Inventory Location Research Articles

Demand Allocation in Multiple-Product, Multiple-Facility, Make-to-Stock Systems

We consider the problem of allocating demand arising from multiple products to multiple production facilities with finite capacity and load-dependent lead times. Production facilities can choose to manufacture items either to stock or to order. Products vary in their demand rates, holding and backordering costs, and service-level requirements. We develop models and solution procedures to determine the optimal allocation of demand to facilities and the optimal inventory level for products at each facility. We consider two types of demand allocation, one in which we allow the demand for a product to be split among multiple facilities and the other in which demand from each product must be entirely satisfied by a single facility. We also consider two forms of inventory warehousing, one in which inventory locations are factory based and one in which they are centralized. For each case, we offer a solution procedure to obtain optimal demand allocations and optimal inventory base-stock levels. For systems with multiple customer classes, we also determine optimal inventory rationing levels for each class for each product. We use the models to characterize analytically several properties of the optimal solution. In particular, we highlight eight principles that relate the effects of cost, congestion, inventory pooling, multiple sourcing, customer segmentation, inventory rationing, and process and demand variability.

Internet book retailing and supply chain management: an analytical study of inventory location speculation and postponement

Abstract Internet retailing models support supply chains where consumer order locations are decoupled from inventory locations. In this setting, retailers dynamically consider inventory location speculation and postponement to fulfill their orders. Particularly, retailers can manage inventory to fulfill orders through two opposing strategies: in-stock inventory and drop-shipping. This paper extends the supply chain management literature by modeling Internet retailers' decisions to balance their offerings between these two strategies. The results show how retailers depend more on both of these strategies as their market share and product popularity increase. Thus, both inventory management strategies may be considered simultaneously to better manage Internet retailers' inventory.

Warehouse-Retailer Network Design Problem

In this paper, we study the distribution network design problem integrating transportation and infinite horizon multiechelon inventory cost function. We consider the trade-off between inventory cost, direct shipment cost, and facility location cost in such a system. The problem is to determine how many warehouses to set up, where to locate them, how to serve the retailers using these warehouses, and to determine the optimal inventory policies for the warehouses and retailers. The objective is to minimize the total multiechelon inventory, transportation, and facility location costs. To the best of our knowledge, none of the papers in the area of distribution network design has explicitly addressed the issues of the 2-echelon inventory cost function arising from coordination of replenishment activities between the warehouses and the retailers. We structure this problem as a set-partitioning integer-programming model and solve it using column generation. The pricing subproblem that arises from the column generation algorithm gives rise to a new class of the submodular function minimization problem. We show that this pricing subproblem can be solved in O(nlog n) time, where n is the number of retailers. Computational results show that the moderate size distribution network design problem can be solved efficiently via this approach.

Inventory Positioning in Multiple Product Supply Chains

In this paper we address the problem of inventory positioning, i.e., the determination of the supply chain node where inventory should be held, to minimize holding costs given a pre-specified order fill rate. A single-echelon inventory system with multiple products models the problem. The value of inventory is assumed to be an increasing function of the amount of processing performed at upstream nodes, while achieved fill-rates are dependent on the distance or time between the inventory storage and customer locations. We propose a novel analytical approach to solve the problem for the case of normally distributed demand that is based on iterative calculations of inventory holding costs at the various potential inventory locations.

Dynamic inventory database management (DIDM): a summary of an internet-based solution for managing complexity of inventory databases

In recent years, fast growth in the development and application of e-business technologies has generated vast interest among practising managers and management scholars in inventory database management. E-business technologies enable an inventory manager to make coordinated decisions on the basis of regularly updated and timely ordered information. The dynamic features of the inventory items and inventory locations make a rationally organised time schedule of regular and irregular updates for inventory databases difficult. Using a game theory strategy of optimal regular updates for dynamic databases can significantly lower costs associated with the database update process. This article describes an internet-based solution of creation, maintenance, update, and query of a computerised inventory database for inventory items and their locations with time-dependent (dynamic) and time-independent (static) attributes. Further research opportunities in inventory database management using e-business applications are discussed.

Production and Distribution Lot Sizing in a Two Stage Supply Chain

We develop a two stage model of a manufacturing supply chain. This two stage production transportation model features capacitated production in two stages, and a fixed cost (or concave cost) for transporting the product between the stages. We prove several properties of this model, which we call the Two Stage Production Distribution Problem (2SPDP) model. By placing "non-speculative" assumptions on production and transportation, we show that our model reduces to a related model, with one capacitated production stage with linear production cost, and transportation between two inventory locations with non-linear transportation cost. Finally, we present polynomial algorithms for this model under several different transportation cost structures and capacity assumptions.

The incidence of diffuse idiopathic skeletal hyperostosis and social status correlations in Lithuanian skeletal materials

AbstractNumerous indications in literature argue that diffuse idiopathic skeletal hyperostosis (DISH) is aetiologically linked with obesity and late onset (type II) diabetes. Thus its incidence should differ in socially stratified societies where individuals have different access to food resources. The incidence of DISH was evaluated in a skeletal sample of 458 adult individuals from the Iron Age, Mediaeval, and Early Modern periods. Social status was defined either by grave inventory (Iron Age) or burial location (within a church, or urban or rural cemeteries). Diagnostic criteria for DISH were right side anterior longitudinal spinal ligament or extra‐spinal ligament (enthesis) ossification. No differences between chronological groups were found. The incidence of DISH had definite age affinity: it increased with age: from 0.00% in 20–30 year olds to 30.23% in the 50+ year old group (p<0.001). It was also closely associated with sex: male/female ratio was 6.9 (p<0.01). Social status was slightly but significantly related with DISH: incidence among high social status individuals was 27.14%, average or urban was 11.86%, poor or rural was 7.14% (p<0.001). Our results confirm that DISH is associated with the male sex and advanced age and support the hypothesis that the incidence of DISH is related to life style, possibly as a result of different nutritional patterns. Copyright © 2003 John Wiley & Sons, Ltd.

PLANNING MULTIPLE LOCATION INVENTORIES

Supplying customer demand from comparable alternate inventory locations when an item is out of stock at its primary stocking point creates a virtual inventory for that item. The expectation is that if more inventories can be drawn upon, the inventory for an item would be lower, the fill rate would be higher, or both. While generally true that safety stocks will be lower, regular stocks, on the other hand, may rise with such cross filling of demand. In this study, a methodology is developed that balances the cross filling effects on both regular and safety stocks for determining whether an inventoried item should be cross‐filled. An example and guidelines are given to show how the methodology can be simplified and applied in practice.

A Joint Location-Inventory Model

We consider a joint location-inventory problem involving a single supplier and multiple retailers. Associated with each retailer is some variable demand. Due to this variability, some amount of safety stock must be maintained to achieve suitable service levels. However, risk-pooling benefits may be achieved by allowing some retailers to serve as distribution centers (and therefore inventory storage locations) for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. We formulate this problem as a nonlinear integer-programming model. We then restructure this model into a set-covering integer-programming model. The pricing problem that must be solved as part of the column generation algorithm for the set-covering model involves a nonlinear term in the retailerdistribution-center allocation terms. We show that this pricing problem can (theoretically) be solved efficiently, in general, and we show how to solve it practically in two important cases. We present computational results on several instances of sizes ranging from 33 to 150 retailers. In all cases, the lower bound from the linear-programming relaxation to the set-covering model gives the optimal solution.

An asymptotically optimal greedy heuristic for the multiperiod single‐sourcing problem: The cyclic case

AbstractThe dynamics of the environment in which supply chains evolve requires that companies frequently redesign their logistics distribution networks. In this paper we address a multiperiod single‐sourcing problem that can be used as a strategic tool for evaluating the costs of logistics network designs in a dynamic environment. The distribution networks that we consider consist of a set of production and storage facilities, and a set of customers who do not hold inventories. The facilities face production capacities, and each customer's demand needs to be delivered by a single facility in each period. We deal with the assignment of customers to facilities, as well as the location, timing, and size of inventories. In addition, to mitigate start and end‐of‐study effects, we view the planning period as a typical future one, which will repeat itself. This leads to a cyclic model, in which starting and ending inventories are equal. Based on an assignment formulation of the problem, we propose a greedy heuristic, and prove that this greedy heuristic is asymptotically feasible and optimal in a probabilistic sense. We illustrate the behavior of the greedy heuristic, as well as some improvements where the greedy heuristic is used as the starting point of a local interchange procedure, on a set of randomly generated test problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 412–437, 2003

Responsibilities for inventory decisions in Polish manufacturing companies

Inventories constitute one of the basic elements of logistics systems. In fact, inventories present only low value unless situated in the right place and time. The basic goal of this paper was to examine how decision-making process is organised in average Polish companies and how they are prepared to the implementation of the concept of manufacturing to the order, postponement and relative inventory location. The paper presents proportions of production to stock and to order with the basic tendencies of utilisation of capacities in Polish companies. Those are general conditions for basic patterns of inventory decision making in the supply chain depending on the location of decoupling points discussed together with the structure and rotation of inventories. The organisational and time framework for decisions on inventories have been presented, trying to relate it to basic patterns occurring in the location of decoupling points. The basic results of research on practices reported by the surveyed Polish companies in the field of inventory management have been resumed in Conclusions and they have been discussed in comparison with some data from Western countries. The research has been based on two surveys administered in Polish companies and additional information obtained from other smaller scale surveys on logistics-decision-making patterns administered by the author.

Uniform distribution of inventory positions in two-echelon periodic review systems with batch-ordering policies and interdependent demands

We consider a two-level inventory system in which there are one supplier and multiple retailers. The retailers face stochastic, interdependent customer demands. Each location employs a periodic-review ( R, nQ), or lot-size reorder point, inventory policy. We show that each location's inventory positions are stationary and the stationary distribution is uniform and independent of any other's.

Inventory cost impact of order processing priorities based on demand uncertainty

AbstractWe evaluate an approach to decrease inventory costs at retail inventory locations that share a production facility. The retail locations sell the same product but differ in the variance of retail demand. Inventory policies at retail locations generate replenishment orders for the production facility. The production facility carries no finished goods inventory. Thus, production lead time for an order is the sojourn time in a single server queueing system. This lead time affects inventory costs at retail locations. We examine the impact of moving from a First Come First Served (FCFS) production rule for orders arriving at the production facility to a rule in which we provide non‐preemptive priority (PR) to orders from retail locations with higher demand uncertainty. We provide three approximations for the ratio of inventory costs under PR and FCFS and use them to identify conditions under which PR decreases retail inventory costs over FCFS. We then use a Direct Approach to establish conditions when PR decreases retail inventory costs over FCFS. We extend the results to orders from locations that differ in the mean and variance of demand uncertainty. The analysis suggests that tailoring lead times to product demand characteristics may decrease system inventory costs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 376–390, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10016

A two-echelon inventory allocation and distribution center location analysis

Abstract The optimization of locations for distribution centers is influenced by the demand for individual products. Lower demand products are often more effectively held in more centralized locations than higher demand products. This paper presents a model for optimizing the location of inventory for individual products in a multi-product two-echelon inventory system and the integration of those decisions into the location analysis for distribution centers. A realistic application of the analysis process is discussed.

A General Framework for the Study of Decentralized Distribution Systems

We develop a general framework for the analysis of decentralized distribution systems. We carry the analysis in terms of a simplified model which entails N retailers who face stochastic demands and hold stocks locally and/or at one or more central locations. An exogenously specified fraction of any unsatisfied demand (demand greater than locally available stock) at a retailer could be satisfied using excess stocks at other retailers and/or stocks held at a central location. We consider inventory ordering and allocation decisions. The operational decisions of inventory and allocation of stocks and the financial decision of allocation of revenues/costs must be made in a way consistent with the individual incentives of the various independent retailers. We develop a “coopetitive” framework for the sequential decisions of inventory and allocation. We introduce the notion of claims that allows us to separate the ownership (with decision rights) and the location of inventories in the system. For the cooperative shipping and allocation decision, we use the concept of core and develop sufficient conditions for the existence of the core. For the inventory decision, we develop conditions for the existence of a pure strategy Nash Equilibrium. For this decentralized system, we show that there exists an allocation mechanism that achieves the first-best solution for inventory deployment and allocation. We develop conditions under which the first-best equilibrium will be unique. Our model can be easily generalized to include complicated ownership structures such as “super dealers,” partnerships, “inventory speculators,” and situations in retail e-commerce settings such as “click-through arrangements,” separation of “demand generators,” and “fulfillment houses,” etc. It can also be applied to situations involving capacity allocations and product substitutions.

Creating an Inventory Hedge for Markov-Modulated Poisson Demand: An Application and Model

Many firms face environments with long manufacturing leadtimes, great product variety, and uncertain, nonstationary demand. A challenge is how to plan production and inventories to provide the best customer service at the least cost. In this paper, we first describe an application at Teradyne in which we implemented an inventory hedge to protect against cyclic demand variability. Based on this experience, we develop a model to better understand the efficacy of this hedging policy. We consider an inventory system for a single aggregate product with a Markov-modulated Poisson demand process. We provide approximate performance measures for this system and develop an optimization problem for determining the size and location of an intermediate-decoupling inventory. We use this optimization to show the value of an intermediate-decoupling inventory as a hedge for cyclic demand environments.

Period changes and Inventory Management: the Three Ages of Retail Logistics

The present research paper establishes a framework for analysing changes in French retail logistics. Unlike other studies, in which only two stages are described (the manufacturer-controlled system as stage 1 and the retailer-controlled system as stage 2), the authors have identified three periods or “ages” in retail logistics. This is done by highlighting the two philosophies that the country’s retailer-controlled systems (stage 2) have successively experience: the first one being based on an instrumental orientation; and the second on managerial vision. To illustrate the proposed model, they refer to the location of inventory in the distribution channel, progressively moving from the downstream (outlet) end of the value chain toward the upstream (factories). Logically, this leads to the establishment of closer relationships between large retailers and manufacturers. The paper concludes with a discussion on the different directions a fourth period in retail logistics could take.

Logistics customer service: performance of Irish food exporters

Customer service in logistics, through its direct impact on a firm’s market share, its total logistics costs and ultimately its profitability, is a critical determinant of competitiveness. Examines what customer service means from a logistics perspective and traces out UK retailers’ changing requirements. It provides the results of a survey which investigates the importance UK grocery retailers place on particular elements of customer service and assesses Irish food exporters’ relative performance, vis‐à‐vis their competitors on the UK market. A comparison of these results with previous research by the same authors concerned with Irish food exporters’ internal measurement of customer service finds that Irish food exporters are perceived to lack flexibility by their grocery customers and that internal measures of customer service are limited. Furthermore, the measures exporters employ for monitoring purposes are not appropriately aligned with those logistics variables which UK retailers consider important. Reconfiguring the supply chain with respect to inventory location is found to be one means of improving perceived flexibility.

Inventory service-levels in the customer supply chain

In this paper we consider an inventory location that serves downstream nodes (e. g. production processes, regional warehouses or customers) in a supply chain. It is pointed out, that the overall optimization of logistical processes should be based on the order delivery time as a critical unifying dimension. It is shown that the standard (\alpha-), (\beta-) and (\gamma)-service-levels used in inventory theory, when considered from the point of view of a downstream node in the supply chain, provide only limited information about the delay the orders observe. A procedure for the determination of the probability distribution of the order waiting time in a discrete time periodic (r,S)-inventory system is developed. Implications for the optimization of sub-processes in the supply chain are discussed. Key words: Inventory management - Service levels - Customer order waiting time - Supply chain optimization

A literature survey on planning and control of warehousing systems

We present a literature survey on methods and techniques for the planning and control of warehousing systems. Planning refers to management decisions that affect the intermediate term (one or multiple months), such as inventory management and storage location assignment. Control refers to the operational decisions that affect the short term (hours, day), such as routing, sequencing, scheduling and order-batching. Prior to the literature survey, we give an introduction into warehousing systems and a classification of warehouse management problems