基于排队的库存服务系统最优控制策略

研究一个连续盘点的(s,Q)补货的库存服务系统。基于排队理论建立库存水平状态平衡方程,并推导出库存水平稳态概率分布以及作为库存控制的系统稳态性能指标。以库存成本最小化为目标,构建服务水平约束的库存控制模型。针对模型的非线性约束与整数型变量的特征,采用一种改进的遗传算法(IGA)用于决策变量的寻优。数值实验表明,当目标服务水平大于库存系统内生的服务水平时,实施服务水平约束能够降低库存控制成本。     

Inventory rationing for the News-Vendor problem with a drop-shipping option

We consider a single-period inventory model for a bricks-and-clicks business. Store inventory can be used to fulfill both store demand and internet demand. Drop-shipping is used as an additional option for internet sale. We analyze two rationing policies for store inventory: a threshold policy and a fixed-portion policy. We formulate the expected profit for both and prove concavity. There exists an optimal order quantity for store inventory and an optimal stock rationing level below which the manager starts to use drop-shipping for internet demand. Numerical examples show that considering the rationing problem for the single-period inventory model, which is ignored in some earlier works, can result in remarkable differences.     

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.     

基于二层信用支付的变质物品库存模型

基于时变需求的库存问题一直是库存管理者关注的重点之一,大多数基于二层信用支付的库存模型都是假设需求率为常数.假设需求率是时间的指数函数,建立了二层信用支付条件下的变质物品库存模型,并证明了最优解是存在且唯一的,给出了确定最优补货策略的算法步骤,最后通过数值例子对主要参数进行了灵敏度分析.     

An optimal algorithm for repairable-item inventory system with depot spares

We consider the problem of determining the spare inventory level for a multiechelon repairable-item inventory system. Our model extends the previous results to the system, which has an inventory at the central depot, as well as at the bases. We have developed an algorithm to find the optimal spare inventory levels, which minimise the total expected cost and simultaneously satisfy a specified minimum service rate. The algorithm is illustrated using examples of various sizes.     

Optimal price and lot size determination for a perishable product under conditions of finite production, partial backordering and lost sale

The paper describes an EOQ model of a perishable product for the case of price dependent demand, partial backordering which depends on the length of the waiting time for the next replenishment, and lost sale. The model is solved analytically to obtain the optimal price and size of the replenishment. In the model, the customers are viewed to be impatient and a fraction of the demand is backlogged. This fraction is a function of the waiting time of the customers. In most of the inventory models developed so far, researchers considered that inventory accumulates at the early stage of the inventory and then shortage occurs. This type of inventory is called IFS (inventory followed by shortage) policy. In the present model we consider that shortage occurs before the starting of inventory. We have proved numerically that instead of taking IFS, if we consider SFI (shortage followed by inventory) policy, we would get better result, i.e., a higher profit. The model is extended to the case of non-perishable product also. The optimal solution of the model is illustrated with the help of a numerical example.     

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.     

Two substitutable perishable product disaster inventory systems

A disaster inventory system is considered in which two substitutable items are stored for disaster management. In the event of disaster management, a particular product may become stock-out and the situation warrants that a demand for the particular product during its stock-out period may be substituted with another available similar product in the inventory. From the utility point of view, continuous review inventory models are quite appropriate in disaster inventory management. In this paper, a continuous review two substitutable perishable product disaster inventory model is proposed and analyzed. Since the inventory is maintained for disaster management, an adjustable joint reordering policy for replenishment is adopted. There is no lead time and the replenishment is instantaneous. For this model, some measures of system performance are obtained. The stationary behavior of the model is also considered. Numerical examples are also provided to illustrate the results obtained.     

An integrated model for warehouse and inventory planning

The purpose of this article is to evaluate the value of integrating tactical warehouse and inventory decisions. Therefore, a global warehouse and inventory model is presented and solved. In order to solve this mathematical model, two solution methodologies are developed which offer different level of integration of warehouse and inventory decisions. Computational tests are performed on a real world database using multiple scenarios differing by the warehouse capacity limits and the warehouse and inventory costs. Our observation is that the total cost of the inventory and warehouse systems can be reduced drastically by taking into account the warehouse capacity restrictions in the inventory planning decisions, in an aggregate way. Moreover additional inventory and warehouse savings can be achieved by using more sophisticated integration methods for inventory and warehouse decisions.     

电子商务环境下考虑退货的选址库存问题模型与算法

选址库存问题(location inventory problem, LIP)是物流系统集成的经典问题之一,也是企业需要面对的管理决策难题。本文考虑在电子商务环境下无质量缺陷的退货商品可简单再包装后重新进入销售市场这一现实情况,对设施选址和库存控制进行集成优化,构建随机需求下有退货的LIP模型。针对此问题求解的复杂性,设计了改进的自适应混合差分进化算法对模型进行整体求解。最后,通过多组算例验证了模型和算法的实用性和优越性,可为设施选址、库存控制和商品配送回收决策提供重要参考依据。     

基于D-S理论的延期支付与存货质押业务决策模型

由于市场的不确定性,延期支付货款和存货质押融资中存在诸多不确定因素,使得资金需求企业难以做出有效的选择。针对此问题,从资金需求企业利润最大化的角度出发,首先分别给出了延期支付和存货质押两种业务下的企业利润模型,进而基于D-S理论建立了两种业务的决策模型。该模型以存货质押和延期支付业务下企业利润差额为目标函数,根据证据推理,以信任函数和似然函数构造出利润差额的上下界概率分布,并据此给出两种业务的决策依据。算例分析表明,对资金需求企业来说,存货质押融资业务并不一定优于延期支付,在特定的市场环境下,需要利用本文提出的模型进行定量计算,从而做出最优的选择。     

On the effect of centralisation on expected profits in a multi-location Newsboy problem

This paper is a multi-location, single-period, single-product inventory problem with an opportunity for centralisation. The decentralised model in which a separate inventory is kept at every location is compared to the centralised system in which the demands are satisfied from one central warehouse. The two systems are then compared when excess demands are penalised and lost, and in the more general case where a portion or all of the excess demand at a location may be reallocated among other locations with the remaining inventory. The revenue, salvage, cost, and penalty functions at each location are assumed to be identical. Expected profits are evaluated and conditions under which the centralised model outperforms the decentralised one are derived.     

Optimal inventory policy for specialty chemical products in multiple packages

Many products are inventoried and sold in multiple outer packages, which causes the manufacturer or distributor to maintain a segmented inventory. Oftentimes, this scenario leads to shortages in some packages and over-stock in other package types. The shortages are usually linked to specific shortage costs, and the over-stock is always associated with some sort of unnecessary holding cost that either erodes profit margins or results in increased costs for the consumer. In this paper, the inventory policy for a specialty chemical manufacturer's cleaner, which is inventoried in four unique packages, is studied. A mathematical model is developed to account for the costs associated with initial procurement, holding and repackaging (shortage), which are the primary costs associated with the inventory system. Based upon this model, an optimal inventory policy is generated that reduces the need for repackaging, without requiring a prohibitive amount of safety stock. A specific historical case is summarized, and the results of this example are compared with the results that the new inventory policy would have produced, given the same circumstances.     

A novel mathematical inventory model for growing-mortal items (case study: Rainbow trout)

Unlike the extensive inventory models for both ameliorating and deteriorating items, incorporating some specific features of these products have mostly been neglected. To fill this research gap, providing an appropriate mathematical inventory model for both ameliorating and deteriorating items is of paramount importance. In this regard, this paper proposes a novel mathematical inventory model for products called growing-mortal items in a two-echelon supply chain consisting of one supplier and one farmer. The proposed inventory model is more precise than analogous inventory models due to the fact that the specific growth function for the item is considered as well as mortality rate. As a case study, the model is applied to rainbow trout, which can be used for other types of growing-mortal items. Moreover, a feeding function is first-ever proposed for rainbow trout regarding the case study. The goal of this paper is to study the growth period in the supplier and then in the farmer sites to maximize the profit of the supplier as a leader and farmer as a follower under a Stackelberg game. To demonstrate how to reduce the inventory system costs by two coordination mechanisms, namely revenue-sharing and revenue and cost sharing, the model is solved under centralized and decentralized cases. Finally, sensitivity analysis on key parameters is also conducted to derive some managerial insights.     

Integrated inventory model with quantity discount and price-sensitive demand

Quantity discount has been a subject of study for a long time; however, little is known about its effect on integrated inventory models when price-sensitive demand is placed. The objective of this study is to find the optimal pricing and ordering strategies for an integrated inventory system when a quantity discount policy is applied. The pricing strategy discussed here is one in which the vendor offers a quantity discount to the buyer. Then, the buyer will adjust his retail price based on the purchasing cost, which will influence the customer demand as a result. Consequently, an integrated inventory model is established to find the optimal solutions for order quantity, retail price, and the number of shipments from vendor to buyer in one production run, so that the joint total profit incurred has the maximum value. Also, numerical examples and a sensitivity analysis are given to illustrate the results of the model.     

Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory

Marketing researchers and practitioners have long recognized the demand of many retail items is proportional to the amount of inventory displayed. Recently, two distinct types of inventory control models reflecting this relationship have appeared in the literature, models in which the demand rate of an item is a function of the initial inventory level and those in which it is dependent on the instantaneous inventory level. We present a comprehensive overview of this literature and demonstrate the equivalence of the two types of models through the use of a simple, periodic-review model. An alternative approach to sensitivity analysis for inventory models with inventory-level-dependent demand is also presented.     

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.     

An Integrated Inventory Model for a Single Product System

In this paper, an inventory model is given which unifies the inventory problem of raw materials and the finished product for a single product manufacturing system. The product is manufactured in batches and the raw materials are obtained from outside suppliers. The objective is to minimize the total variable costs of the system.     

面向两类客户的双渠道采购库存控制策略

采用排队分析技术,构建基于利润最大化的库存控制模型来考察零售商面向两类客户需求的环境下,双渠道采购库存控制策略.首先,建立了库存水平状态稳态概率分布的平衡方程,并推导出其稳态概率分布以及作为构建系统利润函数的稳态性能指标.然后,建立系统利润最优化模型,并设计改进的遗传算法.最后,通过数值实验考察系统库存控制策略以及参数的敏感性.     

随机补货间隔且需求依赖库存水平的库存控制模型

定期补货库存模型在实践中被广泛使用,尤其是在单一供应商中购买多种不同产品的库存系统中更为常见.然而,大多数定期补货库存模型都假设补货的时间间隔是恒定不变的.但在实践中,补货的时间间隔也可能是一个随机的时间长度.提出了一个随机补货时间间隔和需求依赖于当前展示库存水平的库存控制模型,且补货间隔服从指数分布和均匀分布,同时允许短缺发生并且短缺量部分延期供给,并研究了模型最优解的存在性与唯一性.最后,给出了数值算例来说明模型在实际中的应用.