the depot to the bases is modeled as an ample server. At all bases as well as at the depot, ready-for-use spare parts (machines) are kept in stock. Once a machine in the production cell of a certain base fails, it is replaced by a ready-for-use machine from that bases stock, if available. The failed machine is either repaired at the base or repaired at the central repair facility. In the case of local repair, the machine is added to the local spare parts stock as a ready-for-use machine after repair. If a repair at the depot is needed, the base orders a machine from the central spare parts stock to replenish its local stock, while the failed machine is added to the central stock after repair. Orders are satisfied on a first-come-first-served basis while any requirement that cannot be satisfied immediately either at the bases or at the depot is backlogged. In case of a backlog at a certain base, that bases production cell performs worse.To determine the steady state probabilities of the system, we develop a slightly aggregated system model and propose a special near-product-form solution that provides excellent approximations of relevant performance measures. The depot repair shop is modeled as a server with state-dependent service rates, of which the parameters follow from an application of Nortons theorem for Closed Queuing Networks. A special adaptation to a general Multi-Class Marginal Distribution Analysis (MDA) algorithm is proposed, on which the approximations are based. All relevant performance measures can be calculated with errors which are generally less than one percent, when compared to simulation results. The approximations are used to find the stock levels which maximize the availibility given a fixed configuration of machines and servers and a certain budget for storing items. Correspondence to: W.H.M. Zijm