Demand selection decisions for a multi-echelon inventory distribution system

In this paper, we study an integrated demand selection and multi-echelon inventory control problem that generalizes the classical deterministic single distribution centre (DC) multi-retailer model by incorporating demand selection decisions. In addition to the ordering and holding cost components, a concave operating cost of the DC and a capacity on the total market demand served are also considered. For given revenue and cost parameters, the problem is to determine which sets of demand to fulfill and which multi-echelon inventory control policy to implement so as to maximize the net profit. We show that the problem can be formulated as a nonlinear discrete optimization model. We analyse the structural properties of the model and, based on these, outline an approach to solve the model efficiently. We also present some interesting managerial insights obtained from the numerical experiments.     

Demand seasonality in retail inventory management

We investigate the value of accounting for demand seasonality in inventory control. Our problem is motivated by discussions with retailers who admitted to not taking perceived seasonality patterns into account in their replenishment systems. We consider a single-location, single-item periodic review lost sales inventory problem with seasonal demand in a retail environment. Customer demand has seasonality with a known season length, the lead time is shorter than the review period and orders are placed as multiples of a fixed batch size. The cost structure comprises of a fixed cost per order, a cost per batch, and a unit variable cost to model retail handling costs. We consider four different settings which differ in the degree of demand seasonality that is incorporated in the model: with or without within-review period variations and with or without across-review periods variations. In each case, we calculate the policy which minimizes the long-run average cost and compute the optimality gaps of the policies which ignore part or all demand seasonality. We find that not accounting for demand seasonality can lead to substantial optimality gaps, yet incorporating only some form of demand seasonality does not always lead to cost savings. We apply the problem to a real life setting, using Point-of-Sales data from a European retailer. We show that a simple distinction between weekday and weekend sales can lead to major cost reductions without greatly increasing the complexity of the retailer’s automatic store ordering system. Our analysis provides valuable insights on the tradeoff between the complexity of the automatic store ordering system and the benefits of incorporating demand seasonality.     

Profit maximization in an inventory system with time-varying demand,partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

     

Optimal dynamic pricing and inventory control with stock deterioration and partial backordering

This paper studies the optimal dynamic pricing and inventory control policies in a periodic-review inventory system with fixed ordering cost and additive demand. The inventory may deteriorate over time and the unmet demand may be partially backlogged. We identify two sufficient conditions under which (s,S,p) policies are optimal.     

Determining optimal order splitting and reorder level for N-supplier inventory systems

This paper considers multiple-supplier single-item inventory systems, where the item acquisition lead times of suppliers and demand arrival are random, and backorder is allowed. The acquisition takes place when the inventory level depletes to a reorder level, and the order is split among multiple suppliers. The acquisition lead times may have different distributions, the unit purchasing prices from suppliers may be different, and thus the order quantities for different suppliers may be different. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per unit time, consisting of the fixed ordering cost, procurement cost, inventory holding cost and shortage cost, is minimized. We develop a mathematical model describing the system in detail. We also conduct extensive numerical experiments to analyze the advantages and distinct characteristics of multiple-supplier systems.     

Joint pricing and inventory control with a Markovian demand model

We consider the joint pricing and inventory control problem for a single product over a finite horizon and with periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show the existence of an optimal (s, S, p)-type feedback policy for the additive demand model. We extend the model to the case of emergency orders. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing through numerical examples. The results indicate that it is more beneficial to implement dynamic pricing in a Markovian demand environment with a high fixed ordering cost or with high demand variability.     

Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost

This paper deals with an extended EOQ-type inventory model for a perishable product where the demand rate is a function of the on-hand inventory. The traditional parameters of unit item cost and ordering cost are kept constant; but the holding cost is treated as (i) a nonlinear function of the length of time for which the item is held in stock, and (ii) a functional form of the amount of the on-hand inventory. The approximate optimal solution in both the cases are derived. Computational results are presented indicating the effects of nonlinearity in holding costs.     

On a stochastic demand jump inventory model

This paper considers a Quasi-Variational Inequality (QVI) arising from a stochastic demand jump inventory model in a continuous review setting with a fixed ordering cost and where demand is made up of a deterministic part (which is a function of the stock level) punctuated by random jumps. Under some restrictions on the parameters, a solution to the QVI is found which corresponds to an (s,S) policy.     

Towards a normative model for inventory cost management in a generalized ABC classification system

This paper establishes a general ABC inventory classification system as the foundation for a normative model of the maintenance cost structure and stock turnover characteristics of a large, multi-item inventory system with constant demand. For any specified number of inventory classes, the model allows expression of the overall system combined ordering and holding cost in terms of (i) the re-ordering frequencies for the items in each inventory class and (ii) the inventory class structure, that is, the proportion of the total system's items that are in each inventory class. The model yields a minimum total maintenance cost function, which reflects the effect of class structure on inventory maintenance costs and turnover. If the Pareto curve (a.k.a. Distribution-by-value function) for the inventory system can be expressed (or approximated) analytically, the model can also be used to determine an optimal class structure, as well as an appropriate number of inventory classes. A special case of the model produces a simply structured, class-based ordering policy for minimizing total inventory maintenance costs. Using real data, the cost characteristics of this policy are compared to those of a heuristic, commonly used by managers of multi-item inventory systems. This cost comparison, expressed graphically, underscores the need for normative modelling approaches to the problem of inventory cost management in large, multi-item systems.     

On inventory problems with arbitrary cost pattern,demand pattern and demand distribution

A detailed analysis of inventory models without setup costs, arbitrary demand distribution and arbitrary demand and cost pattern is given. First it is shown that the corresponding one-period model without ordering costs may be reduced to another simpler one with appropriately modified demand distribution. Several representations are given for the modified demand distribution. As one of the main results this reduction turns out to be robust in most cases. In a final chapter the results are applied to the determination of an optimal policy for a class of N-period inventory models with convex holding-and shortage costs and without setup costs.     

Lead time and ordering cost reductions in continuous review inventory systems with partial backorders

This paper investigates the impact of ordering cost reduction on the modified continuous review inventory systems involving variable lead time with a mixture of backorders and lost sales. The objective is to simultaneously optimise the order quantity, ordering cost, reorder point and lead time. We first assume the lead time demand follows a normal distribution, then relax this assumption to consider the distribution free case where only the mean and variance of lead time demands are known. An algorithm procedure of finding the optimal solution is developed, and two numerical examples are given to illustrate the results.     

An inventory control problem for deteriorating items with back-ordering and financial considerations

This paper investigates the effects of time value of money and inflation on the optimal ordering policy in an inventory control system. We proposed an economic order quantity model to manage a perishable item over the finite horizon planning under which back-ordering and delayed payment are assumed. The demand and deterioration rates are constant. The present value of total cost during the planning horizon in this inventory system is modeled first, then a three phases solution procedure is proposed to derive the optimal order and shortage quantities, and the number of replenishment during the planning horizon. Finally, the proposed model is illustrated through numerical examples and the sensitivity analysis is reported to find some managerial insights.     

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.     

具有非线性采购成本库存控制问题的研究现状与挑战

库存管理是基于运筹学而发展起来的一门学科,并成为近几十年来运筹学和管理科学重要的研究领域之一。在库存系统中,采购成本是必不可少的成本之一,主要包含产品成本、运输成本、装卸成本等。现实中,采购成本依赖于采购量,且往往是采购量的非线性函数。介绍了几类常见的采购成本函数：依赖于采购量的固定成本、增量折扣、全量折扣、车载容量折扣和凸采购成本等。基于周期盘点库存模型和连续盘点库存模型,综述了带有这些非线性采购成本函数的库存模型研究进展。虽然经过了几十年的研究,但很多带有非线性采购成本的库存模型的最优采购策略因为其复杂性至今未能被完整刻画。通过综述来简单讨论该类问题的挑战和机会。     

An inventory system with unit demand and varying ordering levels

An inventory system with unit demand, varying ordering levels and random lead times is considered in this paper. Ordering level is determined by the number of demands during last lead time. The ordering quantity will be such as to bring back the inventory level to S at the ordering epoch. No backlog is permitted. The time dependent probability distribution of the inventory level is obtained. Correlation between the number of demands during a lead time and the length of the next inventory dry period is obtained and it is illustrated by an example.     

Dynamic inventory and pricing policy in a capacitated stochastic inventory system with fixed ordering cost

We study a dynamic inventory and pricing optimization problem in a periodic review inventory system with setup cost and finite ordering capacity in each period. We show that the optimal inventory control is characterized by an (s,s^′,p) policy in four regions of the starting inventory level.     

Analysis of a two-echelon inventory system with two supply modes

In this paper, we consider a serial two-echelon periodic review inventory system with two supply modes at the most upstream stock point. As control policy for this system, we propose a natural extension of the dual-index policy, which has three base-stock levels. We consider the minimization of long run average inventory holding, backlogging, and both per unit and fixed emergency ordering costs. We provide nested newsboy characterizations for two of the three base-stock levels involved and show a separability result for the difference with the remaining base-stock level. We extend results for the single-echelon system to efficiently approximate the distributions of random variables involved in the newsboy equations and find an asymptotically correct approximation for both the per unit and fixed emergency ordering costs. Based on these results, we provide an algorithm for setting base-stock levels in a computationally efficient manner. In a numerical study, we investigate the value of dual-sourcing in supply chains and illustrate that dual-sourcing can lead to significant cost savings in cases with high demand uncertainty, high backlogging cost or long lead times.     

Integrating inventory control and a price change in the presence of reference price effects: a two-period model

Demand and procurement planning for consumer electronics products must cope with short life cycles, limited replenishment opportunities and a willingness to pay that is influenced by past prices and decreases over time. We therefore propose the use of an integrated pricing and inventory control model with a two-period linear demand model, in which demand also depends on the difference between a price-history-based reference price and the current price. For this model we prove that the optimal joint pricing/inventory policy for the replenishment opportunity after the first period is a base-stock list-price policy. That is, stock is either replenished up to a base-stock level and a list-price is charged, or it is not replenished and a discount is given that increases with the stock-level. Furthermore, we use real-world cell phone data to study the differences between an integrated policy and traditional sequential optimization, where prices are initially optimized based on the expected demand and ordering cost, and the resulting demand distribution is used to determine an optimal inventory policy. Finally, we discuss possible extensions of the model.     

Dynamic realization games in newsvendor inventory centralization

Consider a set N of n (> 1) stores with single-item and single-period nondeterministic demands like in a classic newsvendor setting with holding and penalty costs only. Assume a risk-pooling single-warehouse centralized inventory ordering option. Allocation of costs in the centralized inventory ordering corresponds to modelling it as a cooperative cost game whose players are the stores. It has been shown that when holding and penalty costs are identical for all subsets of stores, the game based on optimal expected costs has a non empty core (Hartman et al. 2000, Games Econ Behav 31:26–49; Muller et al. 2002, Games Econ Behav 38:118–126). In this paper we examine a related inventory centralization game based on demand realizations that has, in general, an empty core even with identical penalty and holding costs (Hartman and Dror 2005, IIE Trans Scheduling Logistics 37:93–107). We propose a repeated cost allocation scheme for dynamic realization games based on allocation processes introduced by Lehrer (2002a, Int J Game Theor 31:341–351). We prove that the cost subsequences of the dynamic realization game process, based on Lehrer’s rules, converge almost surely to either a least square value or the core of the expected game. We extend the above results to more general dynamic cost games and relax the independence hypothesis of the sequence of players’ demands at different stages.     

A multi-agent inventory problem with general transportation costs

This paper addresses the cost allocation problem that arises from an inventory system with multiple item and several agents that place joint orders according to an EOQ policy. In this setting, the cost per a new order has two components: a fixed cost and a variable cost. We assume that the variable part is given by a general function, not necessarily additive. We obtain the optimal policy and we evaluate some proposals of allocation rule for the ordering costs.