一个带有增加量价格折扣的两货栈库存模型

已有的确定性两货栈(其中一个是自己货栈(OW);另一个是租用货栈(RW))库存模型通常不考虑增加量价格折扣,然而在实际生活中,增加量价格折扣却是促使库存管理者加大订货量的一个重要原因.本文通过考虑增加量价格折扣而将两货栈系统作了进一步扩展,在采用间隔式运输模式运送RW的物品到OW的情形下,建立了一个带有增加量价格折扣并允许短缺的两货栈库存模型,提供了一种寻求最优库存策略的简单方法.     

Joint Price and Lot-Size Determination When Supplier Offers Incremental Quantity Discounts

This paper considers the joint pricing and the lot-size determination problem faced by a retailer when he purchases a product for which the supplier offers incremental quantity discounts. Two common demand functions are considered: (1) the constant price-elasticity function, and (2) the linear function. A procedure is provided for each case for calculating the optimal price and the lot-size.     

A Non-Linear Procurement Model with Quantity Discounts

This paper presents a procurement model for a multinational oil company with affiliate plants located worldwide. The proposed model uses a quantity discount relationship to reduce the total procurement cost. We use a non-linear programming method to solve the model and make comparisons with the current approach used by the oil company. The proposed approach has several distinct advantages: assured minimum cost, ease of data management, flexibility in design, and accuracy in results.     

An Algorithm for Selecting Quantity Discounts from Realistic Schedules

Consideration of bounds, discontinuities and the integrality of decision variables is often helpful for responding to many practical requirements. Using the case of quantity discounting as an example, it is shown why the above considerations add realism to a model, and how they may be incorporated in the solution procedure. The bounds on the order quantity are fulfilled by establishing suitable stopping rules, while gaps in order quantities are resolved by modifying the input data. As for integrality, a result is established which shows that the feasible points for the integer optimum can be obtained by suitably rounding those for the continuous optimum. A comprehensive algorithm containing these features is proposed, and analytical proofs of the results are included.     

时值与增加量折扣并允许短缺的变质性物品的EOQ模型(英)

本文在考虑资金时值和增加量折扣的情形下，讨论了允许短缺的变质性物品在有限计划期内的经济批量问题，提供了寻求最优计货次数以及各次订货的最优批量和最优时刻的一个简单的一维方法，并出示了一个数字例子来说明本模型及其求解过程．     

An exact algorithm for the Capacitated Total Quantity Discount Problem

In this paper we analyze the procurement problem of a company that needs to purchase a number of products from a set of suppliers to satisfy demand. The suppliers offer total quantity discounts and the company aims at selecting a set of suppliers so to satisfy product demand at minimum purchasing cost. The problem, known as Total Quantity Discount Problem (TQDP), is strongly NP-hard. We study different families of valid inequalities and provide a branch-and-cut approach to solve the capacitated variant of the problem (Capacitated TQDP) where the quantity available for a product from a supplier is limited. A hybrid algorithm, called HELP (Heuristic Enhancement from LP), is used to provide an initial feasible solution to the exact approach. HELP exploits information provided by the continuous relaxation problem to construct neighborhoods optimally searched through the solution of mixed integer subproblems. A streamlined version of the proposed exact method can optimally solve in a reasonable amount of time instances with up to 100 suppliers and 500 products, and largely outperforms an existing approach available in the literature and CPLEX 12.2 that frequently runs out of memory before completing the search.     

The Role of Quantity Discounts in the Presence of Heterogeneous Buyers

In this paper we develop a model to examine the role of quantity discounts in synchronizing production and order cycles for a system consisting of one manufacturer and two heterogeneous buyers. The model developed can serve as a guideline for the manufacturer and the buyers as how to integrate their decisions to achieve higher benefits. The numerical examples indicate that the benefit of synchronization decreases with the degree of heterogeneity of the buyers. The conditions under which it is profitable for the manufacturer to synchronize with the heterogeneous buyers are demonstrated through numerical examples.     

Economic Order Quantity and Quantity Discounts under Date-terms Supplier Credit: A Discounted Cash Flow Approach

This paper examines economic order quantity and optimal order quantity under both all-units and incremental-quantity discounts when purchase cost, order cost, and carrying cost are all incurred on date-terms supplier credit. Payment dates for the three cost components need not be the same. The traditionally-used periodic-cost minimization methodology which is insensitive to differences in the timing of various within-period cash flows is replaced with a discounted cash flow methodology. Differences in the characteristics of day-terms and date-terms solutions to the quantity discount case are high-lighted.     

基于数量折扣合同和缺货损失的EOQ模型的改进

经济订购批量模型假定需求率、单位持有成本、订货成本为常数下得到总成本最低的订购批量,这些参数常数化的假设在现实中通常难以满足.假定需求和订货费为不确定的、库存成本包括年固定成本(与订货量无关)和年可变成本(与订货量有关),用三角模糊数表示年需求和订货费,通过引入数量折扣合同来量化单位产品进价,分别在不允许缺货和考虑缺货损失两种情况下得到最佳订货量.最后的算例表明了模型的合理性.     

有供应方限制的临时价格折扣与最优存贮模型

供应方提供临时价格折扣，一般都附带特别定货量限制。购买方可在所提供折扣价格条件下从有限种订货量中选择最小的订货量，但不一定是最优订货量。本文提出有供应方限制的临时价格折扣条件下的最优存贮模型和订货策略。并给出应用实例。     

需求随价格变化的具有折扣的易变质物品的库存模型

本文研究了在需求随价格变化及物品易变质的条件下，当供应商给予数量折扣时的库存问题。证明了当供应商给予数量折扣时，零售商的需求量是增大的，并给出了供应商给予数量折扣时零售商的订货量和订货周期的计算方法。对物品变质率和需求价格敏感系数对零售商的订货量、订货周期、出售价格和单位时间利润的影响进行了数值分析，并给出了数值算例。     

含模糊缺陷率且允许缺货的EOQ模型研究

生产系统不完善、自然灾害、运输破损等因素对传统EOQ模型中产品质量100%合格的假设提出了巨大的挑战.本文研究了模糊环境中产品存在质量缺陷情况下允许缺货的库存模型,运用更为一般的LR型模糊数表示缺陷率、缺货成本、订货成本、需求等可能出现不确定情况的参数,建立经济订货批量模型,并运用符号距离法对模型进行反模糊化,确定了使总利润最大化的最优订货批量.最后利用实验仿真验证了模型,分析并揭示了模糊缺陷率等因素对经济订货批量的影响.     

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.     

Rounding Procedures for the Discrete Version of the Capacitated Economic Order Quantity Problem

The capacitated Economic Order Quantity problem (capacitated EOQ) is a well-known problem where products have to be shipped between two points with a vehicle of given capacity. Each shipment has a fixed cost, independent of the shipped quantity, and an inventory cost is generated in the two points. The problem consists in finding the optimal time between consecutive shipments, which minimizes the total cost. The problem is a capacitated variant of the EOQ problem and has a closed form solution. Since such solution is often irrational, it is often rounded to an integer value. In this paper we investigate the errors which are generated by rounding procedures to integer and powers-of-two values. We show that, although in the worst case a tight general relative error of 2 is generated by all the considered rounding procedures, the procedure which rounds to the best between the lower and upper values (integer or powers-of-two) has a performance of $\frac{1}{2}$ ( $\sqrt 2 + 1/\sqrt 2 $ )≈1.06 on classes of instances of high practical relevance.     

损失制库存系统中最优订货量的若干分析

有损失制库存系统中的最优订货问题，一直是供应链管理中的一个重点和难点；本文主要研究两阶段损失制库存系统在总费用最小化的目标下；各阶估贩最优订货量大小，最终给出了第一阶段最优订货量的取值范围和第二阶段中最优订货量的精确表达式，以及当系统参数变动时，订货量的变化情况。     

Capacitated transit assignment with loading priorities

In a transit network involving vehicles with rigid capacities, we advocate the use of strategies for describing consumer behavior. At each boarding node, a user sorts the transit lines in decreasing order of preference, and boards the first vehicle in this list whose residual capacity is nonzero. Since a users position in the queue varies from day to day, the delay experienced is stochastic. This leads to an equilibrium problem where, at a solution, users are assigned to strategies that minimize their expected delay. This situation is formulated as a variational inequality, whose cost mapping is discontinuous and strongly asymmetric, due to the priority of current passengers over incoming users. We prove that the solution set is nonempty and provide numerical results obtained by an efficient solution algorithm.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Fonds pour la formation de chercheurs et laide à la recherche (FCAR).Mathematics Subject Classification (2000):20E28, 20G40, 20C20Accepted: December 20, 2003     

Capacitated Warehouse Location with Concave Costs

The mixed integer-linear models that have been used in most analyses of warehouse location problems fail to capture the potential operating efficiencies associated with large scale facilities. This paper presents an algorithm for finding a minimal cost warehouse system design wherein individual warehouses have limited capacities and exhibit economies of scale. The iterative procedure defines and solves a series of conventional transportation problems in order to converge on the optimal system design. The algorithm is well suited to solving large problems of the type commonly encountered in practice.     

顾客部分延期付款下两级商业信用易腐品订货策略

针对易腐品的经济订货批量问题展开研究。在供应商给零售商提供延迟还款的同时,零售商也给顾客提供部分延期还款条件。分五种情况分别讨论零售商的成本构成,并由此建立数学模型以求解最优订货周期使得零售商单位时间总成本最小化。通过数学证明得到了目标函数的解析性质,结果显示每种情况下在可行域范围内至多存在一个极小值点。以此为基础给出了相应的命题以有效地确定零售商的最优决策。最后通过数值算例说明了模型的有效性。     

Capacitated lot-sizing with extensions: a review

The capacitated lot-sizing problem (CLSP) is a standard formulation for big bucket lot-sizing problems with a discrete period segmentation and deterministic demands. We present a literature review on problems that incorporate one of the following extensions in the CLSP: back-orders, setup carry-over, sequencing, and parallel machines. We illustrate model formulations for each of the extensions and also mention the inclusion of setup times, multi-level product structures and overtime in a study. For practitioners, this overview allows to check the availability of successful solution procedures for a specific problem. For scientists, it identifies areas that are open for future research.