Inventory allocation and shipping when demand temporarily exceeds production capacity

We address the concept of an integrated inventory allocation and shipping model for a manufacturer with limited production capacity and multiple types of retailers with different backorder/waiting and delivery costs. The problem is to decide how to allocate and deliver produced items when the total retailer demand exceeds the production capacity, so that total retailer backorder and delivery costs are minimized. Our analytical model provides optimal allocation and shipping policies from the manufacturer’s viewpoint. We also investigate the allocation strategy of a manufacturer competing with other retailers to directly sell to end consumers.     

An inventory sharing and allocation method for a multi-location service parts logistics network with time-based service levels

We consider a model to allocate stock levels at warehouses in a service parts logistics network. The network is a two-echelon distribution system with one central warehouse with infinite capacity and a number of local warehouses, each facing Poisson demands from geographically dispersed customers. Each local warehouse uses a potentially different base stock policy. The warehouses are collectively required to satisfy time-based service targets: Certain percentages of overall demand need to be satisfied from facilities within specified time windows. These service levels not only depend on the distance between customers and the warehouses, but also depend on the part availabilities at the warehouses. Moreover, the warehouses share their inventory as a way to increase achieved service levels, i.e., when a local warehouse is out of stock, demand is satisfied with an emergency shipment from another close-by warehouse. Observing that the problem of finding minimum-cost stock levels is an integer non-linear program, we develop an implicit enumeration-based method which adapts an existing inventory sharing model from the literature, prioritizes the warehouses for emergency shipments, and makes use of a lower bound. The results show that the proposed inventory sharing strategy results in considerable cost reduction when compared to the no-sharing case and the method is quite efficient for the considered test problems.     

Optimal lateral transshipment policies for a two location inventory problem with multiple demand classes

We consider an inventory model for spare parts with two stockpoints, providing repairable parts for a critical component of advanced technical systems. As downtime costs for these systems are expensive, ready–for–use spare parts are kept in stock to be able to quickly respond to a breakdown of a system. We allow for lateral transshipments of parts between the stockpoints upon a demand arrival. Each stockpoint faces demands from multiple demand classes. We are interested in the optimal lateral transshipment policy. There are three ways in which a demand can by satisfied: from own stock, via a lateral transshipment, or via an emergency procedure. Using stochastic dynamic programming, we characterize and prove the structure of the optimal policy, that is, the policy for satisfying the demands which minimizes the average operating costs of the system. This optimal policy is a threshold type policy, with state-dependent thresholds at each stockpoint for every demand class. We show a partial ordering in these thresholds in the demand classes. In addition, we derive conditions under which the so-called hold back and complete pooling policies are optimal, two policies that are often assumed in the literature. Furthermore, we study several model extensions which fit in the same modeling framework.     

Stock optimization for service differentiated demands with fill rate and waiting time requirements

We develop a computationally efficient optimization procedure to optimize stock and rationing levels for a model consisting of a single product with two priority–demand classes, given by mutually independent, stationary, Poisson demand processes. Each priority class has its own service levels requirements, defined by the class-specific fill rate and expected waiting-time levels. Order lead times are independent and identically distributed random variables. This is the first study in this setting to consider both waiting-time constraints along with fill rate requirements.     

Analytical models for supplier selection and order quantity allocation

In the literature, decision models and techniques for supplier selection do not often consider inventory management of the items being purchased as part of the analysis. In this article, two mixed integer nonlinear programming models are proposed to select the best set of suppliers and determine the proper allocation of order quantities while minimizing the annual ordering, inventory holding, and purchasing costs under suppliers’ capacity and quality constraints. The first model allows independent order quantities for each supplier while the second model restricts all order quantities to be of equal size, as it would be required in a multi-stage (supply chain) inventory model. Illustrative examples are used to highlight the advantages of the proposed models over a previous model introduced in the literature.     

Modelling imperfect advance demand information and analysis of optimal inventory policies

We consider an inventory control problem where it is possible to collect some imperfect information on future demand. We refer to such information as imperfect Advance Demand Information (ADI), which may occur in different forms of applications. A simple example is a company that uses sales representatives to market its products, in which case the collection of sales representatives’ information as to the number of customers interested in a product can generate an indication about the future sales of that product, hence it constitutes imperfect ADI. Other applications include internet retailing, Vendor Managed Inventory (VMI) applications and Collaborative Planning, Forecasting, and Replenishment (CPFR) environments. We develop a model that incorporates imperfect ADI with ordering decisions. Under our system settings, we show that the optimal policy is of order-up-to type, where the order level is a function of imperfect ADI. We also provide some characterizations of the optimal solution. We develop an expression for the expected cost benefits of imperfect ADI for the myopic problem. Our analytical and empirical findings reveal the conditions under which imperfect ADI is more valuable.     

A continuous approximation approach for the integrated facility-inventory allocation problem

In today’s retail business many companies have a complex distribution network with several national and regional distribution centers. This article studies an integrated facility location and inventory allocation problem for designing a distribution network with multiple distribution centers and retailers. The key decisions are where to locate the regional distribution centers (RDCs), how to assign retail stores to RDCs and what should be the inventory policy at the different locations such that the total network cost is minimized. Due to the complexity of the problem, a continuous approximation (CA) model is used to represent the network. Nonlinear programming techniques are developed to solve the optimization problems. The main contribution of this work lies in developing a new CA modeling technique when the discrete data cannot be modeled by a continuous function and applying this technique to solve an integrated facility location-allocation and inventory-management problem. Our methodology is illustrated with the network from a leading US retailer. Numerical analysis suggests that the total cost is significantly lower in the case of the integrated model as compared with the non-integrated model, where the location-allocation and inventory-management problems are considered separately. This paper also studies the effects of changing parameter values on the optimal solutions and to point out some management implications.     

Cooperation and game-theoretic cost allocation in stochastic inventory models with continuous review

We study cooperation strategies for companies that continuously review their inventories and face Poisson demand. Our main goal is to analyze stable cost allocations of the joint costs. These are such that any group of companies has lower costs than the individual companies. If such allocations exist they provide an incentive for the companies to cooperate.     

A joint optimisation model for inventory replenishment,product assortment,shelf space and display area allocation decisions

In this paper, we propose an optimisation model to determine the product assortment, inventory replenishment, display area and shelf space allocation decisions that jointly maximize the retailer’s profit under shelf space and backroom storage constraints. The variety of products to be displayed in the retail store, their display locations within the store, their ordering quantities, and the allocated shelf space in each display area are considered as decision variables to be determined by the proposed integrated model. In the model formulation, we include the inventory investment costs, which are proportional to the average inventory, and storage and display costs as components of the inventory costs and make a clear distinction between showroom and backroom inventories. We also consider the effect of the display area location on the item demand. The developed model is a mixed integer non-linear program that we solved using LINGO software. Numerical examples are used to illustrate the developed model.     

Optimal replenishment policies for deteriorating items with stock sensitive demand under two-level trade credit and limited capacity

Recently, Min et al. [18] established an inventory model for deteriorating items under stock-dependent demand and two-level trade credit and obtained the optimal replenishment policy. Their analysis imposed a terminal condition of zero ending-inventory. However, with a stock-dependent demand, it may be desirable to order large quantities, resulting in stock remaining at the end of the cycle, due to the potential profits resulting from the increased demand. As a result, to make the theory more applicable in practice, we extend their model to allow for: (1) an ending-inventory to be nonzero, (2) a maximum inventory ceiling to reflect the facts that too much stock leaves a negative impression on the buyer and the amount of shelf/display space is limited.     

The newsvendor problem: Review and directions for future research

In this paper, we review the contributions to date for analyzing the newsvendor problem. Our focus is on examining the specific extensions for analyzing this problem in the context of modeling customer demand, supplier costs, and the buyer risk profile. More specifically, we analyze the impact of market price, marketing effort, and stocking quantity on customer demand; how supplier prices can serve as a coordination mechanism in a supply chain setting; integrating alternative supplier pricing policies within the newsvendor framework; and how the buyer’s risk profile moderates the newsvendor order quantity decision. For each of these areas, we summarize the current literature and develop extensions. Finally, we also propose directions for future research.     

Coordination mechanism for capacity reservation by considering production time,production rate and order quantity

In this paper we study the coordination of a dyadic supply chain producing a high-tech product by contracts. The product has a short life cycle and the buyer faces stochastic demands during the selling period. We consider the production time, which causes the inventory costs on supplier’s side. As the supplier builds production capacity in advance, the production rate is limited to the capacity created during the production time. In addition, we take into account the inventory cost and operational cost for the buyer. We examine the model under both full information and partial information updating situations, and propose a coordinating contract for each case. Our analysis includes the study of members’ decisions under both forced and voluntary compliance regimes. Numerical results are presented to provide more insights into the models developed and the mechanisms proposed.     

Revenue management for a supply chain with two streams of customers

In this paper, we consider revenue management for a service supply chain with one supplier and one retailer. The supplier has a limited capacity of a perishable product and both the supplier and the retailer face customers. Each customer may choose to buy a product from either the supplier or the retailer by considering prices and the cost associated with switching. For the centralized model, the supplier determines the selling prices for both herself and the retailer, and the retailer simply collects a commission fee for each product sold. We derive monotone properties for the revenue functions and pricing strategies. Further, we show that the commission fee increases the retailer’s price while decreasing the supplier’s and leads to efficiency loss of the chain. For the decentralized decision-making model, the supplier and the retailer compete in price over time. Two models are considered. In the first, the retailer buys products from the supplier before the selling season and in the second the retailer shares products with the supplier in retailing. For both models, we discuss the existence of the equilibrium and characterize the optimal decisions. Numerical results are presented to illustrate properties of the models and to compare the supply chain performance between the centralized and the decentralized models.     

Optimal model for warehouse location and retailer allocation

Warehouse location and retailer allocation is a high‐level strategic decision problem that is commonly encountered by logisticians and supply chain managers, especially during the supply chain design phase. Considering the product distribution cost and warehouse capital cost trade‐offs, this paper models the warehouse location and retailer allocation problem as a 0–1 integer programming problem and provides an efficient two‐stage set covering heuristic algorithm to solve large‐sized problems. Finally, concluding remarks and some recommendations for further research are also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

基于易逝品需求信息更新的零售商订货策略

供应商为了更好地安排生产计划,降低生产成本,为零售商提供两次订货机会,零售商如何根据供应商提供的订货条件进行合理订货.运用贝叶斯分析的理论建立数学模型,研究了在不同的批发价格下顾客需求信息更新的易逝品的零售商订货策略,扩展了已有的结果并且修正了部分结果.     

Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand

Several leading manufacturers recently combined the traditional retail channel with a direct online channel to reach a wider range of customers. We examine such a dual-channel supply chain under price and delivery-time dependent stochastic customer demand. We consider five decision variables, the price and order quantity for both the retail and the online channels and the delivery time for the online channel. Uncertainty frequently arises in both retail and online channels and so additional inventory management is required to control shortage or overstock and that has an effect on the optimal order quantity, price, and lead time. We developed mathematical models with the profit maximization motive. We analyze both centralized and decentralized systems for unknown distribution function of the random variables through a distribution-free approach and also for known distribution function. We examine the effect of delivery lead time and customers’ channel preference on the optimal operation. For supply chain coordination a hybrid all-unit quantity discount along a franchise fee contract is used. Moreover, we use the generalized asymmetric Nash bargaining for surplus profit distribution. A numerical example illustrates the findings of the model and the managerial insights are summarized for centralized, decentralized, and coordinated scenarios.     

Service and cost benefits through clicks-and-mortar integration: Implications for the centralization/decentralization debate

Traditional “Brick-and-Mortar” operations face the challenge of adapting to a new set of competitive rules made necessary by consumers who want the option of ordering electronically via the Internet. To satisfy these customers, firms must develop strategies that integrate their standard retail in-store channel with this relatively new on-line channel. Therefore, this research is designed to provide insights into supply chain inventory management strategies relevant to “Clicks-and-Mortar” firms trying to satisfy both on-line and in-store sales. Specifically, this work considers the total cost implications of various inventory allocation strategies while maintaining target customer service levels. Analysis focuses on the development of models capable of handling new operating strategies made possible by electronic commerce. The implications of inventory risk pooling are considered in depth, revealing the existence of characteristics that determine whether completely centralized or decentralized policies are preferable.     

A serial inventory system with supplier selection and order quantity allocation

Given the prevalence of both supplier selection and inventory control problems in supply chain management, this article addresses these problems simultaneously by developing a mathematical model for a serial system. This model determines an optimal inventory policy that coordinates the transfer of items between consecutive stages of the system while properly allocating orders to selected suppliers in stage 1. In addition, a lower bound on the minimum total cost per time unit is obtained and a 98% effective power-of-two (POT) inventory policy is derived for the system under consideration. This POT algorithm is advantageous since it is simple to compute and yields near optimal solutions.     

A dynamic model for optimal design quality and return policies

A clearly explained and generous return policy has been established as a competitive weapon to enhance sales. From the firm’s point of view, a generous return policy will increase sales revenue, but will also increase cost due to increased likelihood of return. Design quality of the product has been used as a competitive weapon for a long time. This paper recognizes the relationship between design quality and price of the product, and the firm’s return policy. Quality level in the product would influence the amount of return directly. When the product quality is higher, the customer satisfaction rate will increase and the probability of return will decrease. We develop a profit-maximization model to jointly obtain optimal policies for the product quality level, price and the return policy over time. The model presented in this paper is dynamic in nature and considers the decisions as the product moves through the life cycle. We obtain a number of managerial guidelines for using marketing and operational strategy variables to obtain the maximum benefit from the market. We mention several future research possibilities.