A competitive multiple-product newsboy problem with partial product substitution

This paper studies a multi-product competitive newsboy problem with shortage penalty cost and partial product substitution. We characterize the unique Nash equilibrium of the competitive model and analyze some properties of the equilibrium. An iterative algorithm is developed on the basis of approximating the effective demand as well as the expected profit function for each product. Numerical experiments are conducted to illustrate the impacts of product substitution, demand correlation and demand variation on the optimal order quantities and the corresponding expected profits, and to compare the total optimal inventory level of the competitive case with that of the centralized case. The conclusion that competition always results in a higher total inventory level, even under the effect of product substitution is drawn in the symmetric case.     

Real option games with R&D and learning spillovers

We demonstrate to decision makers how to optimally make costly strategic pre-investment R&D decisions in the presence of spillover effects in an option pricing framework with analytic tractability. Decisions are modeled as impulse-type controls with random outcome. Two firms face two decisions that are solved interdependently in a two-stage game. The first-stage decision is: What is the optimal level of coordination (optimal policy/technology choice)? The second-stage decision is: What is the optimal effort for a given level of the spillover effects and the cost of information acquisition? The framework is extended to a two-period closed-loop stochastic game with (path-dependency inducing) switching costs that make strategy revisions harder. When conditions of learning-by-doing exist, we find that strategy shifts are easier to observe in market environments of high growth and high volatility.     

折扣下多阶段易腐品库存问题的无概率解决方法北大核心CSCDCSSCI

The classic perishable inventory problem assumes that the retailer should not be affected by upstream suppliers in the ordering process. However, real-world operation and management entail a relationship of competition and cooperation between retailers and suppliers. Suppliers therefore influence retailers′ decision-making processes. Suppliers often use discount marketing, which is effective in attracting retailers and increasing the sales volume of products. This also allows retailers to order products at lower cost, creating a win-win scenario. Value discounts and quantity discounts are commonly used in discount marketing. Value discounts allow a retailer to enjoy a cash discount when the retailer′s total order value reaches a certain value, and quantity discounts refer to a price discount offered by the supplier for all products when the retailer′s single order quantity exceeds a fixed value. Most studies in the literature on inventory management assume that the demand or demand distribution is known;however, in reality, it is difficult to obtain accurate demand and demand distribution. Historical demand data are usually the only information that is available. Developments in theoretical computer science allow online learning algorithms to completely depart from the assumption of statistical information and rely only on historical data for decision-making. The Weak Aggregating Algorithm (WAA), an online learning algorithm, constructs online strategy by learning from different experts′ advice and aggregating it;the online strategy can thus track the best expert advice. This assists online decision makers in effectively integrating various types of information and making decisions on such information. This study expands the research on the single-product, multi-period perishable inventory problem in the context of value discounts and quantity discounts without any assumption of statistical information. This article applies the WAA to learning from different experts′ advice in studying the perishable inventory problem when value discounts and quantity discounts can be used. The online ordering strategies (probability-free solutions) are constructed as follows. First, at the beginning of every period, experts recommend their static advice for the specific perishable inventory decision problem;such expert advice is fixed and will not be changed throughout all periods. Second, in the case of value discounts or quantity discounts, the online decision maker applies the WAA to assign different degrees of trust to different experts′ advice and then integrates the advice to make a decision. Last, the actual decision result of the decision problem is obtained, and cumulative gains are computed to evaluate the performance of the experts and the online decision maker. This paper constructs online ordering strategies in different situations. For real-valued order quantities, we aggregate experts′ advice to propose an online order strategy that considers value discounts in detail. We analyze a more practical case in which the order quantity is an arbitrary integer by constructing an online ordering strategy under value discounts through learning from expert advice. We then approach the matter from continuous and discrete angles to propose two explicit online order strategies under quantity discounts. This paper further verifies the performance of the proposed online ordering strategies through theoretical analysis and the use of numerical examples. Competitive performance is measured as the difference between the cumulative gains from using the online ordering strategies and the cumulative gains from following the best expert advice. The theoretical results show that the cumulative gains of the given online ordering strategies are as large as those of the best expert advice and that they outperform their benchmark strategies. The numerical examples indicate that the cumulative gains achieved by the given online ordering strategies fluctuate slightly around those achieved by the optimal expert advice. The competitive performance of the discrete online ordering strategies outperforms that of the continuous online ordering strategies. The theoretical results are therefore effectively validated. The numerical examples also show that different initial probability distributions have little impact on strategies′ competitive performance. In the case of value discounts, the online ordering strategy has better competitive performance for perishable products with a higher unit price, a lower unit cost, and higher value discounts. Regarding quantity discounts, the online ordering strategy performs better when the perishable products have a higher unit price, a lower unit cost, lower quantity discounts, and a lower discount threshold. A consideration of the actual situation leads to explicit ordering rules being proposed in this paper. These enable retailers to make ordering decisions quickly and effectively without information on future demand and thus to meet market demand with the optimal order quantity and maximize their profits. This paper thus provides guidance for perishable goods inventory management. © 2021. Journal of Industrial Engineering and Engineering Management. All rights reserved.     

A free gift card alternative to price discounts in the newsvendor problem

In this paper, we develop a newsvendor model in which the retailer gives “free” gift cards to consumers who purchase a regularly priced product at the end of the selling season instead of discounting the product. The model is developed for a market with patient consumers. We derive the sufficient optimality condition for the retailer's stocking level in the first period and the optimal gift card value in the second period. We also investigate the conditions under which giving gift cards results in higher expected profits than discounting the product. We find that five factors determine the effectiveness of gift cards. The first three factors are consumers' valuation per $1 of gift card, gift card redemption rates, and the average gross margin of the retailer. The last two factors are the degree to which consumers use gift cards to pay for products which they would have purchased from the retailer in the future with cash, and the additional spending above the gift card value consumers make when they redeem the card. The last two factors have a strong interaction. We also find that gift cards can be profitable when patient consumers consistently value each $1 by their redemption probability, even with 100% redemption. Numerical analysis shows that in the presence of patient consumers, increases in the redemption rate may lead to an increase in the expected profit. Similar counter-intuitive behavior of the expected profit occurs with changes in other problem parameters. The analysis also shows that gift cards' profit advantage over discounting increases with the variability of demand. The analysis also indicates that gift cards are most effective for low to medium priced products sold by high margin retailers.     

Defragmenting the Regulatory Process†

The regulatory process is often criticized for being cumbersome and slow, much like a computer whose hard drive is fragmented by files no longer used or useful. Like such a computer, the regulatory process contains many requirements of dubious utility. These include the Paperwork Reduction Act, the Regulatory Flexibility Act, and numerous executive orders. While other parts of the regulatory process such as notice and comment and cost‐benefit analysis have received much more academic attention, these other parts of the process deserve examination as well. This article argues that such an examination will reveal that these statutes and executive orders add little of value to the regulatory process while consuming agency resources. An improved requirement for cost‐benefit analysis with distributional analysis could easily replace virtually all of these requirements and improve regulations while reducing the time needed to promulgate regulations.     

What Affects the Quality of Economic Analysis for Life‐Saving Investments?‡

Economic analysis of life-saving investments in both the public and private sectors has the potential to dramatically improve longevity and the quality of life, but only if the analyses on which decisions are based are done well. In this article, we analyze a data set that provides information on the content and quality of journal articles that measure the cost-effectiveness of life-saving investments. Our study is the first to provide a detailed multivariate analysis of factors affecting objective measures of quality. We also explore whether a series of recommendations by an expert panel convened by the U.S. Public Health Service affect the way analyses of specific life-saving investments are done. Our results suggest that four factors are positively correlated with an index we construct to measure analytical quality: (1) having at least one author affiliated with a university, (2) publication in a journal that has experience in publishing these analyses, (3) if the life-saving investment is located in the United States, and (4) if the analysis considers a measure of social costs or benefits. Somewhat surprisingly, a study's funding source and whether it is affiliated with industry are not significantly correlated with the quality index. Finally, neither time nor the panel guidelines had an impact on the index.     

The single-period inventory problem: Extension to random yield from the perspective of the supply chain

A special form of the single-period inventory problem (newsvendor problem) with a known demand and stochastic supply (yield) is studied. A general analytic solution for two types of yield risks, additive and multiplicative, is described. Numerical examples demonstrate the solutions for special cases of uniform distribution yield risks. An analysis of a two-tier supply chain of customer and producer reveals that the customer may find it optimal to order more than is needed, since a larger order increases the producer's optimal production quantity.     

Late season low inventory assortment effects in the newsvendor problem

The assumption of the newsvendor being able to satisfy demand as long as on-hand inventory is positive does not hold for a non-homogenous product. Consumers who do not find a unit of the product which satisfies their secondary features preferences may not purchase the product even though the newsvendor has positive on-hand inventory. This is likely to occur late in the season as inventory level declines. We solve a newsvendor problem in which the probability of purchase by consumers is increasing in on-hand inventory for any inventory level below that which is needed to have a complete assortment. We identify the sufficient optimality condition for the order quantity. We show that, unlike the case of inventory-dependent demand models in the literature, the optimal order quantity may decrease due to the assortment effect. We investigate two types of pre-end of season discounts, immediate all-units and delayed, as ways to mitigate the late season assortment effect and show that in some cases, they can increase the newsvendor׳s profit and free up the shelf space for other products.     

On Weighing Gains and Investments at the Margin of Risk Regulation

Analysts have long noted an apparent discrepancy in the level of investment seemingly necessary to meet "acceptable" levels of public safety. At the margin of risk regulation, i.e., where safety determination is judged acceptable, the traditional cost-benefit calculus appears to contribute obvious rationale to the final political decision. Efforts are now being made to introduce a measure of consistency into the application of risk-cost benefit analysis to radiological protection. This paper reviews these efforts from a UK perspective. It also looks at how the issue was treated in a public setting through the Sizewell B Public Inquiry.     

Modeling the Cost Effectiveness of Fire Protection Resource Allocation in the United States: Models and a 1980–2014 Case Study

The estimated cost of fire in the United States is about $329 billion a year, yet there are gaps in the literature to measure the effectiveness of investment and to allocate resources optimally in fire protection. This article fills these gaps by creating data‐driven empirical and theoretical models to study the effectiveness of nationwide fire protection investment in reducing economic and human losses. The regression between investment and loss vulnerability shows high R² values (≈0.93). This article also contributes to the literature by modeling strategic (national‐level or state‐level) resource allocation (RA) for fire protection with equity‐efficiency trade‐off considerations, while existing literature focuses on operational‐level RA. This model and its numerical analyses provide techniques and insights to aid the strategic decision‐making process. The results from this model are used to calculate fire risk scores for various geographic regions, which can be used as an indicator of fire risk. A case study of federal fire grant allocation is used to validate and show the utility of the optimal RA model. The results also identify potential underinvestment and overinvestment in fire protection in certain regions. This article presents scenarios in which the model presented outperforms the existing RA scheme, when compared in terms of the correlation of resources allocated with actual number of fire incidents. This article provides some novel insights to policymakers and analysts in fire protection and safety that would help in mitigating economic costs and saving lives.     

A successive approximation algorithm for the multiple knapsack problem

It is well-known that the multiple knapsack problem is NP-hard, and does not admit an FPTAS even for the case of two identical knapsacks. Whereas the 0-1 knapsack problem with only one knapsack has been intensively studied, and some effective exact or approximation algorithms exist. A natural approach for the multiple knapsack problem is to pack the knapsacks successively by using an effective algorithm for the 0-1 knapsack problem. This paper considers such an approximation algorithm that packs the knapsacks in the nondecreasing order of their capacities. We analyze this algorithm for 2 and 3 knapsack problems by the worst-case analysis method and give all their error bounds.     

动态车辆路径问题排队模型分析

分析了一类动态车辆路径问题,其中顾客需求以泊松流形式出现,现场服务时间服从一般分布.提出解决该问题的两种策略:顺序服务策略和中点改进策略,利用排队论、几何概率论等领域的知识分别求出了这两种策略的系统时间,并通过仿真数据实验验证了这两种策略的有效性.     

Simple policies in the economic lot scheduling problem with zero setup costs

The economic lot scheduling problem is analysed for the case when the cost of setups, but not their duration, is assumed to be zero. This would be the case when setups are performed by the machine operators, or when management's goal is holding-cost reduction. Theoretical results are presented describing when the common cycle solution of producing one lot of every item every cycle is optimal or near optimal. Computational results using simulated data are then presented which show that the common cycle solution is nearly optimal in a wide range of practical situations.     

考虑风险规避的秘书问题求解的一个启发式方法

秘书问题是一类序贯观察与选择问题,描述了动态的信息搜索与决策过程.针对现有的以寻找满意解为目标的启发式方法存在诸多局限,提出了新的启发式方法,该方法基于当前观测中侯选项在已观察侯选项中的相对排名、待观测侯选项数量以及决策者的抱负水平,决策者可以通过设定抱负水平灵活决定该启发式方法的结果导向.推导了该启发式方法的性能指标,并通过仿真的方法与已有启发式方法的性能进行了比较.结果发现,该启发式方法在最终选择的侯选项的期望排名和稳定性,以及风险解的避免上均优于已有的启发式方法.     

An Approach for Optimal Allocation of Safety Resources: Using the Knapsack Problem to Take Aggregated Cost‐Efficient Preventive Measures

On the basis of the combination of the well‐known knapsack problem and a widely used risk management technique in organizations (that is, the risk matrix), an approach was developed to carry out a cost‐benefits analysis to efficiently take prevention investment decisions. Using the knapsack problem as a model and combining it with a well‐known technique to solve this problem, bundles of prevention measures are prioritized based on their costs and benefits within a predefined prevention budget. Those bundles showing the highest efficiencies, and within a given budget, are identified from a wide variety of possible alternatives. Hence, the approach allows for an optimal allocation of safety resources, does not require any highly specialized information, and can therefore easily be applied by any organization using the risk matrix as a risk ranking tool.     

Testing the Cultural Theory of Risk in France

Cultural Theory, as developed by Mary Douglas, argues that differing risk perceptions can be explained by reference to four distinct cultural biases: hierarchy, egalitarianism, individualism, and fatalism. This paper presents empirical results from a quantitative survey based on a questionnaire devised by Karl Dake to measure these cultural biases. A large representative sample (N = 1022) was used to test this instrument in the French social context. Correlations between cultural biases and perceptions of 20 social and environmental risks were examined. These correlations were very weak, but were statistically significant: cultural biases explained 6%, at most, of the variance in risk perceptions. Standard sociodemographic variables were also weakly related to risk perceptions (especially gender, social class, and education), and cultural biases and sociodemographic variables were themselves inter correlated (especially with age, social class, and political outlook). The authors compare these results with surveys conducted in other countries using the same instrument and conclude that new methods, more qualitative and contextual, still need to be developed to investigate the cultural dimensions of risk perceptions. The paper also discusses relationships between perceptions of personal and residual risk, and between perceived risk and demand for additional safety measures. These three dimensions were generally closely related, but interesting differences were observed for some risk issues.     

Measuring the benefit of changing the value offering in grocery supply chains

New value-adding solutions are needed for grocery supply chains to gain a sustainable competitive advantage in a market environment characterised by increased competition. This paper discusses two case studies that identify how improvements to the value offering brought about enhancements to the performance of the total supply chain. The concept of ‘time benefit analysis’ is applied to measure the impact of the change. These approaches offer novel and unique techniques for performance measurement and value offering analysis in supply chain management.     

Quantity Flexibility Contract in the Presence of Discount Incentive

We design a new contract, which we refer to as the QFi contract, that combines the quantity flexibility (QF) mechanism and the price‐only discount incentive. Under the QF contract, the buyer does not assume full responsibility for the forecast, yet the supplier guarantees the availability of the forecasted quantity and extra buffer inventory. In contrast, the price‐only discount contract places full inventory burden on the buyer. We show that the proposed QFi contract effectively balances the inventory risk for both the buyer and the supplier considering both the QF and discount mechanisms. We also show that the QFi contract is able to achieve supply chain coordination. More importantly, the QFi contract's coordinating price scheme does not require knowledge of demand distribution. We identify areas where the buyer and supplier may both benefit from implementing the QFi contract as opposed to the extant QF or price‐only (wholesale) discount contractual decisions in a decentralized supply chain. We also specify the conditions under which supply chain coordination can be achieved in a win‐win manner. We conclude with managerial implications and provide directions for future research.     

基于多人合作理论的供应链库存利益分配机制研究

供应链使企业间能通过共享彼此的供求信息大大降低企业的库存量和库存成本并以最快的速度、最好的质量赢得市场。合理的供应链利益分配机制是供应链上的各企业以及供应链系统自身能够持续稳定发展的基础。本文对供应链库存效益进行量化研究,并且应用多人合作理论,采用τ值法给出了供应链库存效益分配模型。     

Reduced costs propagation in an efficient implicit enumeration for the 01 multidimensional knapsack problem

In a previous work we proposed a variable fixing heuristics for the 0-1 Multidimensional knapsack problem (01MDK). This approach uses fractional optima calculated in hyperplanes which contain the binary optimum. This algorithm obtained best lower bounds on the OR-Library benchmarks. Although it is very attractive in terms of results, this method does not prove the optimality of the solutions found and may fix variables to a non-optimal value. In this paper, we propose an implicit enumeration based on a reduced costs analysis which tends to fix non-basic variables to their exact values. The combination of two specific constraint propagations based on reduced costs and an efficient enumeration framework enable us to fix variables on the one hand and to prune significantly the search tree on the other hand. Experimentally, our work provides two main contributions: (1) we obtain several new optimal solutions on hard instances of the OR-Library and (2) we reduce the bounds of the number of items at the optimum on several harder instances.