POWER APPROXIMATIONS FOR A TWO-ECHELON INVENTORY SYSTEM USING SERVICE LEVELS

We consider a two-echelon inventory system with one warehouse and several stores. The warehouse as well as the stores are controlled by periodic review (s, S) inventory policies. We study the interrelationship between the safety stocks at the warehouse and the stores. Stockouts at the warehouse will result in supply delays to the stores and cause the lead time to be stochastic. The stores may react by increasing their safety stock. However, there is a trade-off between the safety stock at the warehouse and the safety stock at the stores. We use a service level at the warehouse to quantify the effect of warehouse stockouts on the lead time to the stores. The service level at the warehouse is considered a decision variable to find the best compromise between the various safety stocks by minimizing the overall costs. Using power approximations for the (s, S) policies, we provide an iterative procedure for adjusting the lead time distribution to the stores; this can result in substantial savings, but it doesn't guarantee the overall optimality. Numerical studies are provided to test the accuracy of approximations. The effects of the different system parameters on the inventory policy give general guidelines for use of the policies.     

DECENTRALIZED MULTIECHELON INVENTORY CONTROL

This paper considers a model for decentralized control of an inventory system consisting of 1 central warehouse and a number of retailers. The cost structure includes holding costs at both echelons and shortage costs proportional to the time until delivery at the retailers. We analyze a procedure for coordinated but still decentralized control of the system. The procedure is based on a simple approximation, in which the stochastic lead times perceived by the retailers are replaced by their correct averages. The approximation enables us to decompose the considered multiechelon inventory problem into a number of single echelon problems, 1 for each installation. The information about how a certain decision at the warehouse affects the retailers is conveyed through the marginal cost increase with respect to a change of the expected lead time. This information about the retailer costs is used as a shortage cost at the warehouse. We show that a coordination procedure based on this information can be used for finding near-optimal reorder points for the system and provide bounds for the approximation errors.     

Single cycle policies for the one-warehouse N-retailer inventory/distribution system

We address a multi-echelon inventory system with one-warehouse and N  -retailers. The demand at each retailer is assumed to be known and satisfied by the warehouse. Shortages are not allowed and lead times are negligible. Costs at each facility consist of a fixed charge per order and a holding cost. The goal is to determine single-cycle policies which minimize the average cost per unit time, that is, the sum of the average holding and setup costs per unit time at the retailers and at the warehouse. We propose a O(NlogN)$\mathrm{O}(N\log N)$ heuristic procedure to compute efficient single-cycle policies. This heuristic is compared with other approaches proposed by Schwarz, Graves and Schwarz and Muckstadt and Roundy. We carry out a computational study to test the effectiveness of the heuristic and to compare the performance of the different procedures. From the computational results, it is shown that the new heuristic provides, on average, better single-cycle policies than those given by the Muckstadt and Roundy method.     

区分仓库与货架库存需求影响效应的零售商库存决策

既往有关库存水平影响需求条件下的库存问题研究中,通常对终端库存水平是否存在货架与零售商仓库库存水平的区别未作深入探讨。本文的研究认为,现实中许多零售商拥有仓库,其现有库存水平包括仓库库存和货架库存两部分,而影响需求的仅为与货架展示能力相关的库存,因此有必要对二者的需求影响效应进行区分。在明确这一区别的前提下,本文首先建立了供应商管理库存情况下库存水平影响需求问题的一般库存模型,给出零售商的最优订货策略;并考虑货架的容量限制,给出零售商启用仓库的判断条件。由于仓库库存仅在能够影响货架展示能力的条件下才能够影响消费需求,本文还进一步讨论了在零售商拥有仓库时,区分货架与仓库的库存水平影响需求条件下的最优库存与订货决策。这对于经营不同特征商品的零售商在进行是否需要拥有仓库,以及拥有仓库条件下的库存决策具有很好的参考价值。     

The cost of using stationary inventory policies when demand is non-stationary

Non-stationary stochastic demands are very common in industrial settings with seasonal patterns, trends, business cycles, and limited-life items. In such cases, the optimal inventory control policies are also non-stationary. However, due to high computational complexity, non-stationary inventory policies are not usually preferred in real-life applications. In this paper, we investigate the cost of using a stationary policy as an approximation to the optimal non-stationary one. Our numerical study points to two important results: (i) Using stationary policies can be very expensive depending on the magnitude of demand variability. (ii) Stationary policies may be efficient approximations to optimal non-stationary policies when demand information contains high uncertainty, setup costs are high and penalty costs are low.     

AN EVALUATION OF ORDER PICKING POLICIES FOR MAIL ORDER COMPANIES

This paper is concerned with the problem of order picking in mail order companies. Order picking is the retrieval of items from their warehouse storage locations to satisfy customer orders. Five order picking policies, strict order, batch, sequential zone, batch zone, and wave, are evaluated using labor requirements, processing time, and customer service as performance measures. A simulation model was developed to investigate these picking policies in a mail order environment. Prior research has focused on the study of individual picking policies. This study extends the prior research by evaluating multiple picking policies under varying operating conditions. The results of the study seem to indicate that (1) wave picking and batch picking perform well across the range of operating conditions considered in this study, and (2) sequential zone and batch zone picking do not perform well, especially as the order volume increases. However, the benefits and drawbacks to each picking policy must be taken into account. The key to effective implementation of an order picking system is to match the firm's business strategy, capabilities, technology, and space requirements with an order picking policy that maximizes the benefits of order picking to the firm and its customers.     

Heuristic Coordination of Decentralized Inventory Systems Using Induced Backorder Costs

In this paper, we investigate a one‐warehouse multiple‐retailer system, where the inventory control decisions are coordinated using a near optimal induced backorder cost, β*. All installations use continuous review installation‐stock (R, Q) policies. The analysis builds on an approximation model where the stochastic warehouse delays are replaced by their correct averages. The contributions include insights as to how β* is influenced by system parameters, and the determination of simple closed form β* estimates. The latter offering a practical means to achieve coordinated control of large size systems.     

A Flexible Evaluative Framework for Order Picking Systems

This paper develops a novel framework to evaluate the integral performance of order picking systems with different combinations of storage and order picking policies. The warehousing literature on order picking mostly considers minimizing either elapsed time or distance as the sole objective, whereas warehouse managers in a supply chain have to look beyond single‐dimensional performance and consider trade‐offs among different criteria. Thus managers still need a unified and efficient framework to select a portfolio of appropriate order picking policies from a multi‐criteria and contextual perspective. Our framework—combining data envelopment analysis, ranking and selection, and multiple comparisons—provides an efficient methodology to simultaneously analyze several interrelated problems in order picking systems with multiple performance attributes, such as service levels and operational costs. We demonstrate our approach through comprehensive evaluations of order picking policies in three low‐level, picker‐to‐parts rectangular warehouses facing demand variations.     

无人仓系统储位分配问题的优化模型与算法

考虑到无人仓系统补货阶段货架上只有部分空余储位的特点，研究了补货商品储位分配问题的优化模型与算法。以同一货架上存放的商品之间关联度之和最大化为目标建立了混合整数规划模型；结合贪婪算法和邻域搜索算法设计了求解模型的两阶段方法。第一阶段利用贪婪算法求初始可行解；第二阶段利用邻域搜索算法对初始可行解进行优化。利用一个具体算例验证了邻域搜索算法的优化效果，结果显示，通过邻域搜索算法对初始可行解的优化，可以使目标函数值至少提升27%。进一步利用多个小规模算例分析了两阶段算法的近似比和求解速度，验证了算法的快速有效性。本文的研究结果不仅解决了货架初始状态非空情况下的储位分配问题，同样适合解决货架初始状态为空的情况，因此更加符合实际场景，可以作为无人仓管理信息系统的核心模型和算法。     

按单装配系统中的协同补货问题研究

多库存品的库存系统中各库存品具有需求相关性在现实中很常见,但许多关于库存的文献并没有考虑这一点.针对按单装配系统的特性,本文研究了不同部件需求具有相关性的情况下的库存控制问题,分析了不同部件独立补货和不同部件协同补货两种补货策略.数值分析表明,按单装配系统中部件协同补货策略比部件独立补货策略具有更低的总成本.     

Retailer Transshipment versus Central Depot Allocation for Supply Network Design

We consider a supply chain structure with shipments from an external warehouse directly to retailers and compare two enhancement options: costly transshipment among retailers after demand has been realized vs. cost‐free allocation to the retailers from the development of a centralized depot. Stochastic programming models are developed for both the transshipment and allocation structures. We study the impact of cost parameters and demand coefficient of variation on both system structures. Our results show an increasing convex relationship between average costs and demand coefficient of variation, and furthermore that this increase is more pronounced for the allocation structure. We employ simulation and nonlinear search techniques to computationally compare the cost performance of allocation and transshipment structures under a wide range of system parameters such as demand uncertainty and correlation; lead times from the external warehouse to retailers, from warehouse to central depot, and from depot to retailers; and transshipment, holding, and penalty costs. The transshipment approach is found to outperform allocation for a broad range of parameter inputs including many situations for which transshipment is not an economically sound decision for a single period. The insights provided enable the manager to choose whether to invest in reducing lead times or demand uncertainty and assist in the selection of investments across identical and nonidentical retailers.     

电子商务环境下的存储策略优化研究:固定存储还是分类随机存储

库位推荐与拣货过程效率的提升是降低仓库运营成本的两个重要方面。而仓库的存储策略会对仓库运营总成本产生重要影响。本文首先在分类随机存储策略与固定存储策略下构建了库位推荐与拣货路径联合优化的混合整数规划模型;其次,基于快销品行业、医药行业和图书行业下的订单结构特点,采用修正的差分进化算法对两种存储策略进行了对比分析。结论表明：存储策略的优劣不仅与订单结构有关,同时也与单位存储成本与单位拣货成本的比重有关。当比重不高于0.25时,三种行业均是固定存储策略的总成本更低;（2）当比重介于0.25和0.26之间时,快销品行业和医药行业均是固定存储策略的总成本更低,而图书行业下是分类随机存储的成本更低;（3）当比重介于0.26和0.27之间时,快销品行业下是固定存储策略的总成本更低,而图书和医药行业下是分类随机存储的总成本更低。（4）当比重不低于0.27时,三种行业下均是分类随机存储策略的总成本更低。本文可以为不同行业下的仓库存储策略的选择提供一定的参考价值。     

Optimal Inventory Control with Retail Pre‐Packs

A pre‐pack is a collection of items used in retail distribution. By grouping multiple units of one or more stock keeping units (SKU), distribution and handling costs can be reduced; however, ordering flexibility at the retail outlet is limited. This paper studies an inventory system at a retail level where both pre‐packs and individual items (at additional handling cost) can be ordered. For a single‐SKU, single‐period problem, we show that the optimal policy is to order into a “band” with as few individual units as possible. For the multi‐period problem with modular demand, the band policy is still optimal, and the steady‐state distribution of the target inventory position possesses a semi‐uniform structure, which greatly facilitates the computation of optimal policies and approximations under general demand. For the multi‐SKU case, the optimal policy has a generalized band structure. Our numerical results show that pre‐pack use is beneficial when facing stable and complementary demands, and substantial handling savings at the distribution center. The cost premium of using simple policies, such as strict base‐stock and batch‐ordering (pre‐packs only), can be substantial for medium parameter ranges.     

A Framework for Facilitating Sourcing and Allocation Decisions for Make‐to‐Order Items

This paper provides a fundamental building block to facilitate sourcing and allocation decisions for make‐to‐order items. We specifically address the buyer's vendor selection problem for make‐to‐order items where the goal is to minimize sourcing and purchasing costs in the presence of fixed costs, shared capacity constraints, and volume‐based discounts for bundles of items. The potential suppliers for make‐to‐order items provide quotes in the form of single sealed bids or participate in a dynamic auction involving open bids. A solution to our problem can be used to determine winning bids amongst the single sealed bids or winners at each stage of a dynamic auction. Due to the computational complexity of this problem, we develop a heuristic procedure based on Lagrangian relaxation technique to solve the problem. The computational results show that the procedure is effective under a variety of scenarios. The average gap across 2,250 problem instances is 4.65%.     

Optimal sampling techniques in off-line quality control

This paper addresses the problem of quality control for manufacturing environments. The quality control station is placed in an off-line position, i.e. external to the item flow. This layout is mandatory when the station is unable (because of costs and times) to inspect the whole set of items produced. The aim of the present study is to describe and evaluate how the limited capacity of the quality control station affects the efficiency of the connected production system and how the service time of the inspection station may be profitably managed as a further variable of the quality inspection process. Optimal policies for both random and deterministic sampling techniques are determined and compared.     

Decentralised bilevel model for shared inventory management

In this study, we consider the case of a large corporation that owns a warehouse and two concurrent chains. The company opted for shared inventory policy. The warehouse is looking into minimising its inventory cost and at the same time reducing the fluctuation of the personnel. The chains, independently, are trying to minimise their inventory costs. The warehouse plays the role of a leader in optimising its objectives and, as followers, the two chains try to satisfy their objectives. The problem is formulated into a decentralised nonlinear bilevel programming problem. We also consider the fuzziness of some parameters due to the imprecise available information. We propose the mathematical model and we solve it for our specific case.     

The Influence of Quality Inspections on the Optimal Safety Stock Level

Due to yields of less than 50% during the production of curved glass for the displays on their new cell phone series, Samsung has to deal with higher than expected production costs of several million dollars. Where there is random yield, production costs as well as holding costs can be reduced by introducing quality inspections, in which defective items are discarded before further production. To achieve the greatest cost savings, it is important to determine the optimal number and positions of these inspections across the production process which, due to several influencing parameters, is not simple. We show how the positions of inspection within a production process influence the safety stock level that is required to buffer against uncertainties due to demand and yield randomness. Our approach is the first one, combining decisions about the number and positions of inspections with inventory control strategies in a warehouse. We achieve a maximum safety stock reduction of more than 30% in our examples, which can be even larger depending on the parameter setting. For a company like Intel, reporting inventories for finished goods of nearly 1.5 billion dollars in the 2014 annual report, this allows for significant savings.     

Coordinated Replenishments from a Common Supplier

Coordinated replenishment strategies may be implemented by jointly ordering multiple items from a common supplier. A major benefit of coordinated replenishment is that it increases the size of shipments, permitting the buyer to enjoy transportation economies without a major increase in average inventory levels. The coordinated replenishment problem is complex because side constraints govern the attainment of transportation rate breaks. The problem is further complicated by the presence of purchase quantity discount opportunities. Thus, the buyer must decide which items to order independently, which items to include in a group order, and the order quantities of each item, governed by the frequency of independent or group orders. We present a mathematical model and a heuristic solution procedure that provide analytical support to the buyer seeking to minimize total costs of replenishing multiple items from a common supplier. The relevant costs are purchase prices, ordering costs, holding costs, and transportation costs. Coordinated replenishment provides nearly a 30 percent reduction in controllable costs relative to independent control. Experimentation with the heuristic has yielded optimal solutions over 88 percent of the time. When optimality was not obtained, the mean penalty was much less than one percent. The average heuristic search was more than two orders of magnitude faster than branch and bound, even for small problems, and possessed a much tighter distribution around the mean search time.     

A coordination mechanism with fair cost allocation for divergent multi-echelon inventory systems

In this paper we study the coordination of inventory control in divergent multi-echelon inventory systems under periodic review and decentralized control. Under decentralized control the installations decide upon replenishment policies that minimize their individual inventory costs. In general these policies do not coincide with the optimal policies of the system under centralized control. Hence, the total cost under decentralized control is larger than under centralized control. We present a simple coordination mechanism that removes this cost inefficiency. The upstream installations increases its base stock level while the downstream installations compensate their supplier for increased costs and provide it with additional side payments. We show that this mechanism coordinates the system; the global optimal policy of the system is the unique Nash equilibrium of the corresponding strategic game. Furthermore, the mechanism results in a fair allocation of the costs; all installations enjoy cost savings.     

A genetic algorithm for determining optimal replenishment cycles to minimize maximum warehouse space requirements

In a supply chain, it is an important issue for logistic managers to offset the replenishment cycles of multiple products sharing a warehouse so as to minimize the maximum warehouse space requirement (MWSR). Most of the studies in the literature assume that warehouses replenish at the beginning of some basic planning period. In this paper, we relax this assumption by allowing the warehouse to replenish at any time. In order to solve this problem, we conduct theoretical analysis based on Fourier series and Fourier transforms and propose a procedure that is used to calculate MWSR efficiently for any given replenishment schedule. Then, we employ this procedure in a genetic algorithm (GA) to search for the optimal replenishment schedule. Using randomly generated instances, we show that the proposed GA significantly outperforms a previously published heuristic.