Data envelopment analysis for environmental assessment: Comparison between public and private ownership in petroleum industry

Environmental assessment recently becomes a major policy issue in the world. This study discusses how to apply Data Envelopment Analysis (DEA) for environmental assessment. An important feature of the DEA environmental assessment is that it needs to classify outputs into desirable (good) and undesirable (bad) outputs because private and public entities often produce not only desirable outputs but also undesirable outputs as a result of their production activities. This study proposes the three types of unification for DEA environmental assessment by using non-radial DEA models. The first unification considers both an increase and a decrease in the input vector along with a decrease in the direction vector of undesirable outputs. This type of unification measures “unified efficiency”. The second unification considers a decrease in an input vector along with a decrease in the vector of undesirable outputs. This type of unification is referred to as “natural disposability” and measures “unified efficiency under natural disposability”. The third unification considers an increase in an input vector but a decrease in the vector of undesirable outputs. This type of unification is referred to as “managerial disposability” and measures “unified efficiency under managerial disposability”. All the unifications increase the vector of desirable outputs. To document their practical implications, this study has applied the proposed approach to compare the performance of national oil firms with that of international oil firms. This study identifies two important findings on the petroleum industry. One of the two findings is that national oil companies under public ownership outperform international oil companies under private ownership in terms of unified (operational and environmental) efficiency and unified efficiency under natural disposability. However, the performance of international oil companies exhibits an increasing trend in unified efficiency. The other finding is that national oil companies need to satisfy the environmental standard of its own country while international oil companies need to satisfy the international standard that is more restricted than the national standards. As a consequence, international oil companies outperform national oil companies in terms of unified efficiency under managerial disposability.     

“Bricks-and-mortar” vs. “clicks-and-mortar”: An equilibrium analysis

The Internet has provided traditional retailers a new means with which to serve customers. Consequently, many “bricks-and-mortar” retailers have transformed to “clicks-and-mortar” by incorporating Internet sales. Examples of companies making such a transition include Best Buy, Wal-Mart, Barnes & Noble, etc. Despite the increasing prevalence of this practice, several fundamental questions remain: (1) Does it pay off to go online? (2) Which is the equilibrium industry structure? (3) What is the implication of this business model for consumers? We study these issues in an oligopoly setting and show that clicks-and-mortar arises as the equilibrium channel structure. However, we find that this equilibrium does not necessarily imply higher profits for the firms: in some cases, rather, it emerges as a strategic necessity. Consumers are generally better off with clicks-and-mortar retailers. If firms align with pure e-tailers to reach the online market, we show that a prisoner’s dilemma-type equilibrium may arise.     

Customization competition between branded firms: Continuous extension of product line from core product

We study a competition of product customization between two branded firms by a game-theoretic approach. Firms produce products with two attributes: one attribute indicates a characteristic with regard to “function” or “design” of a product and the other indicates “taste” or “flavor” of the product, which reflects consumers’ brand/taste preferences. Two branded firms have their own specific core products and our customization is defined as a continuous extension of their product line from the core product only along the “function” attribute. In particular, we allow asymmetric positions of core products, which may create the position advantage/disadvantage between firms. We suppose that consumers incur their selection costs with regard to finding their most favorable item among a rich variety of products and firms incur their customizing costs with regard to extending their product lines. We first show that in the equilibrium, branded firms should fundamentally adopt their customizations to cover the center space in the market as far as possible, regardless of the position of the competitor’s core product. Therefore, the position of the core product contributes to the creation of a competitive advantage: when one firm’s core product is located more closely to the center of the market than the competitor’s, its customization can always cover more range of the center space in the market, while keeping its degree of customization smaller than the competitor’s. Furthermore, we show some implications of unit-cost improvement: in a short run, a firm is better off concentrating on the improvement of the unit selection cost rather than the unit customizing cost. In contrast, in a long run, both firms can benefit from the improvement of the unit customizing cost.     

A comparison of different quantity discount pricing policies in a two-echelon channel with stochastic and asymmetric demand information

In this paper, we study quantity discount pricing policies in a channel of one manufacturer and one retailer. The paper assumes that the channel faces a stochastic price-sensitive demand but the retailer can privately observe the realization of an uncertain demand parameter. The problem is analyzed as a Stackelberg game in which the manufacturer declares quantity discount pricing schemes to the retailer and then the retailer follows by selecting the retail price and associated quantity. Proposed in the paper are four quantity-discount pricing policies: “regular quantity discount”; “fixed percentage discount”; “incremental volume discount” and “fixed marginal-profit-rate discount”. Optimal solutions are derived, and numerical examples are presented to illustrate the efficiency of each discount policy.     

Strategic multi-store opening under financial constraint

This paper analyzes strategic store openings in a situation in which firms can open multiple stores depending on the financial constraints of the firm. Specifically, given any upper limit of the number of store openings that two potentially symmetric firms can open, they sequentially determine the number of store openings, including their locations, to maximize their profits. As a result of our analysis in a microeconomic framework, we show that the equilibrium strategy can be wholly classified into only two following opposite strategies according to the level of their financial constraints involved. When firms can afford to invest significant amounts of money in the market, the leader chooses “segmentation strategy,” in which a part of the market can be monopolized by opening a chain of multiple stores and deterring the follower’s entry. In contrast, when the leader has a severe financial constraint so that it can only monopolize less than half of the market, the leader chooses “minimum differentiation strategy,” where firms open each of their stores at exactly the same point as the rival’s. Under this strategy, the leader necessarily captures just half of the market. Furthermore, we show that regardless of potential symmetry between firms, both first and second mover advantages in terms of profit can occur in the equilibrium.     

A note on demand functions with uncertainty

Demand functions with “additive” and “multiplicative” uncertainty can fail to satisfy the “Slutsky symmetry” conditions required for demand to be based on utility maximization. This makes welfare analysis infeasible, which is important in many applications. Additive uncertainty can also generate negative demand realizations, and this can create non-trivial analytical problems.     

The affect heuristic

This paper introduces a theoretical framework that describes the importance of affect in guiding judgments and decisions. As used here, “affect” means the specific quality of “goodness” or “badness” (i) experienced as a feeling state (with or without consciousness) and (ii) demarcating a positive or negative quality of a stimulus. Affective responses occur rapidly and automatically—note how quickly you sense the feelings associated with the stimulus word “treasure” or the word “hate”. We argue that reliance on such feelings can be characterized as “the affect heuristic”. In this paper we trace the development of the affect heuristic across a variety of research paths followed by ourselves and many others. We also discuss some of the important practical implications resulting from ways that this heuristic impacts our daily lives.     

An application of cooperative game among container terminals of one port

In this paper a two-stage game that involves three container terminals located in Karachi Port in Pakistan is discussed. In the first stage, the three terminals have to decide on whether to act as a singleton or to enter into a coalition with one or both of the other terminals. The decision at this stage should presumably be based on the predicted outcome for the second stage. The second stage is here modelled as a Bertrand game with one outside competitor, the coalition and the terminal in Karachi Port (if any) that has not joined the coalition. Furthermore, three partial and one grand coalition among the three terminals at Karachi Port are investigated. The concepts of “characteristic function” and “core” are used to analyse the stability of these coalitions and this revealed that one combination does not satisfy the superadditivity property of the characteristic function and can therefore be ruled out. The resulting payoffs (profits) of these coalitions are analysed on the basis of “core”. The best payoff for all players is in the case of a “grand coalition”. However, the real winner is the outsider (the terminal at the second port) which earns a better payoff without joining the coalition, and hence will play the role of the “orthogonal free-rider”.     

Optimal pricing and inventory policies: Centralized and decentralized decision making

The paper studies an optimal control problem of pricing and inventory replenishment in a system with serial inventories. Consumer demand for a specific product at a retail outlet depends on price as well as the in-store stock of the product. The hypothesis is that for certain consumer products, a large volume of displayed goods leads consumers to buy more than if the stock is small. In addition to the stock that is on display in the store, there is an inventory of the product in a central warehouse. First we consider a setup in which management of the two stocks is decentralized such that pricing decisions are made by the store manager who also decides on the level of in-store inventory. The warehouse manager makes the replenishment decisions concerning the stock in the warehouse. Next we study the problem where stock management and pricing decisions are centralized. Optimal trajectories for inventories, replenishment rates, and retail price are derived by using phase diagrams and a formal synthesizing procedure.     

Solving the puzzles of structural efficiency

Since the concept of “structural efficiency” first appeared in Farrell [Farrell, M.J., 1957. The measurement of productive efficiency. Journal of the Royal Statistical Society, Series A, Part III 120, 253–281], attempts have been made to derive measures for the performance of a group of production units (often referred to an industry with many firms). Many empirical studies used the technical efficiency of an average unit to measure the structural efficiency of a group, but researchers have been puzzled by the discrepancies between the average of individual efficiency scores and the performance of the group as a whole. In this paper, we point out that the “shadow price model” provides a useful framework for understanding the economic meaning of the structural efficiency as well as its components. By recognizing these components, the puzzles related to the inconsistencies between the individual and group performance can be solved readily.     

Nonlinear boundary value problems for second order differential inclusions

In this paper, we study a class of nonlinear value boundary problems for second order differential inclusions with nonlinear perturbations, which satisfy the generalized Hartman condition weaker than that considered in some papers. Using techniques from multivalued analysis, theory of monotone operators and fixed points, we prove the existence of solutions in both “convex” and “nonconvex” cases. Our framework can be incorporated with Dirichlet, Neumann, and mixed boundary problems.     

On contracts for VMI program with continuous review (r, Q) policy

Based on continuous review (r, Q) policy, this paper deals with contracts for vendor managed inventory (VMI) program in a system comprising a single vendor and a single retailer. Two business scenarios that are popular in VMI program are “vendor with ownership” and “retailer with ownership”. Taking the system performance in centralized control as benchmark, we define a contract “perfect” if the contract can enable the system to be coordinated and can guarantee the program to be trusted. A revenue sharing contract is designed for vendor with ownership, and a franchising contract is designed for retailer with ownership. Without consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the other one is a perfect contract. With consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the performance of the other one depends on system parameters.     

Portfolio insurance: Gap risk under conditional multiples

The research on financial portfolio optimization has been originally developed by Markowitz (1952). It has been further extended in many directions, among them the portfolio insurance theory introduced by Leland and Rubinstein (1976) for the “Option Based Portfolio Insurance” (OBPI) and Perold (1986) for the “Constant Proportion Portfolio Insurance” method (CPPI). The recent financial crisis has dramatically emphasized the interest of such portfolio strategies. This paper examines the CPPI method when the multiple is allowed to vary over time. To control the risk of such portfolio management, a quantile approach is introduced together with expected shortfall criteria. In this framework, we provide explicit upper bounds on the multiple as function of past asset returns and volatilities. These values can be statistically estimated from financial data, using for example ARCH type models. We show how the multiple can be chosen in order to satisfy the guarantee condition, at a given level of probability and for various financial market conditions.     

What “counts” as algebra in the eyes of preservice elementary teachers?

This study examined conceptions of algebra held by 30 preservice elementary teachers. In addition to exploring participants’ general “definitions” of algebra, this study examined, in particular, their analyses of tasks designed to engage students in relational thinking or a deep understanding of the equal sign as well as student work on these tasks. Findings from this study suggest that preservice elementary teachers’ conceptions of algebra as subject matter are rather narrow. Most preservice teachers equated algebra with the manipulation of symbols. Very few identified other forms of reasoning - in particular, relational thinking - with the algebra label. Several participants made comments implying that student strategies that demonstrate traditional symbol manipulation might be valued more than those that demonstrate relational thinking, suggesting that what is viewed as algebra is what will be valued in the classroom. This possibility, along with implications for mathematics teacher education, will be discussed.     

A stochastic and asymmetric-information framework for a dominant-manufacturer supply chain

Consider a dominant manufacturer wholesaling a product to a retailer, who in turn retails it to the consumers at $p/unit. The retail-market demand volume varies with p according to a given demand curve. This basic system is commonly modeled as a manufacturer-Stackelberg ([mS]) game under a “deterministic and symmetric-information” (“det-sym-i”) framework. We first explain the logical flaws of this framework, which are (i) the dominant manufacturer-leader will have a lower profit than the retailer under an iso-elastic demand curve; (ii) in some situations the system’s “correct solution” can be hyper-sensitive to minute changes in the demand curve; (iii) applying volume discounting while keeping the original [mS] profit-maximizing objective leads to an implausible degenerate solution in which the manufacturer has dictatorial power over the channel. We then present an extension of the “stochastic and asymmetric-information” (“sto-asy-i”) framework proposed in Lau and Lau [Lau, A., Lau, H.-S., 2005. Some two-echelon supply-chain games: Improving from deterministic–symmetric-information to stochastic-asymmetric-information models. European Journal of Operational Research 161 (1), 203–223], coupled with the notion that a profit-maximizing dominant manufacturer may implement not only [mS] but also “[pm]”—i.e., using a manufacturer-imposed maximum retail price. We show that this new framework resolves all the logical flaws stated above. Along the way, we also present a procedure for the dominant manufacturer to design a profit-maximizing volume-discount scheme using stochastic and asymmetric demand information.     

On the oscillatory behavior of certain arithmetic functions associated with automorphic forms

We establish the oscillatory behavior of several significant classes of arithmetic functions that arise (at least presumably) in the study of automorphic forms. Specifically, we examine general L-functions conjectured to satisfy the Grand Riemann Hypothesis, Dirichlet series associated with classical entire forms of real weight and multiplier system, Rankin-Selberg convolutions (both “naive” and “modified”), and spinor zeta-functions of Hecke eigenforms on the Siegel modular group of genus two. For the second class we extend results obtained previously and jointly by M. Knopp, W. Kohnen, and the author, whereas for the fourth class we provide a new proof of a relatively recent result of W. Kohnen.     

An abstract Nash–Moser theorem with parameters and applications to PDEs

We prove an abstract Nash–Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the “tame” estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on Riemannian Zoll manifolds. A point of interest is that, in presence of possibly very large “clusters of small divisors”, due to resonance phenomena, it is more natural to expect solutions with only Sobolev regularity.     

Developing real option game models

By mixing concepts from both game theoretic analysis and real options theory, an investment decision in a competitive market can be seen as a “game” between firms, as firms implicitly take into account other firms’ reactions to their own investment actions. We review two decades of real option game models, suggesting which critical problems have been “solved” by considering game theory, and which significant problems have not been yet adequately addressed. We provide some insights on the plausible empirical applications, or shortfalls in applications to date, and suggest some promising avenues for future research.     

Twistor spaces of hypercomplex manifolds are balanced

A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the three structures, and such that the corresponding Hermitian forms are closed, the manifold is said to be hyperkähler. In the paper “Non-Hermitian Yang–Mills connections” [13], Kaledin and Verbitsky proved that the twistor space of a hyperkähler manifold admits a balanced metric; these were first studied in the article “On the existence of special metrics in complex geometry” [17] by Michelsohn. In the present article, we review the proof of this result and then generalize it and show that twistor spaces of general compact hypercomplex manifolds are balanced.     

Conditions that cause risk pooling to increase inventory

We say product A is a partial substitute for product B if a fraction of the customers who prefer B are willing to accept A when B is out of stock. When demand is uncertain, it is intuitive and true that a larger “willing to substitute” fraction implies larger expected profits. A higher “willing to substitute” fraction allows one to pool the risk of individual products. It may also be intuitive that a larger “willing to substitute” fraction might result in lower optimal total inventory. For the full substitution structure, several researchers have shown that for certain distributions such as the exponential, this latter intuition is not true. We show that this full substitution anomaly can occur with any right skewed demand distribution. We assume i.i.d. demand distributions unless we indicate otherwise. We also show that the anomaly can occur for a number of realistic situations of partial substitution with commonly used demand distributions such as Normal, exponential, Poisson, and uniform. We also demonstrate the anomaly for more than one period, with backlogging, lost sales, more than two products, and with setup costs.