Flexible supply policy with options and capacity constraints

This paper considers a class of multi-period flexible supply policies with options and capacity constraints. The main results are to characterize the optimal ordering and purchasing options policy and the minimum expected cost in a period and thereafter under the assumptions about the options and ordering quantities.     

Green product development under competition: A study of the fashion apparel industry

Motivated by the observed industrial issues, we analytically develop a fashion supply chain consisting of one manufacturer and two competing retailers and investigate how retail competition and consumer returns affect green product development in fashion apparel. In the basic model, that is, the pure “product greenness level” game, we find that the optimal greenness level of the fashion product decreases along with the level of market competition. This finding implies that a more competitive market leads to a lower optimal greenness level. We also identify that when the consumer return rate increases, the optimal product greenness level is substantially reduced. In the extended model with joint decisions on greenness and pricing, we find that the optimal product greenness level for the whole channel is always higher in the scenario when both retailers charge a higher retail price than in the case with a lower retail price. As such, the underdevelopment of green fashion products is a result of fashion industry features, such as an extremely competitive environment for green product development, relatively low retail prices for fashion products, and high consumer return rates. Therefore, fashion companies should join a co-opetition game for the green product market and simultaneously enhance their efficiency in managing consumer returns. To support our analytical findings, we conduct extensive industrial interviews with various representative companies. Based on this multi-methodological approach (MMA), this paper generates practice-relevant managerial insights that not only contribute to the literature, but also act as valuable references for industrialists.     

双重价格规制下三渠道季节性产品供应链跨期风险共担机制研究

以双重价格规制下三渠道季节性产品供应链为研究对象,首先通过构建序贯博弈模型,研究供应链的淡季和旺季的最优决策和利润,在此基础上构建跨期风险共担协调契约和模型,以实现供应链总利润最大化和供应链企业的双赢。研究表明,由于渠道1的原材料价格受到上限规制,旺季供应商不能完全兑现制造商的订购量;由于最终产品的价格受到严格规制,旺季产成品的供应短缺的概率增加;跨期风险共担机制使得供应商和制造商的决策与集成供应链的决策完全一致,供应链总利润达到集成决策时的利润水平;研究还表明,供应商和制造商的渠道集成决策下,旺季产成品的供应缺货的概率进一步加大。     

由零售商负责回收的多期闭环供应链网络均衡

本文研究了零售商回收模式下多期闭环供应链网络均衡问题。制造商通过零售渠道将产品销售给消费者,以满足消费市场需求,同时消费产生的废旧品由零售商回收返回制造商处进行再制造,通过产品库存和回收废旧品连接相邻规划期。运用变分不等式理论和互补理论,分别刻画了制造市场、零售市场和消费市场的均衡,接着构建了多期闭环供应链网络均衡模型。利用变分不等式的投影收缩算法,对模型进行求解。算例着重分析了废旧品利用率对网络均衡状态和供应链成员利润的影响。结果表明:当制造商的废旧品利用率逐渐增加时,回收量逐渐增加,制造商的利润先减后增,零售商利润一直增加,而供应链总利润一直增加,供应链网络中的最优决策变量主要受到回收量约束的影响。     

Integrated multi-site aggregate production-pricing planning in a two-echelon supply chain with multiple demand classes

This paper proposes a production and differential pricing decision model in a two-echelon supply chain that involves a demand from two or more market segments. In this framework, the retailer is allowed to set different prices during the planning horizon. While integrated production-marketing management has been a key research issue in supply chain management for a long time, little attention has been given to set prices and marketing expenditures in integrated multi-site (parallel) manufacturing systems and multiple demand classes. Generally, the presence of multiple demand classes induced by different market segments may impose demand leakage and then change production plan and ordering policies throughout the supply chain system. To tackle this problem, this paper develops a novel approach in order to provide an optimal aggregate production and marketing plan by interconnecting the sales channels of the retailer and demand. A non-linear model is established to determine optimal price differentiation, marketing expenditures and production plans of manufacturing sites in a multi-period, multi-product and multi-sale channels production planning problem by maximizing total profit of the supply chain. To handle the model and obtain solutions, we propose an efficient analytical model based upon convex hulls. Finally, we apply the proposed procedure to a clothing company in order to show usefulness and significance of the model and solution method.     

基于商业信用和回购契约的供应链最优化策略研究

本文考虑由单一供应商和零售商组成的供应链系统,当供应商为零售商提供回购契约,同时零售商又为下游顾客提供商业信用契约时,供应商如何设计回购契约来有效协调整个供应链,以及零售商又如何借助回购和商业信用契约来做出自身最优订货策略问题,并建立了相应的决策模型。通过模型分析,给出了供应商和零售商在四种情形下的最优契约设计参数,以及零售商的最优订货决策。研究发现,当满足一定的参数范围时,供应链中两主体同时采用协调契约能够更加有效地增加整个供应链中的订货量和利润,为各主体创造更多新的价值。最后,本文结合数值例子,分析了模型参数变化对最优订货策略和各主体利润的影响。     

An algorithm for solving the multi-period online fulfillment assignment problem

This paper develops an optimal solution procedure for the multi-period online fulfillment assignment problem to determine how many and which of a retailer/e-tailer’s capacitated regional warehouse locations should be set up to handle online sales over a finite planning horizon. To reduce the number of candidate solutions in each period, dominance rules from the facility location literature are extended to handle the nonlinear holding and backorder cost implications of our problem. Computational results indicate that multi-period considerations can play a major role in determining the optimal set of online fulfillment locations. In 92% of our test problems, the multi-period solution incorporated fewer openings and closings than myopic single period solutions. To illustrate the use of the model under changing demands, the multi-period solution yielded different supply chain configurations than the myopic single period solution in over 37% of the periods.     

An a posteriori decision support methodology for solving the multi-criteria supplier selection problem

This research presents a novel, state-of-the-art methodology for solving a multi-criteria supplier selection problem considering risk and sustainability. It combines multi-objective optimization with the analytic network process to take into account sustainability requirements of a supplier portfolio configuration. To integrate ‘risk’ into the supplier selection problem, we develop a multi-objective optimization model based on the investment portfolio theory introduced by Markowitz. The proposed model is a non-standard portfolio selection problem with four objectives: (1) minimizing the purchasing costs, (2) selecting the supplier portfolio with the highest logistics service, (3) minimizing the supply risk, and (4) ordering as much as possible from those suppliers with outstanding sustainability performance. The optimization model, which has three linear and one quadratic objective function, is solved by an algorithm that analytically computes a set of efficient solutions and provides graphical decision support through a visualization of the complete and exactly-computed Pareto front (a posteriori approach). The possibility of computing all Pareto-optimal supplier portfolios is beneficial for decision makers as they can compare all optimal solutions at once, identify the trade-offs between the criteria, and study how the different objectives of supplier portfolio configuration may be balanced to finally choose the composition that satisfies the purchasing company's strategy best. The approach has been applied to a real-world supplier portfolio configuration case to demonstrate its applicability and to analyze how the consideration of sustainability requirements may affect the traditional supplier selection and purchasing goals in a real-life setting.     

Optimal lot-sizing under strict carbon cap policy considering stochastic demand

Due to stringent laws and increasing awareness of customers, organizations are becoming environmental conscious and looking beyond conventional cost minimization/profit maximization approach and striving to curb carbon emission. In this article, we have considered strict carbon cap policy to determine the optimal order quantity, reorder point and number of shipments in a two-echelon supply chain under stochastic demand considering partial backorders. All the major sources of emission such as production, inventory, and transportation have been considered. The objective is to minimize the total expected supply chain cost while satisfying the carbon emission constraint. A numerical example is given to illustrate the solution procedure. Further, sensitivity analyses have been carried out to get insight that how with operational adjustments both cost and emission can be controlled.     

Selling to the “Newsvendor” with a forecast update: Analysis of a dual purchase contract

We consider a supply chain in which a manufacturer sells to a procure-to-stock retailer facing a newsvendor problem with a forecast update. Under a wholesale price contract, the retailer waits as long as she can and optimally places her order after observing the forecast update. We show that the retailer’s wait-and-decide strategy, induced by the wholesale price contract, hinders the manufacturer’s ability to (1) set the wholesale price and maximize his profit, (2) hedge against excess inventory risk, and (3) reduce his profit uncertainty. To mitigate the adverse effect of wholesale price contract, we propose the dual purchase contract, through which the manufacturer provides a discount for orders placed before the forecast update. We characterize how and when a dual purchase contract creates strict Pareto improvement over a wholesale price contract. To do so, we establish the retailer’s optimal ordering policy and the manufacturer’s optimal pricing and production policies. We show how the dual purchase contract reduces profit variability and how it can be used as a risk hedging tool for a risk averse manufacturer. Through a numerical study, we provide additional managerial insights and show, for example, that market uncertainty is a key factor that defines when the dual purchase contract provides strict Pareto improvement over the wholesale price contract.     

Purchasing decisions under stochastic prices: Approximate solutions for order time, order quantity and supplier selection

This paper analyzes purchasing strategies for retailers regarding the best timing and amount of purchases when operating under combined timing and quantity flexibility contracts in an environment of uncertain prices. To decrease the computational complexity and make the procedure adaptable to the case of multiple suppliers, we introduce, analyze, and compare a ??time strategy?? and a ??target strategy?? and then develop a hybrid ??adaptive target strategy?? to facilitate and improve the purchasing decision for the case of option contracts with generally rising prices. The adaptive target strategy is simpler and more intuitive than the traditional binomial lattice method, while the risk of failing to meet a target profit can also easily be calculated. We then extend the solution procedure to maximize expected profits in an environment of selecting among multiple suppliers with potentially different price processes, and we further provide risk analysis to help determine a good estimate for the number of option contracts from different suppliers to generate in order to create adequate risk protection. Numerical analysis demonstrates how the number of candidate suppliers impacts the expected profit and the risk. Monte Carlo simulation results demonstrate that the developed solution procedures provide satisfying outcomes and that the calculation is fast, even for multiple-dimension and multiple-supplier cases.     

Modelling take-up and profitability

We use response data collected by a lender to estimate the probabilities of loan offers being accepted by the applicants and the survival probabilities of default and of paying back early. Combining all those together we estimated the expected profit surface for the lender at the time of application before making an offer to an applicant. The results show how a lender could find the optimal interest rate to increase the expected profit or its market share. We also consider how different optimal decision policies could be applied to different market segments.     

不确定性对混合CVaR约束库存系统的影响

运用应用概率中的随机占优研究需求不确定性对混合CVaR约束库存系统最优订购量和最优利润的影响。引入刻画决策者风险态度的“风险偏好系数”,得到系统最优订购量和最优利润关于风险偏好系数的单调性。研究表明随机大需求总会导致系统较高的最优订购量和最优利润;在割准则序意义下,最优订购量可能随需求可变性的增加而增加也可能随需求可变性的增加而减少;在二阶随机占优且风险偏好系数大于等于1的情况下系统最优利润具有随机单调性,然而当风险偏好系数小于1时最优利润在二阶随机占优意义下的结论不一定成立,我们通过一个数值例子来说明。     

两类供应风险下装配商的最优订购策略

针对两类供应风险(不确定产能与随机产出率)下装配制造商的零部件订购决策这一难题,运用随机非线性规划方法,以装配商期望利润最大化为目标,建立零部件订购决策的多维优化模型,刻画了确定需求下的最优订购量,并对其进行了灵敏性分析。最后,通过数值算例验证了模型结论并进一步探讨不同类供应风险的影响,为装配商的零部件订购决策和风险管理提供有益的管理启示。     

随机需求下物流服务供应链订购策略研究

针对由单个物流服务提供商和集成商组成的物流服务供应链,基于集中化模式、纳什博弈模式和Stackelberg博弈模式三种典型模式,考虑市场需求随机且受服务质量缺陷承诺水平的影响,探讨物流服务供应链的订购与质量缺陷承诺策略问题。通过分析发现:物流服务质量缺陷承诺水平随着市场需求弹性系数的增加而递减,但其受物流服务集成商观测水平的影响却因合作模式不同而变化不一致;集中化模式下的物流服务订购量随着物流服务集成商观测水平或市场需求弹性系数的增大而递减,但在其他两种合作模式下物流服务订购量随着物流服务集成商观测水平或市场需求弹性系数的增加而增加;在三种模式下,物流服务供应链的整体利润随着市场需求弹性系数的增加而递减,但其受物流服务集成商观测水平的影响却因合作模式不同而变化不一致。     

Optimal purchasing cycle length of a deteriorating product for intermediary firms

In a supply chain logistics system, the function of an intermediary firm is to purchase products and to sell those purchased products to the public or to other firms. This article investigates how an intermediary firm can optimally determine the purchasing cycle length of a deteriorating product. By incorporating the special structure of the intermediary firm’s environments and the deteriorating nature of the product, the inventory problem encountered by the intermediary firm is mathematically formulated. The optimal purchasing cycle length is derived such that the total profit is maximized. Several interesting properties of the optimal policy are investigated and an efficient iterative algorithm is provided to search for the optimal policy. Also, the convergence of the iterative algorithm developed in this paper is proved. Finally, a numerical example is provided to illustrate the features of the proposed problem and the iterative search algorithm.     

Stochastic multi-site supply chain planning in textile and apparel industry under demand and price uncertainties with risk aversion

A multi-product, multi-period, multi-site supply chain production and transportation planning problem, in the textile and apparel industry, under demand and price uncertainties is considered in this paper. The problem is formulated using a two-stage stochastic programming model taking into account the production amount, the inventory and backorder levels as well as the amounts of products to be transported between the different plants and customers in each period. Risk management is addressed by incorporating a risk measure into the stochastic programming model as a second objective function, which leads to a multi-objective optimization model. The objectives aim to simultaneously maximize the expected net profit and minimize the financial risk measured. Two risk measures are compared: the conditional-value-at-risk and the downside risk. As the considered objective functions conflict with each other’s, the problem solution is a front of Pareto optimal robust alternatives, which represents the trade-off among the different objective functions. A case study using real data from textile and apparel industry in Tunisia is presented to illustrate the effectiveness of the proposed model and the robustness of the obtained solutions.     

Optimal inventory decisions in a multiperiod newsvendor problem with partially observed Markovian supply capacities

This paper considers a multi-period news-vendor problem with partially observed supply-capacity information which evolves as a Markovian Process. The supply capacity is fully observed by the buyer when the capacity is smaller than the buyer’s ordering quantity. Otherwise, the buyer knows that the current-period supply capacity is greater than its ordering quantity. Based on these two observations, the buyer updates the future supply-capacity forecasting accordingly. With a dynamic programming formulation, we prove the existence of an optimal ordering policy. We also prove that the optimal order quantity is greater than the myopic order quantity.     

Optimal advertising/ordering policy and finance mode selection for a capital-constrained retailer with stochastic demand

In this paper, we discuss how a capital-constrained retailer determines his optimal advertising/ordering policy and selects his financing mode when he faces the following modes: no financing service, bank financing, and supplier/mixed financing. For each mode, we construct an optimization model and present a method for how the retailer determines his corresponding optimal advertising and ordering policies in the terms of his initial capital level. Furthermore, we derive the conditions of retailer selecting the optimal financing mode based on both his initial capital level and the interest rates of the financing services. We show that when the retailer is relatively “poor,” he prefers bank financing mode if the bank interest rate is lower than the supplier, otherwise mixed financing mode; when he is moderately “rich,” he only selects supplier financing mode if the bank interest rate is greater than a threshold value and otherwise bank financing mode; however, when he is relatively “rich,” he always chooses bank financing mode even if the bank interest rate is higher than the supplier. We conduct numerical studies to illustrate the theoretical results and find adopting financing service significantly improves the retailer’s performance especially when he has relatively low initial capital level.     

随机产出下考虑小微供应商成本利润率的供应链决策研究

小微型供应商由于产能、资金等限制,其目标可能是实现成本利润率最优,从而提高企业生存能力。基于该观察,区别于多数文献采用利润最优决策准则,本文研究由小微供应商和零售商组成的单周期供应链决策问题。小微供应商面临产出随机风险,以成本利润率最大为目标进行产能决策,零售商以利润最大为目标确定最优订购量。研究发现小微供应商的成本利润率受到自身成本偏重系数以及零售商盈利能力的共同影响,将出现亏损、合理盈利、超额盈利三种情况。并且,零售商采取不同订货策略也会对小微供应商盈利情况产生差异影响。保守(积极)订货策略下,零售商是否盈利取决于自身单位净利润能否弥补单位缺货损失(自身可盈利空间)。本文研究融合现实普遍存在的产出随机问题,为小微供应商和其他供应链成员的产能/订购决策问题提供有益的管理启示。