基于CVaR的第三方回收闭环供应链的优化与协调

利用条件风险值理论研究了第三方回收闭环供应链的优化与协调问题。在随机需求与收益共享———费用共担契约下,建立了由单个风险规避零售商、单个风险规避制造商和单个风险中性第三方回收商组成的三阶闭环供应链的条件风险值模型和基于条件风险值的最优订购与定价决策模型。在对模型进行分析的基础上,揭示了制造商和零售商的风险规避水平对最优订购量、最优定价、条件风险值及闭环供应链协调性的影响。最后通过一个算例验证了研究结论。     

An economic analysis of the optimal information security investment in the case of a risk-averse firm

This paper presents an analysis of information security investment from the perspective of a risk-averse decision maker following common economic principles. Using the expected utility theory, we find that for a risk-averse decision maker, the maximum security investment increases with, but never exceeds, the potential loss from a security breach, and there exists a minimum potential loss below which the optimal investment is zero. Our model also shows that the investment in information security does not necessarily increase with increasing level of risk aversion of the decision maker. Relationships between vulnerability and investment effectiveness and two broad classes of security breach probability functions are examined, leading to interesting insights that can be used as guidelines for managers to determine the optimal level of security investment for certain types of security threats faced by risk-averse firms. Future research directions are discussed based on the limitations and possible extensions of this study.     

Managing inventory with two suppliers under yield uncertainty and risk aversion

In this paper, we consider a single-product single-period inventory model in which the retailer can source from two suppliers. The primary supplier is cheaper but unreliable in the sense that it generates supply yield uncertainty, whereas the secondary supplier is perfectly reliable but more expensive. The reliable supplier's capacity is fixed and the retailer cannot order more than the quantity reserved in advance. We study the problem in the context of a risk-averse retailer who has to determine the optimal order quantity from the primary supplier and the optimal reserved quantity from the secondary supplier. We develop the model in the perspective of a low risk averse retailer and quantify the risk via an exponential utility function. We show by numerical experiments how the resulting dual sourcing strategies differ from those obtained in the risk-neutral analysis. We also examine the sensitivity of some model-parameters on the optimal decisions.     

Capacity flexibility allocation in an outsourced supply chain with reservation

We consider a contract manufacturer that serves a limited number of outsourcers (customers) on a single capacitated production line. The outsourcers have different levels of demand uncertainty and the contract manufacturer faces the question how to allocate the contractual capacity flexibility in an optimal way. The contractual capacity flexibility is a contract parameter that sets the amount of demand the contract manufacturer is obliged to accept from the outsourcers. We develop a hierarchical model that consists of two decision levels. At the tactical level, the contract manufacturer allocates the capacity flexibility to the different outsourcers by maximizing the expected profit. Offering more flexibility to the more uncertain outsourcer generates higher expected revenue, but also increases the expected penalty costs. The allocated capacity flexibilities (determined at the tactical level) are input parameters to the lower decision level, where the operational planning decisions are made and actual demands are observed. We perform a numerical study by solving the two-level hierarchical planning problem iteratively. We first solve the higher level problem, which has been formulated as an integer program, and then perform a simulation study, where we solve a mathematical programming model in a rolling horizon setting to measure the operational performance of the system. The simulation results reveal that when the acceptance decision is made (given the allocated capacity flexibility decision), priority is given to the less uncertain outsourcer, whereas when the orders are placed, priority is given to the most uncertain outsourcer. Our insights are helpful for contract manufacturers when having contract negotiations with the outsourcers. Moreover, we show that hierarchical integration and anticipation are required, especially for cases with high penalty cost and tight capacities.     

The component procurement problem for the loss-averse manufacturer with spot purchase

This paper studies the purchasing behaviour of a loss-averse engineer-to-order manufacturer, who purchases a key component for his final product from a supplier under a single-wholesale-price contract with spot purchase opportunities, where both the product demand and the component spot price are uncertain. Through newsvendor type of models, we analyze several key issues, including the effects of the manufacturer's loss aversion, and the effects of demand and spot price uncertainties on the manufacturer's decision behaviour. We find that the purchasing behaviour of the loss-averse manufacturer differs from those of the risk-neutral and risk-averse ones. Specifically, we identify some sufficient conditions under which the loss-averse manufacturer may purchase a larger order quantity in advance when demand becomes more uncertain or when the price becomes more uncertain. We also discuss the two-wholesale-price contract and show that fixing the emergency supply price may lead to a smaller order quantity.     

Evaluating Product Plans Using Real Options

Product planning helps a company to strategically plan its current and future product platforms and offer product variants in the marketplace. Product platforming is widely touted as a successful strategy for mass customization. However, due diligence should be exercised before implementing any product platform strategy. The product planning exercise should account for future uncertainties. Traditional financial tools such as the net present value (NPV) are static since they do not compensate for any exogenous and endogenous uncertainties during the course of the project. The crux of the problem lies in the evaluation model that is used for evaluating the product planning projects. While many view uncertainties in a product planning project as problematic, it can also be viewed as a source of new opportunities. We argue that uncertainties should be an integral part of the evaluation model. If the future possibilities (or strategic options) are not considered in the evaluation model, a corporation may face a “myopic syndrome”.

In this article, we consider two important product planning decisions—platform decisions and product variant decisions. The platform decision involves strategic selection of a concept product platform from various possible alternative concept product platforms. The product variant decision involves deciding how long a company should continue to offer its current product variant in the marketplace and whether the existing product variant should be discontinued, scaled down, or scaled up with additional product features. To address the two aforementioned decisions, we developed a real options–based methodology that considers technical, project implementation, and market-related uncertainties. The proposed methodology uses a binomial and quadranomial lattice approach to build a decision tree. Product planning decisions at various decision tree nodes are evaluated using a risk-neutral option valuation methodology. We demonstrate the working of the proposed methodology using an illustrative example.     

Competition under capacitated dynamic lot-sizing with capacity acquisition

Lot-sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot-sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies of scale arising from dynamic lot-sizing costs is developed. Each firm can replenish inventory at the beginning of each period in a finite planning horizon. Fixed as well as variable production costs incur for each production setup, along with inventory carrying costs. The individual production lots of each firm are limited by a constant capacity restriction, which is purchased up front for the planning horizon. The capacity can be purchased from a spot market, and the capacity acquisition cost fluctuates with the total capacity demand of all the competing firms. We solve the competition model and establish the existence of a capacity equilibrium over the firms and the associated optimal dynamic lot-sizing plan for each firm under mild conditions.     

Financial and operational decisions in the electricity sector: Contract portfolio optimization with the conditional value-at-risk criterion

The restructuring of electricity markets around the world have caused increased volatility and uncertainty of the price power. As a result, providers of power now face increased uncertainty and risk in the operational and financial decisions related to procurement. Providers must seek optimal ways to deliver the required volume of power to retailers and end users while managing risk. We consider a mixed-integer programming model for a power providing agent that jointly considers the problem of selecting custom electricity contracts and finding the optimal procurement strategy of meeting contract obligations under spot price uncertainty. A two-stage stochastic integer programming (SIP) model with a conditional value-at-risk (CVaR) constraint to incorporate risk aversion is developed. Computational results are presented that demonstrates the CVaR approach and the results are compared with a corresponding expected cost minimization approach. The SIP model with CVaR will allow acceptance of contracts at lower prices compared to an approach based on a corresponding risk-neutral model as a hedge against uncertainty and mis-specified arbitrage.     

A practical approach to sensitivity analysis in linear programming under degeneracy for management decision making

Linear programming (LP) is a widely used tool in management decision making. Theoretically, sensitivity analysis of LP problems provides useful information for the decision maker. In practice, however, most LP software provides misleading sensitivity information if the optimal solution is degenerate. The paper shows how sensitivity analysis of LP problems can be done correctly when the optimal solution is degenerate. A production planning example is presented to illustrate the incorrect sensitivity analysis results automatically provided by most LP solvers. The general characteristics of the misleading results and the possible effects of this incorrect information on management decisions are also discussed.     

A Robust Optimization Approach to Capital Rationing and Capital Budgeting

We study the pure capital rationing and the horizon capital budgeting problems using a robust optimization framework. The models and the methodology we propose take into account the uncertainty of the input data. The uncertainty of the cash flows is modeled as a range of values that is allowed for each uncertain data. Unlike stochastic models, this approach does not make assumptions on the probability distribution of uncertain data. Moreover, this approach is highly tractable, easy to implement, and provides insights into portfolio selection problems. An attractive point of the model is that the decision maker can set the value of the parameters that control the robustness of the optimal solution, in order to balance the trade-off between protection level and performance. We illustrate our models with examples that show promising results. We also provide new duality and KKT optimality conditions.     

A hierarchical planning system for energy intensive production environments

This paper describes a hierarchical production planning approach with decision support features for energy intensive industries with particular reference to a tile manufacturing factory. In the tiling industry, the facilities which contribute most to the consumption of energy (and, hence, to the production costs) are usually the kilns where the curing operation is carried out. Frequently, the kilns are also the bottleneck in terms of capacity utilization. Thus, in order to save on energy costs, a planning approach which aims at minimizing the number of active kilns throughout the year is needed besides optimizing the process design in the curing department. To achieve the latter goal, it is necessary to take into account demand fluctuations as well as detailed capacity restrictions while deciding on the lot sizes of the products and the kilns on which the products are loaded. Rather than adopting a monolithic mathematical model for developing a desirable production plan, a hierarchical approach which decomposes the problem into two sub-problems is preferred. In the first level, products and capacity are aggregated over the planning horizon to achieve an overall consideration of demand fluctuations over time. Then, the solution provided by the aggregate solution for the current planning period is disaggregated into a detailed lot sizing and loading solution. The disaggregated problem is difficult to solve and hence, a heuristic is proposed here. This planning approach is sustained by a Decision Support System which enables the elimination of possible inconsistencies in the production plan by providing an effective interaction with the decision maker.     

AN INVENTORY MODEL FOR DETERIORATING ITEMS WITH STOCK-DEPENDENT DEMAND UNDER THE CONDITIONS OF INFLATION AND TIME-VALUE OF MONEY

In this paper, we incorporate the effects of inflation and time-value of money in inventory decision making when demand, at each time moment rather than being constant, is considered to be dependent upon current stock level. In addition, the shortages are neither completely backlogged nor completely lost assuming the backlogging rate to be linearly dependent on the amount of demand backlogged. We shall be concerned with finding the optimal number of replenishments and service rate to minimize the total relevant costs over a finite planning horizon. Numerical examples are presented to illustrate the proposed models.     

A centralized/decentralized design of a full return contract for a risk-free manufacturer and a risk-neutral retailer under partial information sharing

We consider the design of full return contract in a simple supply chain with a risk-free manufacturer and a risk-neutral retailer. In this problem, the ordering quantity and the rebate price for unsold products are determined by the retailer and the manufacturer, respectively. We propose an optimal solution procedure in centralized and decentralized decision making environments considering when the information sharing among the retailer and the manufacturer is partial. We provide numerical examples to explain the proposed solution procedures.     

回收数量受价格和随机因素影响的定价模型

假设在再制造闭环供应链中,集中决策者、第三方和制造商分别从最终客户那里回收废旧品,其回收数量受回收价格和随机因素影响,制造商对获得的旧部件进行再制造,如果旧部件不能满足生产需求,制造商将从新部件供应商那里以高价格采购新部件来补充短缺。本文按照废旧品回收的供应链成员不同,建立了3个定价决策模型,证明了每个模型最优解的存在性和唯一性,然后在特殊情形下进一步求得各模型最优解的解析式,最后用具体算例对模型进行了验证。     

Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand

In this paper, a joint pricing and inventory control for non-instantaneous deteriorating items is developed. We adopt a price and time dependent demand function. Shortages is allowed and partially backlogged. The major objective is to determine the optimal selling price, the optimal replenishment schedule and the optimal order quantity simultaneously such that, the total profit is maximized. We first show that for any given selling price, optimal replenishment schedule exists and unique. Then, we show that the total profit is a concave function of price. Next, we present a simple algorithm to find the optimal solution. Finally, we solve a numerical example to illustrate the solution procedure and the algorithm.     

Robust analogizing and the outside view: two empirical tests of case‐based decision making

Executives use analogies to improve strategic decisions. However, existing research provides little guidance on the types and number of analogies that produce the best decisions. We examine models of analogy and present findings from two empirical tests. The first test, a study of private‐equity investment decisions, finds that an ‘outside view’—forming a reference class of analogies—performs better than a few analogies familiar to the decision maker. The second test, a study of film revenue forecasts, compares a new model we call similarity‐based forecasting (SBF) with existing methods. The study finds that SBF, which combines elements of reference class forecasting and case‐based decision making, produces better forecasts than regression models. We discuss the consequences of our findings for research and practice. Copyright © 2012 John Wiley & Sons, Ltd.     

Coordination of planning and scheduling decisions in global supply chains with dual supply modes

We address the problem of coordinating aggregate planning decisions and short-term scheduling decisions in supply chains with dual supply modes. We consider long lead time, less expensive sea shipments that are based on demand forecast, and responsive but costly air shipments that are based on revised forecast closer to the demand period. The planning problem determines the sea shipment order quantity and inventory level, while the scheduling model determines the schedule and quantity of air shipments. Results from our numerical experiments suggest that our model leads to consistent cost improvements over a wide range of operating scenarios.     

Risk Aversion and Tacit Collusion in a Bertrand Duopoly Experiment

Recent research has found significant differences in the ability of subjects tacitly to collude, depending on the nature of the strategic interaction (e.g., Cournot vs. Bertrand or substitutes vs. complements goods). We investigate the relationship between subject-specific risk tolerance and tacit collusion in Bertrand duopoly experiments. We find that less risk-averse subjects price higher than do their more risk-averse counterparts, but this relationship is only significant when actions are strategic substitutes. When we analyze pair-level data, we find that non-risk averse subject pairs price significantly higher than do risk averse and mixed pairs in both the substitutes and complements treatments.     

Myopic optimal policy for a multi-period, two-delivery-lead-times, stochastic inventory problem with minimum cumulative commitment and capacity

This paper studies a single-product, multi-period, stochastic inventory problem that imposes the lower and upper bounds on the cumulative order quantity during a planning horizon and allows two delivery lead times. This model includes three features. The first one is that a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity during the planning horizon is constrained with the capacity. The second one is that the buyer agrees to purchase the product at least a certain percentage of the purchased capacity during the planning horizon. The third one is that the supplier allows the buyer to order the product with two-delivery-lead-times. We identify conditions under which a myopic ordering policy is optimal. We also develop an algorithm to calculate the optimal capacity when the minimum cumulative order quantity commitment is a certain percentage of the capacity. We then use the algorithm to evaluate the effect of the various parameters on the buyer’s minimum expected total cost during the planning horizon. Our computation shows that the buyer would benefit from the commitments and two-delivery-lead-times.     

Customer and retailer rebates under risk aversion

In a supply chain setting, we analyze a manufacturer's customer and retailer rebates, which are sales incentives offered to the end buyers and retailers, respectively. The performance of both rebates is influenced by the retailer's objective and response to the promotion due to his intermediary position in the channel. Earlier studies investigating rebates in distribution channels have traditionally assumed that the retailer is risk neutral with the objective of maximizing expected profits. In our paper, we consider a risk-averse retailer. We formally model risk aversion by adopting the Conditional-Value-at-Risk (CVaR) decision criterion. Using a stochastic and (effective) price dependent demand, we analyze the manufacturer's rebate amount decisions and the retailer's joint inventory and pricing decisions in a game theoretical framework. We provide several structural properties of the objective functions and show monotonicity of the retailer's decisions in the degree of risk aversion. For the case of retailer rebates, we characterize the unique equilibrium, and for the case of customer rebates, we prove the existence of an equilibrium. Using numerical examples, we provide further insights on the impact of risk aversion. For example, given an exogenous wholesale price, we observe a threshold value on the retailer's risk-aversion parameter below (above) which the manufacturer is better off with retailer rebates (customer rebates); implying that the manufacturer's preferred rebate type can be different depending on whether the retailer is risk neutral or sufficiently risk averse.