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.     

基于(Q,r)补货策略的寄售库存模式研究

本文运用数学建模和数值分析的方法研究了基于(Q,r)补货策略的寄售库存模式中合同参数的优化问题。在该模式下,供应商确定Q、r值,并维持(z,Z)的库存水平,零售商对低于下限z或超过上限Z的库存收取罚金b。研究结果表明,零售商可以通过设置合理的罚金b来激励供应商选择合理的r和Q,使得最低的期望库存水平高于z,并且使成本达到最优。     

Stock Replenishment Quantities for Unbounded Linear Increasing Demand: An Interesting Consequence of the Optimal Policy

This paper shows that, with the exception of the first lot quantity, the E.O.Q. can be used for determining replenishment quantities, when demand is increasing linearly, with little cost penalty.     

Stock Control with Random Opportunities for Replenishment

In most stock control systems, stock is replenished by re-ordering either at regular intervals or upon depletion below an agreed level. Situations sometimes arise, however, in which replenishment tends to be governed by the incidence of external opportunities which occur at irregular intervals, usually as a result of a complex schedule of production or distribution. Conventional stock control procedures can then become difficult to operate effectively; this article discusses an alternative procedure which can be used in such circumstances, and shows how optimum control levels may be calculated.     

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.     

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.     

A New Optimal Algorithm for the Joint Replenishment Problem

In this paper, we propose a new optimal algorithm for the Joint Replenishment Problem. The proposed algorithm can be used to determine the optimal strict-cyclic policy, as well as the optimal among all cyclic policies for the joint replenishment problem. Computational experiments on randomly generated problems reveal that the proposed algorithm performs better than existing optimal algorithms for the problem.     

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.     

The Trended Inventory Lot Sizing Problem with Shortages Under a New Replenishment Policy

In the past few years, considerable attention has been given to the inventory lot sizing problem with trended demand over a fixed horizon. The traditional replenishment policy is to avoid shortages in the last cycle. Each of the remaining cycles starts with a replenishment and inventory is held for a certain period which is followed by a period of shortages. A new replenishment policy is to start each cycle with shortages and after a period of shortages a replenishment should be made. In this paper, we show that this new type of replenishment policy is superior to the traditional one. We further propose four heuristic procedures that follow the new replenishment policy. These are the constant demand approximation method, the equal cycle length heuristic, the extended Silver approach, and the extended least cost solution procedure. We also examine the cost and computation time performances of these heuristic procedures through an empirical study. The number of test problems solved to optimality, average and maximum cost deviation from optimum were used as measures of cost performance. The results of the 10 000 test problems reveal that the extended least cost approach is most cost effective.     

允许租用货栈的库存系统的最优进货策略

本文从实际背景出发，提出了允许租用货栈的库存系统的库存模型，在一般时变需求并允许短缺的假定下，得到了寻求该系统最优进货策略的一种交替逼近方法。并给出了数字例子。     

A Note on the Joint Replenishment Problem under Constant Demand

This note considers the joint replenishment inventory problem for N items under constant demand. The frequently-used cyclic strategy (T; k₁, …, k _N ) is investigated: a family replenishment is made every T time units and item i is included in each k _i th replenishment. Goyal proposed a solution to find the global optimum within the class of cyclic strategies. However, we will show that the algorithm of Goyal does not always lead to the optimal cyclic strategy. A simple correction is suggested.     

On the Joint Calculation of Safety Stocks and Replenishment Order Quantities

It has been well established that for optimum operation of a re-order level policy, re-order levels and replenishment order quantities should be jointly calculated. There exist many solutions to this stock control problem. A number of these involve approximations which simplify the mathematics of the problem but yield non-optimal solutions, while others raise the question of whether the additional computational effort required, due to mathematical complexity, is economically justified.This paper describes that if the lead time demand can be considered as normally distributed and lead time is constant, then it is possible to arrive at optimal values of safety stocks-consequently re-order levels-and order quantities, with minimum computational effort, through a nomogram which accomplishes a major part of the necessary computations.The flow chart of a program that can make the calculations is also presented.     

一类变质性物品在考虑信用期时的补货策略

随着人们物质生活的不断丰富,库存控制系统所处的环境变得既复杂又多变,光靠规模化的经营已经不能满足顾客的需要,经典的EOQ模型的订购批量解也与实际的最优值之间具有很大的差距.由次,本文修改了EOQ模型中的一些假设,在考虑信用期的情况下,研究了需求率为常数、物品存贮寿命为两参数维布尔分布的单一变质性物品在有限计划期内的补货策略,证明了最优补货策略的存在性及惟一性,同时给出了求解最优补货策略的算例,得到了应用更为广泛的结论.     

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.     

An Integrated Inventory-Routing System for Multi-item Joint Replenishment with Limited Vehicle Capacity

In this paper, we develop a mathematical programming approach for coordinating inventory and transportation decisions in an inbound commodity collection system. In particular, we consider a system that consists of a set of geographically dispersed suppliers that manufacture one or more non-identical items, and a central warehouse that stocks these items. The warehouse faces a constant and deterministic demand for the items from outside retailers. The items are collected by a fleet of vehicles that are dispatched from the central warehouse. The vehicles are capacitated, and must also satisfy a frequency constraint. Adopting a policy in which each vehicle always collects the same set of items, we formulate the inventory-routing problem of minimizing the long-run average inventory and transportation costs as a set partitioning problem. We employ a column generation approach to determine a lower bound on the total costs, and develop a branch-and-price algorithm that finds the optimal assignment of items to vehicles. We also propose greedy constructive heuristics, and develop a very large-scale neighborhood (VLSN) search algorithm to find near-optimal solutions for the problem. Computational tests are performed on a set of randomly generated problem instances.The work of this author was supported by a scholarship of the Faculty of Engineering of Ubonratchathani University, Ubonratchathani, Thailand., The work of this author was supported in part by the National Science Foundation under Grant No. DMI-0085682.     

通货膨胀对带有时变需求的变质性物品库存补充策略的影响

本文在考虑通货膨胀的情形下，建立了带有时变需求的变质性物品在有限计划期内的库存补充模型，提供了最优补充次数、最优补充周期长度以及各次补充的最优补充量的一种简单而有效的逼近方法，并用数学例子说明了该方法的实现过程．     

Optimum Ordering Policy for a Multi Item Single Supplier System

An algorithm is presented in this paper for determining the optimum ordering policy in a situation where a number of items are supplied by a single supplier. A problem involving 15 items, which are supplied by a single supplier, is solved for illustrating the recommended procedure.