Inventory management of multiple items with irregular demand: A case study

We present the case of a Greek commercial enterprise facing the problem of managing the inventories of thousands of different items, supplied by more than 20 European and Asian manufacturers and sold to a large number of different-type customers. A key feature of the problem is that the demand for the vast majority of items is intermittent and lumpy, thus not allowing the use of the usual normal or Poisson distributions. The paper describes the solutions given to several practical problems in the course of developing an easy-to-use yet effective and all-encompassing inventory control system. Emphasis is placed on the accurate modeling of demand by means of a gamma distribution with a probability mass at zero or a package Poisson distribution for very-slow-moving items. Using those models and simple quantitative tools we develop an efficient procedure for approximate but quite accurate determination of the base stock levels that achieve the desired fill rates in the proposed periodic review system. We briefly describe the computerized implementation of the new system and the very encouraging results.     

An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging

In the present paper, we extend Padmanabhan and Vrat's model by proposing a time-proportional backlogging rate to make the theory more applicable in practice. The existence and uniqueness of the solutions of the relevant systems are examined. Subsequently, a numerical example is presented to illustrate the application of developed model.     

Inventory management under highly uncertain demand

We show that base-stock levels first increase and then decrease as the standard deviation increases for a variety of non-negative random variables with a given mean and provide a distribution-free upper bound for optimal base-stock levels that grows linearly with the standard deviation and then remains constant.     

Inventory and sales effort management under unobservable lost sales

A retailer needs to make decisions regarding how much to order and how much sales effort to exert in an environment with uncertain demand. One intrinsic complexity in a typical retail environment is caused by the fact that the retailer can obtain information about demand only based on sales, as demand itself is unobservable. Taking a Bayesian approach, Lariviere and Porteus (1999) show that in such a setting a retailer should stock more to increase the probability of an exact demand observation. In this article, we extend their work by allowing the retailer to control both the stocking quantity and sales effort, which can be used to affect demand. We show that their insights with respect to information stalking carry over to this setting. In addition, our model allows gaining a better understanding of optimal sales effort strategies. We find that demand management has a dual role in supporting information gathering: while at the beginning of a product life cycle it is optimal to support learning effects by sharply reducing sales effort, at later stages of the product life cycle an aggressive strategy of increased promotional activities can be used to harvest the information gathered in earlier periods.     

Inventory model of deteriorating items on non-periodic discrete-time domains

In this paper, we demonstrate how to model a discrete-time dynamic process on a non-periodic time domain with applications to operations research. We introduce a discrete-time model of inventory with deterioration on domains where time points may be unevenly spaced over a time interval. We formalize the average cost function composed of storage, depreciation and back-ordering costs. The optimal condition is given to locate the optimal point that minimizes the average cost function. Finally, we present simulations to demonstrate how a manager can use this model to make inventory decisions.     

Inventory model with deteriorating items,ramp-type demand and partially backlogged shortages for a two warehouse system

In this paper, we consider a two warehouse inventory model, an owned one (OW) and a rented one (RW). Inventory deteriorates in the two warehouses at different constant rates, demand rate is a general ramp-type function of time and shortages are partially backlogged at a constant rate. Existence and uniqueness of the optimal solution is discussed. An algorithm is developed to obtain the overall optimal replenishment policy, which would enable the manager to decide upon the feasibility of renting a warehouse. The dynamics of the model and application of the algorithm are demonstrated through numerical examples. Sensitivity analysis is conducted with respect to model parameters and some important observations are drawn.     

Production under periodic demand update prior to a single selling season: A decomposition approach

This paper focuses on dynamic, continuous-time production control problems in the fashion industry. Similar to the classical news-vendor problem, we consider a single product-type and the cumulative demand for items is not known until the end of the production horizon and therefore must be forecasted. Since there are periodic updates before a single selling season, actual demand during a period of time can only be determined by the end of the period. If the overall demand is overestimated, excessive inventory holding and production costs are paid and surpluses are sold at low prices at the end of the production horizon. If it is under-estimated, then sales are lost. The objective is to dynamically determine production orders which minimize overall expected costs. Since the optimal feedback for such a problem is characterized by thresholds evolving with time and system states, there is a significant computational burden in determining them. With the aid of the variational analysis and a decomposition, we derive a closed-form solution for the thresholds. A numerical study carried out to compare the decomposition and straightforward simulation-based solutions indicates the high accuracy of the suggested approach while the computational burden is dramatically reduced.     

On “An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging” by Dye and Ouyang

In 2005, Dye and Ouyang proposed an EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging, and then established the unique optimal solution to the problem when building up inventory is not profitable. However, they did not provide the optimal solution to the problem when building up inventory is profitable. In this note, we establish an appropriate model in which building up inventory is profitable, and then provide an algorithm to find the optimal solution to the problem. A numerical example is used to illustrate the proposed model.     

Inventory management under date-terms supplier trade credit with stochastic demand and leadtime

Executives and academics alike are expressing increasing interest in supplier trade credit. We consider a form of credit known as ‘date-terms’ where the credit period extends to a specified date in the month following the invoice. We extend published research to consider both demand and supply uncertainty, employing a gamma distribution to model demand during the leadtime and reorder period. Taking an applied perspective, we evaluate four heuristics against an optimal solution for the case where pragmatic restrictions are placed on the reorder period. We evaluate how the reorder period and the performance of heuristics are affected by various environmental parameters (based on industrial data) and comment on the ramifications of this form of trade credit.     

Inventory model of deteriorated items with a constraint: A geometric programming approach

An inventory model for deteriorating items is built-up with limited storage space. Here, demand rate for the items is finite, items deteriorate at constant rates and are replenished instantaneously. Following EOQ model, the problem is formulated with and without truncation on the deterioration term and ultimately is converted to the minimization of a signomial expression with a posynomial constraint. It is solved by modified geometric programming (MGP) method and non-linear programming (NLP) method. The problem is supported by numerical examples. The results from two versions of the model (with and without truncation) and two methods (i.e. MGP and NLP) are compared.     

Asymptotic behavior of a differential operator with discontinuities at two points

In this paper, we study a Sturm–Liouville operator with eigenparameter‐dependent boundary conditions and transmission conditions at two interior points. By establishing a new operator A associated with the problem, we prove that the operator A is self‐adjoint in an appropriate space H, discuss completeness of its eigenfunctions in H, and obtain its Green function. Copyright © 2010 John Wiley & Sons, Ltd.     

Constrained Lot-Sizes under Conditions of Inventory Growth

When average aggregate inventory levels are constrained to equal a constant level over time, optimal lot sizes can be identified which strike a balance between holding costs and set-up costs among items which form the aggregate. However, when it is desirable to change aggregate inventory levels over time, assumptions implicit in the traditional formulation are violated. The procedure proposed generates lot sizes which are consistent not only with the current average aggregate inventory level but also with its projected growth over the planning horizon. Comparison is made to lot sizes generated by the misapplication of traditional lot sizing methods to the inventory growth situation.     

Inventory of damagable items with variable replenishment rate,stock-dependent demand and some units in hand

Items made of glass, ceramics, etc., break/get damaged during the storage due to the accumulated stress of heaped stock. For the first time, a deterministic inventory model of such a damagable item is developed with variable replenishment when both demand and damage rates are stock-dependent in polynomial form. Here replenishment rate for the first cycle is partly instantaneous and partly varies with demand. For the next cycle, the variable replenishment is augmented when the inventory level falls to Q₀, the instantaneous replenishment amount for the first cycle. After this, the cycle repeats itself. The amount, Q₀ is also here varied and the optimum Q₀ and Q (inventory level) are evaluated following the profit maximization principle in integral form. The model is illustrated numerically and sensitivity analyses are presented.     

Reflected backward stochastic differential equations with two barriers and Dynkin games under Knightian uncertainty

This paper is concerned with a class of reflected backward stochastic differential equations (RBSDEs in short) with two barriers. The first purpose of the paper is to establish existence and uniqueness results of adapted solutions for such RBSDEs. Most of existing results on adapted solutions for RBSDEs with two barriers are heavily based on either the Mokobodski condition or other restrictive regularity conditions. In this paper, the two barriers are modeled by stochastic differential equations with coefficients satisfying the local Lipschitz condition and the linear growth condition, which enables us to weaken the regularity conditions on the boundary processes. Existence is proved by a penalization scheme together with a comparison theorem under the Lipschitz condition on the coefficients of RBSDEs. As an application, it is proved that the initial value of an RBSDE with two barriers coincides with the value function of a certain Dynkin game under Knightian uncertainty.     

Inventory management of spare parts in an energy company

We address the problem of how to determine control parameters for the inventory of spare parts of an energy company. The prevailing policy is based on an (s, S) system subject to a fill rate constraint. The parameters are decided based mainly on the expert judgment of the planners at different plants. The company is pursuing to conform all planners to the same approach, and to be more cost efficient. Our work focuses on supporting these goals. We test seven demand models using real-world data for about 21?000 items. We find that significant differences in cost and service level may appear from using one or another model. We propose a decision rule to select an appropriate model. Our approach allows us to recommend control parameters for 97.9% of the items. We also explore the impact of pooling inventory for different demand sources and the inaccuracy arising from duplicate item codes.     

The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade credit in the supply chain management

Min et al. [1] (J. Min, Y.W. Zhou, J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Appl. Math. Model. 34 (2010) 3273–3285.) develop an inventory model for deteriorating items under stock-dependent demand and two-level trade credit. They provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions that could maximize the retailer’s average profit per unit time. Basically, their paper is correct and interesting. Recently, several researchers have been showing a huge interest in developing simple and easy to implement solution procedures in management science. Therefore this paper indicates that Min et al.’s solution procedure can be further improved and simplified. So, the main purpose of this paper is to present simple and easy to understand solution procedures to locate the optimal solutions of an inventory model that considers deteriorating items under stock-dependent demand and two-level trade credit.     

供应商管理库存的渠道利润优化分析

本文研究了供应链管理的渠道利润问题。对有确定需求、有初始库存和库存短缺的一种畅销商品,建立了供应商管理库存的渠道利润模型。通过对此模型的进一步分析,证明了在短期激励下供应商管理库存的渠道利润优于一般库存的渠道利润;也证明了在长期激励下,供应商管理库存可以产生比短期激励下更优的渠道利润,也优于一般库存的渠道利润。这一结果对于供应链环境下的库存管理在理论和工程上具有实际意义。     

不对称信息下的制造商——供应商库存博弈

在分析信息对称情况下制造商和供应商库存分散控制策略和集中控制策略的基础上 ,运用转移支付联盟博弈讨论了制造商和供应商库存协调策略 ,然后分三种情况探讨了不对称信息下供应商和制造商库存协调、协调的有效性以及达到双赢所要遵循的原则 .