Optimal Distributed Dynamic Advertising

We propose a novel approach to modeling advertising dynamics for a firm operating over a distributed market domain based on controlled partial differential equations of the diffusion type. Using our model, we consider a general type of finite-horizon profit maximization problem in a monopoly setting. By reformulating this profit maximization problem as an optimal control problem in infinite dimensions, we derive sufficient conditions for the existence of its optimal solutions under general profit functions, as well as state and control constraints, and provide a general characterization of the optimal solutions. Sharper, feedback-form characterizations of the optimal solutions are obtained for two variants of the general problem. The first author gratefully acknowledges financial support by the NSF, the DAAD, the SFB 611 (Bonn), and the Max-Planck-Institut für Mathematik (Leipzig) through an IPDE fellowship.     

利润最大问题与弱DEA有效(C2GS2)

对利润最大问题[1]本文用不同于文[1]的方法来讨论.通过解这一个问题,不但知道在一定条件下有最大利润的决策单元的弱DEA有效性(C2GS2),而且找到所有有最大利润的决策单元.     

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。     

A fuzzy goal programming approach to integrated loading and scheduling of a batch processing machine

This paper concerns a real-life problem of loading and scheduling a batch-processing machine. The integrated loading and scheduling problem is stated as a multicriteria optimization problem where different types of objectives are included: (1) short-term objectives of relevance to the shop floor, such as throughput maximization and work-in-process inventory minimization, and (2) long-term objectives such as balancing of end product inventory levels and meeting financial targets imposed by the higher production planning level. Two types of uncertainty are considered: (1) uncertainty inherent in loading and scheduling objective targets (goals) such as the allocated budget and end product demand, and (2) uncertainty in importance relations among the objectives. These two types of uncertainty are modelled using fuzzy sets and fuzzy relations, respectively. A fuzzy goal programming model and the corresponding method are developed which handle both fuzzy and crisp goals and fuzzy importance relations among the goals. Numerical examples are given to illustrate the effectiveness of the developed model.     

A slacks-based measure of efficiency in data envelopment analysis

In this paper, we will propose a slacks-based measure (SBM) of efficiency in Data Envelopment Analysis (DEA). This scalar measure deals directly with the input excesses and the output shortfalls of the decision making unit (DMU) concerned. It is units invariant and monotone decreasing with respect to input excess and output shortfall. Furthermore, this measure is determined only by consulting the reference-set of the DMU and is not affected by statistics over the whole data set. The new measure has a close connection with other measures proposed so far, e.g., Charnes–Cooper–Rhodes (CCR), Banker–Charnes–Cooper (BCC) and the Russell measure of efficiency. The dual side of this model can be interpreted as profit maximization, in contrast to the ratio maximization of the CCR model. Numerical experiments show its validity as an efficiency measurement tool and its compatibility with other measures of efficiency.     

Measurement of a linkage among environmental,operational, and financial performance in Japanese manufacturing firms: A use of Data Envelopment Analysis with strong complementary slackness condition

This study investigates a linkage among environmental, operational and financial performance in Japanese manufacturing industry. All manufacturing firms examined in this study are listed in Tokyo stock exchange market. We use DEA (Data Envelopment Analysis) as an evaluation methodology. This study finds that large firms have managerial capabilities to improve their operational and environmental performance. The improvement leads to the enhancement of their financial performance. However, we cannot find such a business linkage in small and medium-sized firms. They improve their operational performance and then direct themselves toward the improvement of their environmental performance. Their environmental performance is, not the first priority, the second priority for the small and medium-sized firms even though Japanese government is currently making a policy pressure on all manufacturing firms to pay attention to various environmental issues related to the global warming and climate change. The environmental protection policy is effective on only large Japanese manufacturing firms that have technological and financial capabilities for environmental protection.     

基于双边市场理论的金融超市竞争定价策略研究

基于双边市场理论,重点分析金融超市在双寡头垄断情形下的竞争定价策略。即在在一般定价模型的基础上,构建起加入金融超市双边用户交易次数为歧视标准的价格歧视竞争模型。并且围绕金融超市追求长期利益和短期利益两种不同动机,对采取该策略均衡时最终用户的均衡进入价格、金融超市利润和市场份额进行比较分析。最后,给出金融超市实施价格歧视策略的对策和建议。     

Towards profitability: a utility approach to the credit scoring problem

Since credit scoring was first applied in the 1940s the standard methodology has been to treat consumer lending decisions as binary classification problems, where the goal has been to make the best possible ‘good/bad’ classification of accounts on the basis of their eventual delinquency status. However, the real goal of commercial lending organizations is to forecast continuous financial measures such as contribution to profit, but there has been little research in this area. In this paper, continuous models of customer worth are compared to binary models of customer repayment behaviour. Empirical results show that while models of customer worth do not perform well in terms of classifying accounts by their good/bad status, they significantly outperform standard classification methodologies when ranking accounts based on their financial worth to lenders.     

Resource Analysis in Project Evaluation: A Multicriteria Approach

In this paper we develop and demonstrate the application of a goal programming model. It is designed to assist top management in incorporating organizational goals when allocating funds to competing projects. Investment decisions, however, normally involve several, often conflicting goals. The fact that some of these goals cannot be measured in dollars or other scales further complicates the problem. Among the many proposed methodologies of multicriteria decision-making (MCDM), goal programming (GP) is perhaps the most popular and widely used. It provides optimal solutions; however, it has a major drawback: the decision-maker must specify the goals and priorities a priori. To overcome this problem, we suggest the Delphi method, a systematic procedure to obtain a consensus from a group of participants. It is conducted prior to GP to (1) identify the goals, (2) determine priorities among the goals, and (3) establish a target level for each goal. To test the practicality and extent of applicability, the proposed model is directly applied to evaluate rural road projects of the Division of Transportation, Bureau of Indian Affairs (BIA), US Department of Interior.     

Adapting Multi-criteria Planning to the Nigerian Economy

Techniques of development planning involve physical and financial aspects. Financial planning refers to the allocation of monetary resources; in Nigeria the previous development plans and budgets, which had been based on the incremental approach, contained various shortcomings, resulting in the deliberate inflation of estimated expenditure, and consequently it has been associated with retarded growth and conflicts between ministries. In addition, the approach does not adequately relate national objectives to their priorities. Conventional mathematical programming models are unable to allocate resources effectively in a conflicting environment. This paper proposes a goal programming model for allocating a country's scarce resources among competing sectors during a planned period. The goal programming model is shown to be adequate for allocating resources under the conflicting conditions of national planning. The model can help to determine all the priorities for the goals.     

Multiple criteria decision making with interactive over-achievement programming

Whereas in goal programming the under-achievement with respect to (usually) unattainable goals are minimized, we propose the maximization of the over-achievements with respect to feasible goals or required values. An interactive algorithm, in which the over-achievements are maximized via a barrier function, is presented to implement the proposed approach.     

A dynamic bank portfolio planning model with multiple scenarios,multiple goals and changing priorities

The paper discusses a practical application of a two-stage linear goal programming model to the management of the domestic and foreign currency denominated assets and liabilities of a large bank in Finland. The planning horizon includes three one-year planning periods. A number of alternative scenarios are used to describe uncertainty concerning future developments in these periods. The scenarios are related to general economic conditions as well as the state of the domestic and foreign financial markets. The bank is assumed to have multiple conflicting goals with different and changing priorities. The goals deal with expected profits, risk, liquidity, capital adequacy, growth, customer relationships and several other aspects of the bank's operations.     

Newsvendor solutions via conditional value-at-risk minimization

In this paper, we consider the minimization of the conditional value-at-risk (CVaR), a most preferable risk measure in financial risk management, in the context of the well-known single-period newsvendor problem, which is originally formulated as the maximization of the expected profit or the minimization of the expected cost. We show that downside risk measures including the CVaR are tractable in the problem due to their convexity, and consequently, under mild assumptions on the probability distribution of products’ demand, we provide analytical solutions or linear programming (LP) formulation of the minimization of the CVaR measures defined with two different loss functions. Numerical examples are also exhibited, clarifying the difference among the models analyzed in this paper, and demonstrating the efficiency of the LP solutions.     

Three fuzzy goal programming models for index portfolios

Studies show that most actively managed mutual funds struggle to beat the market, driving an increase in the popularity of index investing. Index investing instruments, including index funds and Exchange-traded Funds, aim to track market performance. This study pursues both tracking error minimization and excess return maximization, two conflicting objectives, to construct an index portfolio. In the real-world financial environment, the desires and expectations of decision makers are generally imprecise. This study applies fuzzy theory to deal with imprecise objectives. This study represents minimizing tracking error and maximizing excess return as ‘fuzzy goals’ to improve traditional goal programming, which is suitable for handling multiple conflicting objectives, but subject to establishing crisp goals. Three fuzzy goal programming (FGP) models that track indexes are compared and discussed, and the results show that through certain membership functions and tracking models, an index tracking portfolio with a tracking error lower than the 0050 index fund, and a similar excess return to 0050 index fund can be constructed using additive type FGP. max-min type FGP underperforms the additive type FGP in index fund construction.     

On Lagrangian duality in vector optimization: applications to the linear case

We recall a general scheme for vector problems based on separation arguments and alternative theorems, and then, this approach is exploited to study Lagrangian duality in vector optimization. We show that the vector linear duality theory due to Isermann can be embedded in this separation approach. The theoretical part of this paper serves the purpose of introducing two possible applications. Some well-known classical applications in economics are the minimization of costs and the maximization of profit for a firm. We extend these two examples to the multiobjective framework in the linear case, exploiting the duality theory of Isermann. For the former, we consider the minimization of costs and of pollution as two different and conflicting goals; for the latter, we introduce as second objective function the profit for a competitor firm. This allows us to study the relationships between the shadow prices referred to the two different goals and to introduce a new representation of the feasible region of the dual problem.     

Firm and industry level profit efficiency analysis using absolute and uniform shadow prices

We discuss the nonparametric approach to profit efficiency analysis at the firm and industry levels in the absence of complete price information. Two new insights are developed. First, we measure profit inefficiency in monetary terms using absolute shadow prices. Second, we evaluate all firms using the same input–output prices. This allows us to aggregate firm-level profit inefficiencies to the overall industry inefficiency. Besides the measurement of profit losses, the presented approach enables one to recover absolute price information from quantity data. We conduct a series of Monte Carlo simulations to study the performance of the proposed approach in controlled production environments.     

Radial and non-radial decompositions of profit change: With an application to Indian banking

Grifell-Tatje and Lovell [Grifell-Tatje, E., Lovell, C.A.K., 1999. Profits and productivity. Management Science 45, 1177–1193] made significant contributions to the literature on the extended radial DEA framework by decomposing profit change into six mutually exclusive components. Their approach, however, poses two basic problems. First, the radial estimates on these components might give conflicting signals about the direction of profit change after the full radial efficiencies are achieved when slacks are present. Second, evaluations of these components, using base-period prices as weights, can be potentially misleading. To address these concerns, we first introduce non-radial DEA models, and then, provide a few strong theoretical arguments in favor of using as weights either current-period prices or an average price covering both periods to value the contributions of each of these components. The Indian banking sector is taken as a case study to illustrate the radial and non-radial decompositions of profit change so as to empirically examine the role of competition on profit change and its drivers. Our broad empirical results are as follows: first, radial and non-radial models yield diametrically opposite results on the contributions of various components. Second, the increasing efficiency change trends in all ownership groups after 2002 indicate that the Government reform process instituted on the banking industry has had a favorable effect on the performance of the Indian banking sector. Third, despite the fact that nationalized banks are the oldest banks, their output and resource allocation behaviors do not reflect their learning experience.     

Optimal inventory policies for profit maximizing EOQ models under various cost functions

In this paper, we establish and analyze three EOQ based inventory models under profit maximization via geometric programming (GP) techniques. Through GP, we find optimal order quantity and price for each of these models considering production (lot sizing) as well as marketing (pricing) decisions. We also investigate the effects on the changes in the optimal solutions when different parameters are changed. In addition, a comparative analysis between the profit maximization models is conducted. By investigating the error in the optimal price, order quantity, and profit of these models, several interesting economic implications and insights can be observed.     

Optimal contracts and the manufacturer’s pricing strategies in a supply chain with an inequity-averse retailer

Studies in the supply chain literature have typically focused on profit or revenue maximization and assumed that agents within the supply chain are self-interested and only care about their own monetary payoffs. Research in these areas, however, rarely considers an important phenomenon called inequity aversion in which the object pursued by agents within the supply chain is not only their own profit maximization but also the equity of profit allocation. In fact, when agents within a supply chain collaborate with each other to serve a market, the scheme of profit allocation between them usually plays a determinate role in cooperation. Taking into account the impact of agents’ behavior of inequity aversion on the coordination of the supply chain, this paper investigates the optimal contracts and the manufacturer’s pricing strategies in a single-manufacturer and single-retailer supply chain. In this way, we obtain two interesting results: (1) the retailer’s equity aversion largely affects the manufacturer’s decision making, which is not always bad for the manufacturer; and (2) the retailer’s inequity aversion as well as the consumer’s price-sensitive coefficient plays a dominant role in the manufacturer’s decision making.