Facility Location: A Robust Optimization Approach

In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi‐period fixed‐charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi‐dimensional box, and demand within a multi‐dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.     

A multi-stage stochastic supply network design problem with financial decisions and risk management

In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the investments to make in alternative activities to those directly related with the supply chain design. Uncertainty is assumed for demand and interest rates, which is described by a set of scenarios. Therefore, for the entire planning horizon, a tree of scenarios is built. A target is set for the return on investment and the risk of falling below it is measured and accounted for. The service level is also measured and included in the objective function. The problem is formulated as a multi-stage stochastic mixed-integer linear programming problem. The goal is to maximize the total financial benefit. An alternative formulation which is based upon the paths in the scenario tree is also proposed. A methodology for measuring the value of the stochastic solution in this problem is discussed. Computational tests using randomly generated data are presented showing that the stochastic approach is worth considering in these types of problems.     

面向新零售的生鲜连锁企业城市配送网络优化研究

城市配送网络优化是生鲜连锁经营企业实施新零售的关键环节,本文研究新零售背景下生鲜企业城市配送网络面临的多业态门店选址及末端需求点分配问题。本文系统考虑多业态零售门店选址布局及覆盖范围、冷链设施配置、冷藏品类选择等生鲜新零售特征构建非线性混合整数规划模型,并设计混合拉格朗日松弛算法求解模型,通过与CPLEX对比验证本文算法的有效性。根据典型生鲜连锁企业重庆果琳的实际数据,运用本文模型及算法得到重庆果琳多业态零售门店布局、门店线上订单覆盖范围、门店冷藏最优品类和门店冷链设施配置方案,并探讨需求规模变动、消费者自提意愿、线上订单规模和气温变化等因素对城市配送系统的影响。结果发现相比重庆果琳现有配送网络,优化方案平均成本降低2.52%;生鲜连锁企业损耗成本占总成本超过70%,配置冷链设施总成本仅降低0.32%;需求规模变动对城市配送网络及单位配送成本的影响较小;消费者自提意愿、线上订单规模和气温变化不影响城市配送网络结构且对总成本影响较小。     

Using branch-and-price approach to solve the directed network design problem with relays

We present node-arc and arc-path formulations, and develop a branch-and-price approach for the directed network design problem with relays (DNDR). The DNDR problem can be used to model many network design problems in transportation, service, and telecommunication system, where relay points are necessary. The DNDR problem consists of introducing a subset of arcs and locating relays on a subset of nodes such that in the resulting network, the total cost (arc cost plus relay cost) is minimized, and there exists a directed path linking the origin and destination of each commodity, in which the distances between the origin and the first relay, any two consecutive relays, and the last relay and the destination do not exceed a predefined distance limit. With the node-arc formulation, we can directly solve small DNDR instances using mixed integer programming solver. With the arc-path formulation, we design a branch-and-price approach, which is a variant of branch-and-bound with bounds provided by solving linear programs using column generation at each node of the branch-and-bound tree. We design two methods to efficiently price out columns and present computational results on a set of 290 generated instances. Results demonstrate that our proposed branch-and-price approach is a computationally efficient procedure for solving the DNDR problem.     

Explicit versus Implicit Profit Sharing and the Determination of Wages:

ABSTRACT: This paper considers the claim that explicit profit sharing reduces the marginal cost of labour This is contrasted with the view that implicit profit sharing occurs through wage bargaining Using a microeconomic data set from the UK we find no evidence that the introduction of profit sharing reduces base wages and hence the marginal cost of labour However firm profitability is found to have a positive effect on wages which supports the hypothesis of implicit profit sharing through wage bargaining These findings suggest that it is hard to justify the favourable tax treatment of profit related pay found in the UK     

A Single‐Period Assortment Optimization Model

This paper studies a single‐period assortment optimization problem with unequal cost parameters. The consumer choice process is characterized by a Multinomial Logit (MNL) model. When the store traffic is a continuous random variable, we explicitly derive the structure of the optimal assortment. Our approach is to use a comprehensive measure–profit rate to evaluate the profitability of each variant and then determine which product should be offered. We demonstrate that the optimal assortment contains the few items that have the highest profit rate. When the store traffic is discrete, the optimal solution is difficult to obtain. We propose a “profit rate” heuristic, which is inspired by the result for the case of continuous store traffic. In a special case with equal cost parameters and normal demand distribution, the profit rate heuristic is indeed optimal. Using randomly generated data, we test the effectiveness of the heuristic and find that the average percentage error is less than 0.1% and that the hit rate is above 90%. Our research provides managerial insights on assortment planning and accentuates the importance of measuring the profitability of each product when the demand is random and cannibalization among different products exists.     

Two-level network design with intermediate facilities: An application to electrical distribution systems

We consider the two-level network design problem with intermediate facilities. This problem consists of designing a minimum cost network respecting some requirements, usually described in terms of the network topology or in terms of a desired flow of commodities between source and destination vertices. Each selected link must receive one of two types of edge facilities and the connection of different edge facilities requires a costly and capacitated vertex facility. We propose a hybrid decomposition approach which heuristically obtains tentative solutions for the vertex facilities number and location and use these solutions to limit the computational burden of a branch-and-cut algorithm. We test our method on instances of the power system secondary distribution network design problem. The results show that the method is efficient both in terms of solution quality and computational times.     

基于上游成员的机会成本和消费者偏好的供应链产品策略

基于对上游成员的机会成本和消费者在质量偏好上的异质性的考虑,本文研究中心化和由一零售商与一制造商（供应商）组成的分散化供应链在质量和数量上的最优产品策略。通过构建问题的理论模型及分析,分别获得最优解和博弈均衡解。进而利用灵敏度分析和算例讨论了消费者对质量偏好的异质性和上游成员的机会成本对供应链的产品策略、供应链的利润和消费者剩余的影响。研究发现：当边际质量成本较低时,供应链产品策略应主要考虑满足大众需求;而当边际质量成本和消费者对质量偏好的异质性程度都较高时,供应链只需考虑部分高质量敏感的消费者;当消费者对质量的平均偏好水平较低,边际质量成本较高和顾客需求趋于同质时,产品应考虑退出市场;此外,成员的权利均衡有助于完善供应链利润和社会福利,而零售商的强势帮助消费者培育和提高产品质量。最后,占据先动优势的一方在利润分配时基本上占上风。     

考虑最坏中断损失下的P-中位设施选址问题的模型与算法研究

蓄意突袭以及恐怖袭击会造成设施服务的突然中断成为网络系统的主要危害之一,因此网络设施选址决策应该同时考虑正常和紧急状态下系统的运作成本.本文研究考虑最坏中断损失下的网络设施选址问题,建立了该问题的双层规划模型,上层规划涉及设施选址决策,下层规划研究确定设施位置后,设施中断产生最大损失的问题.本文运用基于拉格朗日松弛的混合遗传算法来求解该双层规划问题.将European150数据集作为研究对象,对比研究了本文研究问题与传统的P-中位选址问题的结果,分析不同选址策略下网络系统的效率被中断影响的程度是不同的.最后通过改变一些关键参数,比如常规运作权重、设施数量、中断设施数量,对相关结果进行了分析.     

A Parametric Approach for a Nonlinear Discrete Location Problem

A discrete location problem is formulated for the design of a postal service network. The cost objective of this problem includes a nonlinear concave component. A parametric integer programming algorithm is developed to find an approximate solution to the problem. The algorithm reduces the problem into a sequence of p-median problems and deals with the nonlinear cost by a node-replacement scheme. Preliminary computational results are presented.     

Bertrand模型与超模博弈

将近年来博弈论中出现的一种新的研究方法--超模博弈理论应用于Bertrand寡头博弈中,对于具有一般成本函数的差异产品的Bertrand寡头博弈,当企业的策略只是选择价格水平时,比较了博弈为超模和对数超模博弈的充分条件,表明虽然一个对数超模博弈一定是拟超模的,因而较超模博弈的适用范围更广泛,但二者的充分条件之间不具备可比性,即不能由其中一个推出另外一个.同时既使该博弈既不是超模的也不是对数超模的,仍可能存在对利润函数的其它单调转换使博弈成为超模的.当边际生产成本为常数时,给出了具体的反例.当企业的策略为同时选择价格和广告水平,且企业的边际生产成本为常数时,表明在一般的假设下博弈为超模博弈,从而说明了为什么通常情况下较高的广告水平对应着较高的价格.     

考虑交易安全风险控制投入的在线旅游供应链网络均衡模型

基于包括供应商、平台和消费市场的三层供应链网络结构，利用变分不等式刻画均衡态时在线旅游供应链网络各成员的最优经济行为，以及平台交易安全风险控制投入对供应链平台企业、供应链整体的风险水平和期望收益的影响。研究发现，在平台企业风险控制投入相同情况下，平台和消费市场的产品交易数量和价格大致相同，验证了模型的合理性和有效性。其次，随着交易安全风险控制投入的增加，平台自身交易安全风险下降，供应链网络整体的交易安全水平和交易数量上升，但平台自身的期望收益下降。最后，随着更多的平台加入，平台的期望收益下降，市场需求价格下降，消费者获利。但部分平台企业的搭便车行为，会导致供应链整体的交易安全风险水平上升。     

Closed-loop supply chain configuration for new and reconditioned products: An integrated optimization model

Closed-Loop Supply Chain Management (CLSCM) is considered as a strategic response to the call for corporate sustainability while further expanding the scope of value creation to include product reconstruction. The Closed-Loop Supply Chain (CLSC) performance is directly related to the CLSC network design. The CLSC network design, with long-term and strategic connotations, involves selection of an integrated network of partner organizations to be engaged on one hand in the forward supply chain processes relevant to families of existing and new products and also involved in reverse supply chain activities relevant to reconstruction of the returned products. At the tactical level, Closed-Loop Supply Chain Configuration (CLSCC) attempts to address issues pertinent to launch of a new product and its reconstruction. The CLSC network design is well studied in the current literature, but addressing the CLSCC is neglected. To study the CLSCC problem we: (a) develop an integrated optimization model for problem; (b) present a real-world case study of a battery manufacturer; (c) based on the case study, we conduct a comprehensive set of computational experiments followed by a series of what-if analyses to compare profitability of the Forward Supply Chain Configuration (FSCC) versus the CLSCC; and (c) discuss the key observations and managerial implications drawn from the computational experiments, applicable to other real-world instances. The significant outcomes of the study suggest that: (i) performance of the firm׳s base case integrated CLSCC model is significantly better than the current supply chain model (ii) the sales-price ratio of new battery is found to be negatively related with the maximum acquiring price of used batteries; (iii) combination of sales price ratios of new and reconditioned batteries determines the total net profit for a given return rate. Finally, important managerial insights and scope for future research are discussed.     

Locating Emergency Warning Sirens

In this paper, we report on the application of set covering and maximal covering location models to the problem of locating emergency warning sirens in a midwestern city. Two siren types are available, each having different costs and covering radii. Using a modified version of the set covering location model, we analyze the cost implications of several policy options being considered by the city's planners. Results of the study indicate that location covering models can be powerful and efficient tools in the design of such systems, and their use can lead to significant cost savings. In addition, such models provide decision makers the flexibility to examine the inherent costs associated with various policy options.     

公平关切下基于网络平台销售、回收的E-闭环供应链的主导模式研究

在"互联网+"的大环境下,考虑网络平台的公平关切影响,对不同主导模式下的E-闭环供应链的销售、回收进行研究。文章构建了无公平关切制造商主导、无公平关切网络平台主导、考虑公平关切制造商主导、考虑公平关切网络平台主导的E-闭环供应链四种决策模式。针对每种模型,分析了相应的销售价格、服务水平、回收价格和最优利润等决策变量。研究发现：（1）无论网络平台是否考虑公平关切,制造商主导情况下的销售价格、服务水平和制造商利润均高于网络平台主导的情况;（2）闭环供应链的回收价格只与加工成本、回收再造成本和网络平台收取的回收服务佣金有关;（3）公平关切都会使产品销售价格、服务水平和制造商的利润降低;（4）当网络平台主导系统时,公平关切程度较低,网络平台的利润大于制造商主导时的利润,但当公平关切程度较大时,网络平台的利润则小于制造商主导时的利润。（5）当制造商主导系统时,网络平台的利润随其公平关切的程度先增后减。（6）公平关切相当于让利于消费者,且公平关切程度越大,对消费者的让利幅度越大,对制造商越不利。但在实际中,当网络平台主导系统时,网络平台并不会主动进行公平关切,而在制造商主导系统的情况下,网络平台会考虑一定程度的公平关切,或者由于受消费者的信任压力、政府部门的管理要求和竞争等因素的影响,而不得不考虑公平关切问题。文章的研究结论进一步丰富完善了E-闭环供应链的理论基础。     

Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns

In this paper we study a class of locations models where facilities are not perfectly reliable and failures may be correlated. We analyze problems with Median and Center objectives under complete and incomplete customer information regarding the state of facilities. The goal is to understand how failure probabilities, correlations, availability of information, and problem objective affect the optimal location patterns. In particular, we want to find analytical confirmations for location patterns observed in numerical experiments with network location models. To derive closed-form analytical results the analysis is restricted to a simple (yet classic) setting: a 2-facility problem on a unit segment, with customer demand distributed uniformly over the segment (results can be extended to other demand distributions as well). We derive explicit expressions for facility trajectories as functions of model parameters, obtaining a number of managerial insights. In addition we provide the decomposition of the optimal cost into the closed form components corresponding to the cost of travel, the cost of facility unreliability and the cost of incomplete information. Most of the theoretical insights are confirmed via numerical experiments for models with larger (3–5) number of facilities.     

When Does a Retailer's Advance Selling Capability Benefit Manufacturer,Retailer, or Both?

Advance selling (AS) from a retailer to consumers is commonly observed in practice. With an AS capability, a retailer has the option to sell in advance or not. Having the AS option seems to increase flexibility and thus profit for a retailer. However, we show that the AS option can hurt the retailer's profit as well as supply chain performance. We identify two thresholds for a product's marginal production cost. A retailer's AS option benefits both the manufacturer and retailer when the marginal production cost is high, that is, above both thresholds. It benefits the manufacturer but hurts the retailer when the marginal production cost is moderate, that is, between the two thresholds. The result is ambiguous when the marginal production cost is low, that is, below both thresholds. We find that consumer valuation uncertainty under AS is the key driving force for the surprising result that having the retailer's AS option can hurt the retailer. When compared to the scenario where the retailer does not have the AS option, we find that the manufacturer's optimal wholesale price weakly decreases under the retailer's AS option if the marginal production cost is high. The statement is reversed if the marginal production cost is moderate or low.     

客户转换成本对三级价格歧视的影响分析

本文在给定市场划分条件下,研究了客户转换成本约束下垄断厂商的利润最大化问题,把完全价格歧视和零歧视两种极端情形拓展到一般形式。给出三级价格歧视下利润、价格、产出的计算公式,并详细讨论需求曲率和成本函数斜率的影响     

Graph theory and computer aided facilities design

Four variations of an algorithm based upon graph theory are developed for solving the facilities design problem. The facilities design problem involves locating economic activities, each of which requires a given amount of space, on a floor within a building in such a manner to optimize an appropriate measure of effectiveness such as, for example, the total cost of materials handling. This problem has been called the location-allocation problem in some of the earlier management science literature. The algorithm uses strings to represent the graphs in order to be able to handle the computing more effectively. The algorithm is illustrated throughout the article by an example. Experience with both FORTRAN and PL/1 is reported. The topic is likely to be of interest to facilities designers, graph theoreticians and computer scientists.     

买方抗衡势力下双渠道促销合作微分博弈研究

在企业多周期连续促销背景下,假设需求受上下游企业促销努力水平、产品商誉和消费者支付意愿的共同影响,考虑产品商誉和消费者支付意愿的动态变化,构建双渠道模式制造商和零售商线上线下联合促销的四种微分博弈模型,以解决供应链上企业的促销决策问题。结果表明,两阶段补偿契约提高了零售商促销的积极性,实现上下游企业利润的帕累托改进,在买方抗衡势力的作用下,制造商将进一步提高促销成本分担比例使得零售商达到集中决策下的最优促销努力水平,但该契约对制造商促销努力激励不足。为此,进一步设计两阶段成本分担契约以实现同时激励上下游企业的促销努力,无论买方抗衡势力如何变化该契约都不会造成上下游企业的决策偏离,实现供应链完美协调。