Multi-Item Inventory Aggregation into Groups

The problem of grouping the many items in stock into a few groups with the provision of a common order cycle or common order quantity per group is modelled as a dynamic program. It is shown that by a simple reorganization of the stock items, the computation time of the dynamic program can be reduced to a manageable size. Further the order cycle grouping is shown to be, usually, superior to the order quantity grouping scheme. Also, the composition of the order cycle grouping is found to be remarkably close to that of the well known A/B/C system of stock control therby giving theoretical credence to that system.     

快速补货模式下的动态定价与库存联合策略

在供应有限的情况下,研究常规补货和快速补货下商品动态定价问题.首先,建立了动态规划模型,理论证明了最优库存策略是基于(s,S)策略下改进的基本库存策略.其次,提出了一种启发式策略求复杂系统的最优策略,启发式算法能够求出最优价格和最优库存水平.最后,数值算例研究表明,库存管理中采用快速补货提高了零售商的利润;初始库存水平越高零售商的利润越高.     

Non-Stationary Ordering Policies for Multi-Item Inventory Systems Subject to a Single Resource Constraint

This paper studies the multi-item inventory problem with a single constraint. Two well-known approaches to this problem are the Lagrangian method and the fixed-cycle approach. Both of these methods generate stationary ordering policies. A competing approach is presented here that generates non-stationary ordering policies, with order quantities that vary over time. These non-stationary policies are, in all cases, preferred to those generated by the Lagrangian approach, and in some cases preferred to those generated by the fixed-cycle approach. Computational results comparing the three methods are also given.     

An Optimal Method for a Deterministic Joint Replenishment Inventory Policy in Discrete Time

In this paper we derive an optimal solution to the multi-item single-supplier inventory problem with two types of set-up costs. In the case considered, replenishment opportunities are restricted to the beginning of the discrete time periods.     

An Optimal Heuristic For Coordinated Multi-Item Inventory Replenishments

The inventory control problem can be vastly simplified if the replenishments of inventory items are coordinated with one another. That is, whenever an item is replenished, n other items, where n is a decision variable, are also replenished. One way to ensure this would be to classify the inventory items into several groups with a common order interval for each group. In this paper we establish that the optimal groups will be consecutive by hD/A, where h, D and A are the holding cost, demand rate and set-up cost of an item respectively. Using this property of consecutiveness, we develop a fast converging heuristic to create m groups optimally, m = 2, 3,..., M. The heuristic is a substitute for the dynamic programme which would otherwise be necessary and it has the potential for nomographic applications.     

Inventory Replenishment Policies — Computational Solutions

Relatively minor changes in the assumptions associated with the classical deterministic models for inventory control can give rise to models which are difficult or impossible to analyse by analytical means.A low-cost computational procedure is outlined and applied to two such models associated with the no-shortage policy. The situations examined involve trends in demand and linear inflation in costs.     

Inventory Replenishment Policy for Increasing Demand

The Donaldson model for inventory replenishment is investigated for a general class of increasing demands. In particular, it is shown that the system of reorder times is uniquely specified and well-behaved when the demand f(t) is log-concave, i.e. the derivative of log f(t) is a decreasing function of time. In addition, a numerical procedure is outlined which will produce the set of optimal times at which to re-order, provided the demand f(t) is of sufficiently simple form, for example a simple power law or exponential demand.     

Inventory Replenishment Policy for Cyclic Demand

We consider optimal replenishment policy in the case of deterministic demand, with demand a known function which is periodic in time. The general formulation is a special case of Donaldson's fixed-horizon model, and two common situations are discussed: (i) demand varies sinusoidally; and (ii) there is an abrupt increase or decrease in demand, represented mathematically by a discontinuity in the demand rate.     

联合订货下基于ø-散度的多产品库存鲁棒优化模型

针对多产品联合库存决策问题,在市场需求不确定条件下,建立了考虑联合订货成本的多产品库存鲁棒优化模型。针对不确定市场需求,采用一系列未知概率的离散情景进行描述,给出了基于最小最大准则的鲁棒对应模型,并证明了(s,S)库存策略的最优性。进一步,在仅知多产品市场需求历史数据基础上,采用基于ø-散度的数据驱动方法构建了满足一定置信度要求的关于未知需求概率分布的不确定集。在此基础上,为获得(s,S)库存策略的相关参数,运用拉格朗日对偶方法将所建模型等价转化为易于求解的数学规划问题。最后,通过数值计算分析了Kullback-Leibler散度和Cressie-Read散度以及不同的置信水平下的多产品库存绩效,并将其与真实分布下应用鲁棒库存策略得到的库存绩效进行对比。结果表明,需求分布信息的缺失虽然会导致一定的库存绩效损失,但损失值很小,表明基于文中方法得到的库存策略能够有效抑制需求不确定性扰动,具有良好的鲁棒性。     

The Finite Horizon Trended Inventory Replenishment Problem With Shortages

A new type of replenishment policy is suggested for an inventory item having a finite shortage cost and linear trend in demand over a finite time horizon. The optimal solution of the suggested replenishment policy has a lower total cost as compared with the optimal solution for the traditional replenishment policies.     

Optimal Replenishment Strategy for Inventory Mechanism with Step-Shaped Demand

Journal of Optimization Theory and Applications - This paper extends the classical economic order quantity inventory model to that the planning horizon consists of two stages—a finite...     

A Simple Inventory Replenishment Policy for Demand with Uncertainty

Research indicates that the economic order quantity is preferred to alternative techniques because it is less nervous to forecast errors. This paper attempts to establish that no statistical relationship exists between the size of forecast error and the performance of some lot-size techniques. A heuristic rule is also presented for deterministic demand. The rule does well on the examples considered and is shown to be more stable than E.O.Q.     

A Simple Inventory Replenishment Decision Rule for a Linear Trend in Demand

We consider the situation of a deterministic demand pattern having a linear trend. The problem is to select the timing and sizes of replenishments so as to keep the total of replenishment and carrying costs as low as possible. An earlier developed heuristic for the general case of a deterministic, time-varying, demand pattern is specialized to the case of a linear trend. The simple decision rule is shown to lead to small cost penalties in two examples that have been exactly analyzed in an earlier article in this journal.     

Inventory Replenishment Policy for Linearly Increasing Demand Considering Shortages-An Optimal Solution

An optimal solution for inventory replenishment policy for an item having a deterministic demand pattern with linear increasing trend is developed considering shortages. Numerical examples are given to illustrate the results.     

Alternative Solution Methods for the Inventory Replenishment Problem under Increasing Demand

Two solution methods are offered for the no-shortage stock control problem under linearly increasing demand. The heuristic of the first "myopic" method is also exploited in the second method, which is based on a dynamic programming formulation. The DP formulation is not only trivial to solve computationally, but also offers ready-made sensitivity analyses. Unlike the other method, it also readily extends to more complicated models.     

Two New Heuristic Procedures for the Joint Replenishment Problem

In this paper, we develop two new efficient heuristic procedures for the joint replenishment problem. Each of the two heuristic procedures generates iteratively a near-optimal replenishment policy starting with ordering frequencies that are derived from the solution to a relaxed version of the joint replenishment problem. Both heuristic procedures are illustrated with an example problem involving five jointly ordered items. Seven more illustrative problems, taken from the joint replenishment problem literature, are also solved to assess the cost performance of the two heuristic procedures. They both provide the global optimal replenishment policies for all the illustrative problems.