A sustainable supply chain network considering lot sizing with quantity discounts under disruption risks: centralized and decentralized models

This study proposes a framework for the main parties of a sustainable supply chain network considering lot-sizing impact with quantity discounts under disruption risk among the first studies. The proposed problem differs from most studies considering supplier selection and order allocation in this area. First, regarding the concept of the triple bottom line, total cost, environmental emissions, and job opportunities are considered to cover the criteria of sustainability. Second, the application of this supply chain network is transformer production. Third, applying an economic order quantity model lets our model have a smart inventory plan to control the uncertainties. Most significantly, we present both centralized and decentralized optimization models to cope with the considered problem. The proposed centralized model focuses on pricing and inventory decisions of a supply chain network with a focus on supplier selection and order allocation parts. This model is formulated by a scenario-based stochastic mixed-integer non-linear programming approach. Our second model focuses on the competition of suppliers based on the price of products with regard to sustainability. In this regard, a Stackelberg game model is developed. Based on this comparison, we can see that the sum of the costs for both levels is lower than the cost without the bi-level approach. However, the computational time for the bi-level approach is more than for the centralized model. This means that the proposed optimization model can better solve our problem to achieve a better solution than the centralized optimization model. However, obtaining this better answer also requires more processing time. To address both optimization models, a hybrid bio-inspired metaheuristic as the hybrid of imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) is utilized. The proposed algorithm is compared with its individuals. All employed optimizers have been tuned by the Taguchi method and validated by an exact solver in small sizes. Numerical results show that striking similarities are observed between the results of the algorithms, but the standard deviations of PSO and ICA–PSO show better behavior. Furthermore, while PSO consumes less time among the metaheuristics, the proposed hybrid metaheuristic named ICA–PSO shows more time computations in all small instances. Finally, the provided results confirm the efficiency and the performance of the proposed framework and the proposed hybrid metaheuristic algorithm.

     

Supply chain multi-state risk assessment using universal generating function

Abstract

This paper proposes a new approach to assess the supply risk beyond the classical binary assumption of either delivering the whole quantity or not. Given today’s stochastic nature of supply and the dynamic nature of demand, the different supply activities along with the chain exhibit a multi-state behaviour increasing the complexity of their risk assessment. The new approach utilizes the universal generating function (UGF) to model the different suppliers’ echelons with their various supply risk levels along all the stages of the supply chain as a multi-state risk system. The developed model was successfully implemented to assess the supply risk in a multi-state strawberry supply chain and outperformed classical approaches. Results from the case study and the validation analysis illustrated the ability of the new approach to capture the various supply levels with their associated risks leading to more informative risk assessment process. Furthermore, the developed model improved the visibility for the purchasing managers downstream in terms of the different trade-offs between supply levels and their risks as well as some financial thresholds. The new multi-state approach contributes to the emerging supply chain risk assessment trend by offering a more realistic modelling method to capture the risk of all available supply levels along the delivery chain.     

Robust Stochastic Lot‐Sizing by Means of Histograms

Traditional approaches in inventory control first estimate the demand distribution among a predefined family of distributions based on data fitting of historical demand observations, and then optimize the inventory control using the estimated distributions. These approaches often lead to fragile solutions whenever the preselected family of distributions was inadequate. In this article, we propose a minimax robust model that integrates data fitting and inventory optimization for the single‐item multi‐period periodic review stochastic lot‐sizing problem. In contrast with the standard assumption of given distributions, we assume that histograms are part of the input. The robust model generalizes the Bayesian model, and it can be interpreted as minimizing history‐dependent risk measures. We prove that the optimal inventory control policies of the robust model share the same structure as the traditional stochastic dynamic programming counterpart. In particular, we analyze the robust model based on the chi‐square goodness‐of‐fit test. If demand samples are obtained from a known distribution, the robust model converges to the stochastic model with true distribution under generous conditions. Its effectiveness is also validated by numerical experiments.     

考虑随机市场需求的双渠道供应链风险补偿策略研究——从质量与价格竞争视角

在由两个供应商和单个零售商构成的二级双渠道供应链系统中，分析了随机市场需求以及供应商之间同时存在价格与质量竞争的情形下的双渠道供应链协调问题。在供应链集中决策、无风险补偿及有风险补偿三种情境下，构建了基于质量和价格的风险补偿模型并求得纳什均衡解。研究结果表明：存在可行的需求风险补偿策略使得供应链达到协调水平，并且需求风险补偿策略对零售商更加有利；在需求风险补偿策略下，需求风险补偿价格与其对应批发价格正相关，与其产品质量水平负相关；价格竞争程度对零售商订货量具有负向影响作用，对供应链总利润影响作用随着竞争程度增加而减弱，质量竞争程度对零售商订货量和供应商产品质量水平具有正向影响作用，对供应链总利润影响呈倒U型关系；需求风险补偿策略能够激励零售商的订货行为，强化价格竞争程度和质量竞争程度对供应商订货量和供应链总利润的影响；在供应链系统中双渠道营销模式下的供应链总利润要优于单渠道营销模式下的供应链总利润。本文结论不仅详细剖析了风险补偿策略对双渠道供应链协调的影响关系，也理清了价格与质量竞争对各方行为策略的影响机理。     

两种订货模式下订购和促销联合优化策略

本文基于CVaR决策准则,通过构建需求依赖于促销的一般需求模型,其中包括加法和乘法需求模型作为特例,考察了一次订货和允许紧急订货两种模式下风险厌恶零售商关于促销和库存的联合优化问题。讨论了紧急订购成本、风险厌恶以及市场需求变动对最优策略的影响,并对两种模式下零售商的最优策略和收益进行了比较分析,结果表明:在两种订货模式下,零售商的最优订购量和促销努力均随风险厌恶程度的增大而降低;紧急订货模式下的促销努力和实现的收益大于一次订货模式,且在加法需求模型下,紧急订货模式下的初次订购量小于一次订货模式的最优订购量。运用随机变量一阶和二阶交替随机占优的概念刻画了市场需求变动下零售商如何调整最优策略的充分条件。最后实施数值实验验证了理论分析结果。     

Risk based facility location by using fault tree analysis in disaster management

Determining the locations of facilities for prepositioning supplies to be used during a disaster is a strategic decision that directly affects the success of disaster response operations. Locating such facilities close to the disaster-prone areas is of utmost importance to minimize response time. However, this is also risky because the facility may be disrupted and hence may not support the demand point(s). In this study, we develop an optimization model that minimizes the risk that a demand point may be exposed to because it is not supported by the located facilities. The purpose is to choose the locations such that a reliable facility network to support the demand points is constructed. The risk for a demand point is calculated as the multiplication of the (probability of the) threat (e.g., earthquake), the vulnerability of the demand point (the probability that it is not supported by the facilities), and consequence (value or possible loss at the demand point due to threat). The vulnerability of a demand point is computed by using fault tree analysis and incorporated into the optimization model innovatively. To our knowledge, this paper is the first to use such an approach. The resulting non-linear integer program is linearized and solved as a linear integer program. The locations produced by the proposed model are compared to those produced by the p-center model with respect to risk value, coverage distance, and covered population by using several test problems. The model is also applied in a real problem. The results indicate that taking the risk into account explicitly may create significant differences in the risk levels.     

非平稳需求下考虑碳配额的供应链选址-库存模型与算法研究

针对非平稳需求下考虑碳配额的多期、多需求情景的三级供应链选址-库存问题，构建了库存策略（t，s，S）下供应链运营期望收益最大化的两阶段选址-库存随机优化模型，依据供应链企业不同着眼点下的决策流程，提出了一种三步骤的分层级启发式算法，该算法包含了选址导向和需求导向的两种子问题序贯求解模式。数值算例验证了在不同问题规模及需求类型下算法求解的有效性，同时分析了供应链网络设计、各成本占比和运营收益对不同供应链成本结构、需求不确定性与碳配额的敏感性，并给出了管理上的启示。     

Managing Retail Shelf and Backroom Inventories When Demand Depends on the Shelf‐Stock Level

Inventory displayed on the retail sales floor not only performs the classical supply function but also plays a role in affecting consumers’ buying behavior and hence the total demand. Empirical evidence from the retail industry shows that for some types of products, higher levels of on‐shelf inventory have a demand‐increasing effect (“billboard effect”) while for some other types of products, higher levels of on‐shelf inventory have a demand‐decreasing effect (“scarcity effect”). This suggests that retailers may use the amount of shelf stock on display as a tool to influence demand and operate a store backroom to hold the inventory of items not displayed on the shelves, introducing the need for efficient management of the backroom and on‐shelf inventories. The purpose of this study is to address such an issue by considering a periodic‐review inventory system in which demand in each period is stochastic and depends on the amount of inventory displayed on the shelf. We first analyze the problem in a finite‐horizon setting and show under a general demand model that the system inventory is optimally replenished by a base‐stock policy and the shelf stock is controlled by two critical points representing the target levels to raise up/drop down the on‐shelf inventory level. In the infinite‐horizon setting, we find that the optimal policies simplify to stationary base‐stock type policies. Under the billboard effect, we further show that the optimal policy is monotone in the system states. Numerical experiments illustrate the value of smart backroom management strategy and show that significant profit gains can be obtained by jointly managing the backroom and on‐shelf inventories.     

A shelf-space optimization model when demand is stochastic and space-elastic

The more customer demand is impulse-driven, the more it is space-dependent and the more it is subject to variation. We investigate the corresponding problem of retail shelf-space planning when demand is stochastic and sensitive to the number and position of facings. We develop a model to maximize a retailer׳s profit by selecting the number of facings and their shelf position under the assumption of limited space. The model is particularly applicable to promotional or temporary products.We develop the first optimization model and solution approach that takes stochastic demand into account, since the current literature applies deterministic models for shelf-space planning. By the means of an innovative modeling approach for the case with space- and positioning effects and the conversion of our problem into a mixed-integer problem, we obtain optimal results within very short run times for large-scale instances relevant in practice. Furthermore, we develop a solution approach to account for cross-space elasticity, and solve it using an own heuristic, which efficiently yields near-optimal results. We demonstrate that correctly considering space elasticity and demand variation is essential. The corresponding impacts on profits and solution structures become even more significant when space elasticity and stochastic demand interact, resulting in up to 5% higher profits and up to 80% differences in solution structures, if both effects are correctly accounted for. We develop an efficient modeling approach, compare the model results with approaches applied in practice and derive rules-of-thumb for planners.     

供需不确定条件下基于CVaR的零售商库存鲁棒优化模型

在经典报童模型下考虑供应和需求不确定性,研究了具有风险厌恶的零售商库存优化问题。采用条件风险值（CVaR）对库存绩效进行度量,构建了基于CVaR的零售商库存运作模型;在此基础上,考虑上游供应商供货能力和下游市场需求不确定性,并采用一系列未知概率的离散情景进行描述,给出了供需不确定条件下基于CVaR的零售商库存鲁棒优化模型。进一步,采用区间不确定集对未知情景概率进行建模,给出了基于最大最小准则的鲁棒对应模型。针对同时考虑供需不确定性导致的模型非凸性,采用标准对偶理论将其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不同风险厌恶程度和不确定性程度对零售商库存决策以及库存绩效的影响。结果表明,供需不确定性的存在虽然会导致零售商库存绩效损失,但损失值较小。特别地,依据文中模型得到的鲁棒库存策略在多数情况下能够保证零售商获得更优的库存绩效。此外,不确定性和风险厌恶程度的增加虽然会影响零售商库存决策和运作绩效,但在同等风险厌恶态度下,随着不确定性程度的增加,基于文中方法得到的鲁棒库存策略仍能确保零售商获得理想的库存绩效,表明文中所建模型在应对供需不确定性方面具有良好的鲁棒性。     

不确定环境下考虑风险厌恶的生产-分销网络优化模型及试验设计

考虑上游生产和下游需求不确定性，研究了由工厂、分销中心及终端市场构成的生产-分销网络优化设计问题。针对上游生产不确定性，考虑产生故障和无故障两种状态；针对下游市场需求不确定性，考虑其具有低、中和高三种状态。由于生产发生故障可能导致不合格品的产生，进一步考虑了在上游生产环节是否实施产品监测问题。综合网络运作成本和由不确定性导致的绩效风险，建立了由风险厌恶水平和悲观系数刻画的基于均值-条件风险值（CVaR）准则的生产-分销网络两阶段随机规划模型。特别地，针对由网络潜在节点数众多所导致的不确定情景规模过大的问题，采用情景缩减技术进行了情景筛选，降低了所建模型的求解难度。最后，进行了数值计算，分析了相关参数对网络运作绩效的影响，并给出了期望成本和条件风险值两个目标权衡的帕累托有效前沿。进一步，通过回归试验设计检验了决策者风险厌恶水平和悲观系数对所设计的生产-分销网络绩效的影响程度。结果表明，相对于决策者的风险厌恶程度，悲观系数对网络运作绩效的影响更大。     

An integrated supplier selection and inventory problem with multi-sourcing and lateral transshipments

In this research, we consider the supplier selection problem of a firm offering a single product via multiple warehouses. The warehouses face stationary, stochastic demand and replenish their inventory via multiple suppliers, to be determined from a set of candidates, with varying price, capacity, quality, and disruption characteristics. Additionally, the warehouses may simultaneously replenish their inventory from other warehouses proactively. With these characteristics, the problem is a multi-sourcing, supplier selection, and inventory problem with lateral transshipments. Even though the benefits of multi-sourcing and lateral transshipments have been presented in the literature individually to mitigate risks associated with uncertain demand and disrupted supply, the intertwined sourcing and inventory decisions under these settings have not been investigated from a quantitative perspective. We develop a decomposition based heuristic algorithm, powered with simulation. While the decomposition based heuristic determines a solution with supplier selection and inventory decisions, the simulation model evaluates the objective function value corresponding to each generated solution. Experimental results show, contrary to the existing literature, inferior decisions may result when considering the selection of suppliers solely on unit and/or contractual costs. We also evaluate the impact of multi-sourcing with rare but long disruptions compared to frequent but short ones.     

顾客有限“碳行为”偏好对选址-路径-库存联合优化的影响

针对考虑顾客有限“碳行为”偏好的选址-路径-库存联合优化问题,引入环保度系数作为碳排放量的特征向量,在低碳产品加价率存在的情况下,刻画了顾客有限“碳行为”偏好和市场逆需求系数对低碳产品需求量的影响,构建了选址-路径-库存系统中考虑有“碳行为”偏好的联合优化模型,并分析了顾客行为偏好对企业收益的影响。使用基于NNC的多目标求解方法,对考虑成本和碳排放的双目标问题进行处理并得到一组Pareto解集,数值实验证明了产品环保度、顾客有限“碳行为”偏好对企业运作方案和收益水平的影响。     

基于二阶段随机规划的城市医疗废弃物回收网络设计

城市医疗废弃物日益增加,且回收需求量受诸多因素的影响,难以准确预测,假定回收需求为确定值的医疗废弃物网络优化设计不能与实际需求相匹配。本文考虑了离散随机参数环境下,医疗回收网络设计中选址规划、分配计划及运输规划的协同优化问题,建立了以选址成本、运输成本最小为目标,设施与车辆能力限制为约束的二阶段随机规划模型。根据模型特点,设计了基于Benders decomposition的求解算法,同时,设计了一系列加速技术用于提高算法的求解效率。最后,以国内某城市医疗回收网络为背景设计算例,检验本文模型和求解策略的可行性和有效性。结果表明：相比确定性规划,随机规划的解能够节约总成本,结合一系列加速技术的Benders decomposition方法比CPLEX与纯的Benders decomposition更有优势。     

A Maximum Entropy Joint Demand Estimation and Capacity Control Policy

We propose a tractable, data‐driven demand estimation procedure based on the use of maximum entropy (ME) distributions, and apply it to a stochastic capacity control problem motivated from airline revenue management. Specifically, we study the two fare class “Littlewood” problem in a setting where the firm has access to only potentially censored sales observations; this is also known as the repeated newsvendor problem. We propose a heuristic that iteratively fits an ME distribution to all observed sales data, and in each iteration selects a protection level based on the estimated distribution. When the underlying demand distribution is discrete, we show that the sequence of protection levels converges to the optimal one almost surely, and that the ME demand forecast converges to the true demand distribution for all values below the optimal protection level. That is, the proposed heuristic avoids the “spiral down” effect, making it attractive for problems of joint forecasting and revenue optimization problems in the presence of censored observations.     

On multi-criteria chance-constrained capacitated single-source discrete facility location problems

This work aims at investigating multi-criteria modeling frameworks for discrete stochastic facility location problems with single sourcing. We assume that demand is stochastic and also that a service level is imposed. This situation is modeled using a set of probabilistic constraints. We also consider a minimum throughput at the facilities to justify opening them. We investigate two paradigms in terms of multi-criteria optimization: vectorial optimization and goal programming. Additionally, we discuss the joint use of objective functions that are relevant in the context of some humanitarian logistics problems. We apply the general modeling frameworks proposed to the so-called stochastic shelter site location problem. This is a problem emerging in the context of preventive disaster management. We test the models proposed using two real benchmark data sets. The results show that considering uncertainty and multiple objectives in the type of facility location problems investigated leads to solutions that may better support decision making.     

Managing Demand Risk in Tactical Supply Chain Planning for a Global Consumer Electronics Company

We consider the problem of managing demand risk in tactical supply chain planning for a particular global consumer electronics company. The company follows a deterministic replenishment‐and‐planning process despite considerable demand uncertainty. As a possible way to formally address uncertainty, we provide two risk measures, “demand‐at‐risk” (DaR) and “inventory‐at‐risk” (IaR) and two linear programming models to help manage demand uncertainty. The first model is deterministic and can be used to allocate the replenishment schedule from the plants among the customers as per the existing process. The other model is stochastic and can be used to determine the “ideal” replenishment request from the plants under demand uncertainty. The gap between the output of the two models as regards requested replenishment and the values of the risk measures can be used by the company to reallocate capacity among different products and to thus manage demand/inventory risk.     

基于库存价值改变和随机需求的经济订货批量模型

大多数库存研究的重点都集中在各种复杂的限制条件和模型的变换上.没有考虑到库存本身可能发生贬值或增值的情况,而实际中库存本身常常会发生价值变化.针对以往库存模型中没有考虑库存价值变化的问题,提出了在需求为随机连续分布、库存价值发生变化情况下的单周期经济订货批量模型,给出了最优订货策略.模型中以先进先出为假设条件,基于报童模型的思想,以订货量为决策变量、期望收益为目标函数,结合随机需求的分布情况得到最优订货量和最大期望收益,并给出了相应的数学证明.通过算例对模型进行说明,并对影响最优订货批量和最大期望收益的各个参数进行敏感性分析.     

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.     

考虑长期运力合同的班轮收益管理运输路径优化模型

基于收益管理的方法,文章对随机需求环境下班轮运力分配和路径优化问题进行了定量研究。首先针对海运收益管理的特征,建立了考虑长期运力合同、空箱调运的轮运力分配和路径选择随机规划模型,然后应用稳健优化方法对此模型进行求解。最后,通过数值仿真得到了优化的舱位分配方案,比较发现稳健优化模型取得了较确定性规划模型更好的收益,显示了模型和方法对于集装箱海运企业的收益管理问题具有应用价值。