Optimal production strategy under demand fluctuations: Technology versus capacity

This paper provides a comparative analysis of five possible production strategies for two kinds of flexibility investment, namely flexible technology and flexible capacity, under demand fluctuations. Each strategy is underpinned by a set of operations decisions on technology level, capacity amount, production quantity, and pricing. By evaluating each strategy, we show how market uncertainty, production cost structure, operations timing, and investment costing environment affect a firm’s strategic decisions. The results show that there is no sequential effect of the two flexibility investments. We also illustrate the different ways in which flexible technology and flexible capacity affect a firm’s profit under demand fluctuations. The results reveal that compared to no flexibility investment, flexible technology investment earns the same or a higher profit for a firm, whereas flexible capacity investment can be beneficial or harmful to a firm’s profit. Moreover, we prove that higher flexibility does not guarantee more profit. Depending on the situation, the optimal strategy can be any one of the five possible strategies. We also provide the optimality conditions for each strategy.     

Real options in strategic investment games between two asymmetric firms

This paper examines strategic investment games between two firms that compete for optimal entry in a project that generates uncertain revenue flows. Under asymmetry on both the sunk cost of investment and revenue flows of the two competing firms, we investigate the value of real investment options and strategic interaction of investment decisions. Compared to earlier models that only allow for asymmetry on sunk cost, our model demonstrates a richer set of strategic interactions of entry decisions. We provide a complete characterization of pre-emptive, dominant and simultaneous equilibriums by analyzing the relative value of leader’s and follower’s optimal investment thresholds. In a duopoly market with negative externalities, a firm may reduce loss of real options value by selecting appropriate pre-emptive entry. When one firm has a dominant advantage over its competitor, both the dominant firm and dominated firm enter at their respective leader’s and follower’s optimal thresholds. When the pre-emptive thresholds of both firms happen to coincide, the two firms enter simultaneously. Under positive externalities, firms do not compete to lead.     

Optimal capacity for substitutable products under operational postponement

We consider a monopolist producing two substitutable products with one flexible (shared) capacity. The demand of each product is a linear function of the prices of both products, and is subject to an additive shock. We study the impact of two key drivers, namely the degree of substitution between the products and the level of operational postponement, on the optimal capacity and the resulting expected profit. We show that the relationship between the optimal capacity and the degree of product substitution is not impacted by the different postponement strategies the firm can utilize or by the different settings (forced clearance versus holdback) considered in the previous literature. On the other hand, how capacity is affected by postponement critically depends on how closely substitutable the products are. In particular, we show that the well-known result that operational postponement and capacity are strategic complements in a single-product setting (Van Mieghem and Dada, 1999) no longer holds in our setting, because the two substitutable products are now linked through consumer-driven substitution, which the firm can influence through pricing. In particular, capacity and operational postponement (in the form of quantity postponement) can be either strategic substitutes or strategic complements, and this depends on both the firm’s cost structure and the degree of substitution between the products. We also study the impact of forced clearance on the firm’s expected profit and find that clearance deteriorates the firm’s earnings more when the products it offers are highly differentiated.     

A staggered-grid numerical algorithm for the extended Boussinesq equations

A second-order accurate numerical scheme is developed to solve Nwogu’s extended Boussinesq equations. A staggered-grid system is introduced with the first-order spatial derivatives being discretized by the fourth-order accurate finite-difference scheme. For the time derivatives, the fourth-order accurate Adams predictor–corrector method is used. The numerical method is validated against available analytical solutions, other numerical results of Navier–Stokes equations, and experimental data for both 1D and 2D nonlinear wave transformation problems. It is shown that the new algorithm has very good conservative characteristics for mass calculation. As a result, the model can provide accurate and stable results for long-term simulation. The model has proven to be a useful modeling tool for a wide range of water wave problems.     

Approximate analytical solutions for Kolmogorov’s equations

This paper reports the explicit analytical solutions for Kolmogorov’s equations. Kolmogorov’s equations are commonly used to describe the structure of local isotropic turbulence, but their exact analytical solutions have not yet been found. In this paper, the closed-form solutions for two kinds of Kolmogorov’s equations are obtained. The derivations of the approximate solutions are based on the homotopy analysis method, which is a new tool for obtaining the approximate analytical solutions of both strong and weak nonlinear differential equations. To examine the validity of the approximate solutions, numerical comparisons between results from the homotopy analysis method and the fourth-order Runge-Kutta method are carried out. It is shown that the results are in good agreement.     

Licensing radical product innovations to speed up the diffusion

We present a differential game to study how companies can simultaneously license their innovations to other firms when launching a new product. The licensee may cannibalize licensor’s sales, albeit this can be compensated by gains from royalties. Nonetheless, patent royalties are generally so low that licensing is not an attractive strategy. In this paper we consider the role of licensing to speed up the product diffusion. Word of mouth by licensee’s customers and licensee’s advertising indirectly push forward sales of the licensing company, accelerating new product diffusion. We find evidence that licensing can be a potentially profitable strategy. However, we also find that a weak Intellectual Property Right (IPR) protection can easily diminish the financial attractiveness of licensing.     

A study on the method of fundamental solutions using an image concept

In this paper, both analytical and semi-analytical solutions for Green’s functions are obtained by using the image method which can be seen as a special case of method of fundamental solutions (MFS). The image method is employed to solve the Green’s function for the annular, eccentric and half-plane Laplace problems. In addition, an analytical solution is derived for the fixed-free annular case. For the half-plane problem with a circular hole and an eccentric annulus, semi-analytical solutions are both obtained by using the image concept after determining the strengths of two frozen image points and a free constant by matching boundary conditions. It is found that two frozen images terminated at the two focuses in the bipolar coordinates for the problems with two circular boundaries. A boundary value problem of an eccentric annulus without sources is also considered. Error distribution is plotted after comparing with the analytical solution derived by Lebedev et al. using the bipolar coordinates. The optimal locations for the source distribution in the MFS are also examined by using the image concept. It is observed that we should locate singularities on the two focuses to obtain better results in the MFS. Besides, whether the free constant is required or not in the MFS is also studied. The results are compared well with the analytical solutions.     

Dual role of price and myopia in a marketing channel

In this paper we study a dynamic two-player channel where the manufacturer controls the wholesale price and the investment in quality and the retailer chooses the retail price. We consider that the retail price affects both the demand and the perceived quality of the brand and that its variations contribute to the building of an internal reference price. One of the model’s distinctive features is that it accounts for the two meanings of price, i.e., its classical objective measure of the cost of acquiring a particular quantity of the product, and its subjective roles as an assessment of the quality of the product and an evaluation of gains or losses (deal vs. sacrifice) resulting from buying a “cheap” or an “expensive” product. This dual computation is done with respect to the internal reference price.     

The impact of disaster on the strategic interaction between company and government

A company allocates a resource between safety effort and production. The government earns taxes on production. The disaster probability is modeled as a contest between the disaster magnitude and the two players’ safety efforts. The model illustrates that safety efforts are strategic substitutes and inverse U shaped in the disaster magnitude. The company’s safety effort increases, and the government’s safety effort decreases, in taxation. Taxation can ameliorate companies’ free riding on governments’ safety efforts. With sufficiently large production, the government prefers, and the company does not prefer, raising taxation above 0%. For the government, an upper limit usually exists above which taxation cannot be profitably increased. The model shows how both or no players exert safety efforts when the disaster magnitude is small and large respectively, and how they free ride on each other’s safety efforts when the disaster magnitude is intermediate. The company free rides when the unit production cost is low so that the large profits outweigh the negative impact of the disaster. With endogenized taxation determined by the government, the tax rate decreases in the disaster magnitude, the unit production cost, the government’s unit cost of safety effort, and how the company is negatively affected by the disaster. The tax rate increases in the company’s resource and how the government is negatively affected by the disaster. The tax rate is weakly U shaped in the company’s unit safety effort. The model is illustrated with numerical examples and with the oil spill disasters by BP in 2010 and by Exxon Valdez in 1989.     

Strategic response to pollution taxes in supply chain networks: Dynamic,spatial, and organizational dimensions

This paper presents a model of the strategic behavior of firms operating in a spatial supply chain network. The manufacturing and retailing firms engage in an oligopolistic, noncooperative game by sharing customer demand such that a firm’s decisions impact the product prices, which in turn result in changes in all other firms’ decisions. Each firm’s payoff is to maximize its own profit and we show that, in response to such changes in prices and to exogenous environmental taxes, the manufacturing firms may strategically alter a variety of choices such as ’make-buy’ decisions with respect to intermediate inputs, spatial distribution of production, product shipment patterns and inventory management, environmental tax payment vs recycling decisions, and timing of all such choices to sustainably manage the profit and the environmental regulations. An important implication is that effects of a tax depends on the oligopolistic game structure. With respect to methods, we show that this dynamic game can be represented as a set of differential variational inequalities (DVIs) that motivate a computationally efficient nonlinear complementarity (NCP) approach that enables the full exploitation of above-mentioned salient features. We also provide a numerical example that confirms the utility of our proposed framework and shows substantial strategic reaction can be expected to a tax on pollution stocks.     

Separation in homogeneous systems with independent identical elements

The paper considers strategic defense and attack of a system which can be separated into independent identical homogeneous parallel elements. The defender distributes its resource between separation of the elements and their protection from outside attacks. The attacker distributes its effort evenly among all attacked elements. The vulnerability of each element is determined by a contest success function between the attacker and the defender. The defender can choose a subset of the elements to defend. The attacker does not know which elements are protected and can choose a number of randomly chosen elements to attack. Separation efficiency conditions are formulated dependent on the defender’s and attacker’s budgets, separation costs, contest intensity, and system demand. An algorithm for determining the optimal number of protected elements is suggested for the case when both the defender and the attacker can choose the number of protected and attacked elements freely. The article considers both the cases without and with performance redundancy. Illustrative numerical examples are presented.     

Solution of Poisson’s equation by analytical boundary element integration

The solution of Poisson’s equation is essential for many branches of science and engineering such as fluid-mechanics, geosciences, and electrostatics. Solution of two-dimensional Poisson’s equations is carried out by BEM based on Galerkin Vector Method in which the integrals that appear in the boundary element method are expressed by analytical integration. In this paper, the Galerkin vector method is developed for more general case than presented in the previous works. The integrals are computed for constant and linear elements in BEM. By employing analytical integration in BEM computation, the numerical schemes and coordinate transformations can be avoided. The presented method can also be used for the multiple domain case. The results of the analytical integration are employed in BEM code and the obtained analytical expression will be applied to several examples where the exact solution exists. The produced results are in good agreement with the exact solution.     

Lead-time hedging and coordination between manufacturing and sales departments using Nash and Stackelberg games

In a firm, potential conflict exists between manufacturing and sales departments. Salespersons prefer to order from manufacturing departments in advance so that they can secure products in the amount they need to satisfy customers in time. This time in advance strategy is defined as “lead-time hedging.” While this hedging strategy is good for the sales department to guarantee the right quantity at the right time for customers, it adds additional costs and pressure to the manufacturing department. One scheme to resolve this conflict is to introduce a fair “internal price,” charged by the manufacturing department to the sales department. In this paper, two models involving a fair internal price are introduced. In one model, a Nash game is played to reach an optimal strategy for both parties. In the other model, a Stackelberg game is played in which the manufacturing department serves as the leader. We show that these two models can successfully reduce lead-time hedging determined by the salesperson and can increase the firm’s overall profit, as compared to the traditional model without considering the internal price. More insights have also been analyzed that include the comparisons of the manufacturer’s and the salesperson’s profits among the traditional model, the Nash game model, the Stackelberg game model, and the centralized global optimization model.     

Visualizing preferences on spheres for group decisions based on multiplicative preference relations

Decision makers’ choices are often influenced by visual background information. One of the difficulties in group decision is that decision makers may bias their judgment in order to increase the possibility of a preferred result. Hence, the method used to provide visual aids in helping decision making teams both to observe the background context and to perceive outliers is an important issue to consider. This study proposes an extended Decision Ball model to visualize a group’s decisions. By observing the Decision Balls, each decision maker can: see individual ranking as well as similarities between alternatives, identify the differences between individual judgments and the group’s collective opinion, observe the clusters of alternatives as well as clusters of decision makers, and discover outliers. Thus, this method can help decision makers make a more objective judgment.     

Dynamics of a new family of iterative processes for quadratic polynomials

In this work we show the presence of the well-known Catalan numbers in the study of the convergence and the dynamical behavior of a family of iterative methods for solving nonlinear equations. In fact, we introduce a family of methods, depending on a parameter m∈N∪{0}. These methods reach the order of convergence m+2 when they are applied to quadratic polynomials with different roots. Newton’s and Chebyshev’s methods appear as particular choices of the family appear for m=0 and m=1, respectively. We make both analytical and graphical studies of these methods, which give rise to rational functions defined in the extended complex plane. Firstly, we prove that the coefficients of the aforementioned family of iterative processes can be written in terms of the Catalan numbers. Secondly, we make an incursion into its dynamical behavior. In fact, we show that the rational maps related to these methods can be written in terms of the entries of the Catalan triangle. Next we analyze its general convergence, by including some computer plots showing the intricate structure of the Universal Julia sets associated with the methods.     

Theoretical analysis and numerical simulation of Parrondo’s paradox game in space

A multi-agent spatial Parrondo game model is designed according to the cooperative Parrondo’s paradox proposed by Toral. The model is composed of game A and game B. Game A is a zero-sum game between individuals, reflecting competitive interaction between an individual and its neighbors. The winning or losing probability of one individual in game B depends on its neighbors’ winning or losing states, reflecting the dependence that individuals has on microhabitat and the overall constraints that the microhabitat has on individuals. By using the analytical approach based on discrete-time Markov chain, we analyze game A, game B and the random combination of game A+B, and obtain corresponding stationary distribution probability and mathematical expectations. We have established conditions of the weak and strong forms of the Parrondo effect, and compared the computer simulation results with the analytical results so as to verify their validity. The analytical results reflect that competition results in the ratchet effect of game B, which generates Parrondo’s Paradox that the combination of the losing games can produce a winning result.     

A variational iteration method for solving Troesch’s problem

Troesch’s problem is an inherently unstable two-point boundary value problem. A new and efficient algorithm based on the variational iteration method and variable transformation is proposed to solve Troesch’s problem. The underlying idea of the method is to convert the hyperbolic-type nonlinearity in the problem into polynomial-type nonlinearities by variable transformation, and the variational iteration method is then directly used to solve this transformed problem. Only the second-order iterative solution is required to provide a highly accurate analytical solution as compared with those obtained by other analytical and numerical methods.     

Effects of sourcing structure on performance in a multiple-product assemble-to-order supply chain

This paper addresses the strategic pricing decisions of a decentralized assemble-to-order system, and the effects of sourcing structure on system performance. We consider an assemble-to-order system consisting of two substitute products and three components manufactured by different suppliers. Demand for the products is price-sensitive. The selling prices for the products are jointly determined by firms in the system. We study the system under both centralized and decentralized decision-making situations. For the centralized system, we demonstrate that there exists a unique optimal pricing solution. For the decentralized system, we show that there exists a unique Nash equilibrium in the players’ pricing game. We further analyze the effects of different sourcing structures on the system performance and the assembler’s performance. We find that reduction of suppliers in the system does not guarantee improvement of system performance. Different sourcing structures have different impacts on performance. When the two dedicated components are sourced from a single supplier and the common component is sourced from another independent supplier, the system and the assembler’s performance become worse. We show that the decentralized system can be effectively coordinated and the system performance can be improved with a simple profit-sharing contract. Finally, we provide comprehensive numerical examples to demonstrate some important managerial insights.     

An analytical study of the modification ability of distribution centers

This paper considers a two-level vendor managed inventory (VMI) system comprising a distribution center (DC) and a retailer. Both the DC’s and the retailer’s replenishment decisions follow the order-up-to-level policy and aim at maximizing the profit of the overall system. We critically examine the potential of the DC’s ability to modify delivery decisions, identify and quantify the cost factors that influence the DC’s modification ability, establish a relationship between the DC’s location and its modification ability, and show the trade-off between the DC’s modification ability and related costs. Our analysis provides a new insight into the role of the DC and reveals the full potential of the VMI system. Our findings and their practical implications, demonstrated with the aid of computational examples, are helpful for enhancing the practice of VMI at both strategic and operational levels.     

Product-design and pricing strategies with remanufacturing

In this paper, we consider a supply chain that consists of an original equipment manufacturer (OEM) producing new products and a remanufacturer recovering the used items. The OEM often faces a strategic dilemma when determining the degree of disassemblability of its product design, as high disassemblability decreases the OEM’s production costs as well as the remanufacturer’s recovery costs. However, high disassemblability may be harmful to the OEM in a market in which the remanufacturer is encouraged to intensify price competition with the OEM because design for high disassemblability leads to larger cost savings in remanufacturing. We first formulate a two-period model to investigate the OEM’s product-design strategy and the remanufacturer’s pricing strategy in an extensive-form game, in which the equilibrium decisions of the resulting scenarios are derived. Next, we show the thresholds that determine whether remanufacturing is constrained by collection, the thresholds for the remanufacturer’s choice of a profitable pricing strategy, and the thresholds for determining the OEM’s product-design strategy. Finally, we expand the model for a multiple-period problem to show that the main insights obtained from the two-period model can be applied.