Linear Demand Research Articles

Solutions to insufficient incentives for developing green tourism by travel agencies: government intervention

PurposeThis research aims to develop an improved model with government intervention and find the government policy for developing green tourism to induce the travel agencies have incentives to produce green tourism products.Design/methodology/approachThis research employs Stackelberg game theory to study two travel agencies in the horizontal direction of the tourism supply chain. Two deterministic, price-sensitive linear demand functions are utilized for these two different tourism products to derive possible analytical solutions.FindingsNo travel agency is willing to produce green tourism products without government intervention. The solution proposed in this paper is that a government should subsidize green travel agencies for their production of green tourism products, and create a tax for non-green traditional travel agencies for the production of non-green traditional tourism products. The amount of government subsidies for green tourism products plus the tax on non-green traditional tourism products equals the difference in unit cost of the two products. The travel agency that produces green tourism products has incentive to produce if there is government intervention.Practical implicationsThis paper provides the stakeholders with three practical implications. The first one is that the amount of subsidy for green travel agencies can be paid by taxing non-green ones. This is the optimal solution. The second one for both the tourism sector and government is that technological innovation in cooperation between government and tourism industry such as low-carbon technology is critical to reduce the cost difference between green travel agency products and non-green ones. The third one is that green travel agencies that produce green tourism products can also fulfill their corporate social responsibilities and enhance their social image.Originality/valueThis paper is unique in that it develops a model to resolve the problem of insufficient incentives. In terms of government intervention, this article also considers tax policy in addition to subsidy policy which is different from previous literature.

Empirical risk minimization for big data driven prescriptive analytics: An exploration of two-stage stochastic programs with recourse

In the operations research literature, data driven analyses using big data are receiving more and more interest and attention. However, big data driven operational analyses are still limited in scope, with only unconstrained big data driven problems, e.g. the newsvendor problem, being comprehensively explored. If big data driven analyses are to become a core part of operations research and practice, one must be able to formulate and solve constrained big data driven models. We therefore propose a direct empirical risk minimization (DERM) method for formulating and solving a class of constrained big data driven operation research problems. In big data driven problems, relevant operational prescriptions are dependent on a set of observed features. In this paper, we assume linear feature relationships, which enable us to fundamentally base the DERM method on linear stochastic programming. The assumption of linear feature relationships is also seen in the literature on big data driven newsvendor models. We prove that if a big data driven solution exists, the DERM method will always, for the class of constrained problems we study, arrive at a feasible solution of the initial operational problem. Moreover, we exemplify the DERM method by formulating and solving two specific big data driven operational problems. In the numerical study of the two operational problems, we show, that under linear demand, the DERM method outperforms, with regard to cost, two benchmark methods and a big data driven method from literature.

Empirical framework for Cournot oligopoly with private information

AbstractWe propose an empirical framework for asymmetric Cournot oligopoly with private information about variable costs. First, considering a linear demand for a homogeneous product with a random intercept, we characterize the Bayesian Cournot–Nash equilibrium. Then we establish the identification of the joint distribution of demand and firm‐specific cost distributions. Following the identification steps, we propose a likelihood‐based estimation method and apply it to the global market for crude oil and quantify the welfare effect of private information. We also consider extensions of the model to include product differentiation, conduct parameters, nonlinear demand, or selective entry.

Optimizing Inventory Model for Negative Exponential and Linear Split Demand and Gompertz Distribution Deterioration with Shortages

This article introduces a mathematical model for optimizing total profit by considering various complex factors, including time-dependent shortages, split demand, Gompertz distribution degradation, a linear holding cost function, and partial backlog issues. The two stages of demand, which are time-dependent linear demand and price-dependent exponential demand, occur when there are no shortages. A comprehensive approach to inventory management decision-making is illustrated through a sensitivity analysis and numerical example, highlighting the influence of system limitations on the optimization outcomes. This model is an effective tool for improving inventory management practices and assessing concavity while maximizing profitability. With MATLAB, relationships between model parameters are graphically represented.

Is monopoly truly effective for producers?

PurposeThe paper is devoted to modeling a pricing policy of competitive firms in a “closed” economy framework.Design/methodology/approachThe proposed model can be regarded as an analog to CGE model and is based on the intersectoral balance methodology incorporating linear demand functions for goods and services.FindingsBy performing different model experiments, we show that a certain degree of competition can bring more profit to all competing firms, than in case of complete absence of such competition, what is also supported by empirical investigation. This finding implies that monopolies may perform worse than competitive firms, what contradicts with the modern provisions of economic theory, stating that monopoly is the most lucrative type of market structure for a producer. The discovered effect occurs due to the aggressive pricing policy, adopted by monopolies, spurring up the inflation spiral, which is most obvious if monopolies are strongly interdependent in terms of production matrix. This inflation spiral drives prices too high, what negatively reflects on firms’ costs and, consequently, results in monopolies receiving less profit.Originality/valueThe proposed model can also be useful for understanding and assessing various economic consequences after different external or internal shocks, what is especially crucial when conducting monetary or fiscal policy.

Advanced Controller System with Hybrid Renewable Sources Enabling Vehicle-To-Grid and Grid-To-Vehicle Operations

Power demand is rising worldwide, forcing the search for an alternative source to solve the imminent power crisis, which is expected to be accomplished through the deployment of grid synchronized electric vehicles (EV). Wind and solar energy are incorporated into this integration to those concerns. One smart grid innovation that permits energy exchange between the EV and the grid is vehicle to grid (V2G) technology. For the purpose of charging EVs, this research proposes employing hybrid energy. Here, the neighboring household’s linear and non linear demands are powered by the excess electricity from the photovoltaics (PV) panel, wind turbine, and AC generator that is utilized to charge the EV battery. Because of its dependability and independence from the real system model, a proportional integral (PI) controller is used to maximize the DC voltage extracted from the PV panel. The improved DC voltage overall is a result of the SEPIC converter’s improved DC output. Concurrently, an AC generator is incorporated into the system to supply extra power to the grid. An artificial neural network (ANN) controller is used to convert the power generated by the PV panel’s Sepic conversion process into an improved output that is then converted to AC using a 3 phase Voltage Source Inverter (VSI). Harmonic components in the VSI output are corrected with an LC filter to ensure grid compatibility and safe current injection into the grid. This paper discusses the usage of a bidirectional converter to adjust the EV battery’s voltage. MATLAB 2021a / Simulink software is used to simulate and validate the proposed approach.

Third-Degree Price Discrimination in Two-Sided Markets

We investigate the welfare effects of third-degree price discrimination by a two-sided platform that enables interaction between buyers and sellers. Sellers are heterogeneous with respect to their per-interaction benefit, and, under price discrimination, the platform can condition its fee on sellers’ type. In a model with linear demand on each side, we show that price discrimination (i) increases participation on both sides, (ii) enhances total welfare, and (iii) may result in a strict Pareto improvement, with both seller types being better off than under uniform pricing. These results, which are in stark contrast to the traditional analysis of price discrimination, are driven by the existence of cross-group network effects. By improving the ability to monetize seller participation, price discrimination induces the platform to attract more buyers, which then increases seller participation. The Pareto improvement result means that even those sellers who pay a higher price under discrimination can be better off, because of the increased buyer participation. This paper was accepted by Joshua Gans, business strategy. Funding: A. de Cornière acknowledges funding from ANR [Grant ANR-17-EURE-0010] (Investissements d’Avenir program). Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.02788 .

A dynamic surge pricing model throughout product lifecycle

The shorter lifecycle and faster upgrading of the product make the potential demand change rapidly, thereby pricing based on market changes is critical to increasing profits. In response to changes in the potential demand, we present a dynamic surge pricing model that characterizes sales trajectories and gradient pricing. We introduce the Lotka–Volterra system to construct the sale-forecast system and prove its effectiveness in predicting the product lifecycle curve that reflects the change of the potential demand. In contrast to the linear demand function, we propose a gradient pricing mechanism based on marginal sales and total sales to describe the relationship between price and potential demand throughout the life cycle. Particularly, the dynamic surge pricing model degrades to Cournot model in the maturity phase of the market. We characterize the dynamic equilibrium and conduct the sensitivity analysis of parameters, showing that the dynamic surge pricing model outperforms Cournot model in terms of profit. A numerical example illustrates that the profit of the dynamic surge pricing model is nearly 21.82% higher than that of Cournot model.

Representative days and hours with piecewise linear transitions for power system planning

Electric demand and renewable power are highly variable, and the solution of a planning model relies on capturing this variability. This paper proposes a hybrid multi-area method that effectively captures both the intraday and interday chronology of real data considering extreme values, using a limited number of representative days, and time points within each day. An optimization-based representative extraction method is proposed to improve intraday chronology capturing. It ensures higher precision in preserving data chronology and extreme values than hierarchical clustering methods. The proposed method is based on a piecewise linear demand and supply representation, which reduces approximation errors compared to the traditional piecewise constant formulation. Additionally, sequentially linked day blocks with identical representatives, created through a mapping process, are employed for interday chronology capturing. To evaluate the efficiency of the proposed method, a comprehensive expansion co-planning model is developed, including transmission lines, energy storage systems, and wind farms.

Buyers- Suppliers Win-Win Cash Flow Inventory Model with Linear Demand under Various Production Industries

Buyers- Suppliers Win-Win Cash Flow Inventory Model with Linear Demand under Various Production Industries

How power structure and markup schemes impact supply chain channel efficiency under price-dependent stochastic demand

Although considerable attention has been separately given to factors such as power structures, price-dependent demand, and markup pricing schemes, there has been limited exploration of the combined effects of these factors on supply chain efficiency and the leader’s advantage. We propose a game theoretic model in which a manufacturer sells a single product to a newsvendor retailer who sets both optimal order quantity and selling price under uncertain price-dependent demand. Furthermore, we examine a supply network wherein a single retailer fulfills orders using a global manufacturer for regular orders and a local manufacturer to clear any shortages. Through numerical analysis, we show that the retailer always prefers to charge a percentage markup. In a two-player game, channel efficiency is higher when the retailer is the leader under linear demand; however, under iso-elastic demand, the manufacturer being a leader brings a higher channel efficiency. When a local manufacturer is involved as a second manufacturer, channel efficiency is higher when the retailer remains a follower, as this induces more fierce wholesale price competition between the two manufacturers. Additionally, when demand uncertainty is high in the two-player game with linear demand, the retailer as a follower can achieve higher profits, whilst high uncertainty under iso-elastic demand decreases both players’ profits. Moreover, it becomes advantageous for the retailer to have a local manufacturer as demand uncertainty increases, even when the local manufacturer announces the wholesale price first.

Inventory Model for Deteriorating Pharmaceutical Items with Linear Demand Rate

Good management of goods is needed so that the inventory activities of a business can run smoothly as the part of supply chain management which aims to monitor the flow of stock of goods from the purchasing process, and storage to the point of sale. In terms of inventory or supplies of pharmaceutical goods, conditions such as shortages or stockouts must also be considered which are a matter of control, management, and security. In this study, an inventory model is formulated with deterioration or damage to pharmaceutical goods that occurs due to the length of time when the goods are stored with a linear demand level. In the optimal solution, the inventory time occurs when it reaches the zero point (t1) of 0.34 and the cycle length (T1) of 0.83 with an average minimum total cost (TC) of $445.25 per cycle which is completed by WolframAlpha software. Sensitivity analysis changes the value results in the value of (TC) which that increases for all parameters. In increasing the linear function variables (a and b), it produces t1 and T1 stable values. An increase in the cost of each item damage (DC) and constant damage rate (theta) produces a t1 stable value, but the value of T1 increases. The increase in storage costs (h) results in a decrease in the value of t1 and T1. An increase in the cost of shortages (s) results in an increase in the value of t1 and a decrease in the value of T1.

Advertising fee as a new supply chain coordination approach between hotels and online travel agencies

PurposeChannel coordination has become an essential part of researching hotel supply chain management practices. This paper develops an improved channel coordination approach to coordinate the profit distribution between hotels and online travel agencies (OTAs) achieved through an introduction of advertising fees. This direction further improves the decentralization of cooperation and achieves Pareto improvement to achieve mutual profitability.Design/methodology/approachThe methodology used in this study involves Stackelberg game theory employed for the decision-making and analysis of both the hotel and OTA. The OTA, acting as the leader, offers a hotel a contract specifying the commission rate that the hotel will pay to the respective OTA. The hotel, acting as a follower, sets a self-interested room rate as a given response. A deterministic, price-sensitive linear demand function is utilized to derive possible analytical solutions once centralized, noncooperative decentralization and cooperative decentralized channel occurs.FindingsResults show that a new channel coordination approach is possible, namely via advertising fees. Prior to channel coordination, the OTA tends to set a higher commission rate, and the hotel sets a higher room rate in response under noncooperative decentralization. As such, this results in a lower channel-wide profit for all. One way to reduce channel-wide profit loss is to use a method of cooperative decentralization, which can, and will result in optimal profit as centralization takes place. However, the lack of incentives makes cooperative decentralization unfeasible. Further improvement is possible by using advertising fees based on a cooperative decentralization agreement, which can reach Pareto improvement.Practical implicationsThis paper helps the OTA industry and hotel owners cooperate by way of smoother coordination. This study provides practitioners with two important practical implications. The first one is that the coordination between the hotel industry and OTA through cooperative decentralization allows for the achievement of higher profitability than that of noncooperative decentralization. The second one is that this paper solves the outstanding problem of insufficient incentives characteristic of cooperative decentralization by means of an advertising fee as a new supply chain coordination approach.Originality/valueThis paper offers both the problem and solution regarding the lack of incentives that hamper cooperative decentralization without the use of advertising fees. This paper is unique in that it derives analytical solutions regarding commissions levied in a typical hotel supply chain under noncooperative decentralization.

Vertical contracting between a vertically integrated firm and a downstream rival

Compared to linear tariffs, two-part tariffs are generally perceived as being more efficient since double marginalization is avoided. We investigate the efficiency of two-part tariffs vs. linear tariffs when a vertically integrated firm sells its input also to an independent downstream firm selling a differentiated substitute product. We find that a linear tariff can generate higher consumer surplus and overall welfare than a two-part tariff when the independent downstream firm is rather powerful in negotiating the contract terms, and downstream competition is in prices (Bertrand competition). In that case, the integrated firm makes more profits under a linear tariff than under a two-part tariff. In contrast, under downstream Cournot competition two-part tariffs are always welfare-superior. Under linear demand, we find that, irrespective of the mode of downstream competition and the distribution of bargaining power, the preferred contract type of the integrated firm is always welfare-superior.

The combined effects of interest and inflation rates on inventory systems: A comparative analysis across countries

Interest and inflation rates are among the most important economic indicators of any country. Inventory management is also known as one of the most critical components of supply chains and logistics systems. This study conducts a comparative study to analyze the combined effects of interest and inflation rates on inventory systems in different countries as part of macroeconomics. To do so, a novel inventory model is developed by accounting for interest rate, inflation, and increasing linear demand over time which affect inventory costs. In terms of the main parameters, the developed model is divided into two groups, where each group is solved separately. The results demonstrate that Venezuela, Sudan, Zimbabwe, Iran, and Liberia are the five countries with the most potential volume of hoarding of goods. These countries should increase their interest rates by at least 118.06%, 22.42%, 7.84%, 10.84%, and 6.94%, respectively, to counter the increasing amount of hoarding. Moreover, the findings reveal that Venezuela, Zimbabwe, Iran, Sudan, and Turkey, have the highest cost of inventory systems.

Roadmaps for heating and cooling system transitions seen through uncertainty and sensitivity analysis

Future district heating systems should enable efficient and economic energy supply, which can be achieved by lowering the system temperatures and boosting it at demand-side. Current solutions include the ultra-low-temperature district heating (ULTDH) and fifth generation district heating and cooling (5GDHC) systems. The transition towards these systems is subject to multiple future uncertainties such as the energy price, investment cost, and demand changes, which were missing in previous works. To investigate the effects of these uncertainties on conclusions brought by established design roadmaps for future DHCs, a five-step framework, which combines the energy system optimization with stochastic simulations, uncertainty analysis and sensitivity assessment, is developed in this study. The framework is applied on a hypothetical 0.25 km2 square district with varying uncertain parameters. Based on stochastic cases, the index named cost-saving probability (CSP) is utilized to reflect the potential of being economic attractive when comparing the energy systems. For the transition towards the ULTDHC, 5GDHC, and individual systems, the most sensitive factors for the CSP are the area demand density, overlapping heating and cooling demand, and linear demand density, respectively. The investment in thermal energy storage (TES) becomes important only when the integration of a larger share of renewable energy is targeted. A roadmap summarizing the promoting and hindering factors for the system transition is provided, pointing out the future focus area for DHC design. The results from the sensitivity analysis also revealed the limited role of TES in integrating variable renewable energy in high-efficiency DHC systems.

Public–Private Collusion

We study collusion between a public firm and a private firm facing linear demand and quadratic costs. We characterize the collusive outcome that results from Nash bargaining and compare it to the non-cooperative outcome. If the public firm’s taste for consumer surplus is mild, both firms reduce output (as in a private duopoly). If it is intermediate, while the public firm reduces output, the private firm expands output to such an extent that total output increases. If it is strong, the private firm’s output expansion does not compensate for the public firm’s output contraction, and thus total output decreases. We also characterize collusion sustainability, and assess the impact of relative bargaining power, degree of cost convexity, public firm’s taste for total surplus, and cost asymmetry. We conclude that, by reducing the productive inefficiency that is caused by the public firm being more expansionary, collusion may lead to higher profits and consumer surplus.

Implications of product substitutability in a distribution channel

This paper examines the effect of product substitutability on the equilibrium profits in a distribution channel of two symmetric manufacturers selling substitutable products to consumers through a nonexclusive retailer. Conventional wisdom suggests that when the products are more substitutable, the retailer will be better off while the manufacturers will be worse off, owing to the dominance of the competition effect of substitutability. In this work, we identify the hitherto neglected demand effect of substitutability and show that the relative strength between the competition and demand effects is the key to this result. As the products become more substitutable, the upstream competition does intensify, but vitally, the demand may expand. We show that the interests of the retailer and manufacturers can be aligned in terms of product substitutability, depending on both the demand and supply factors. Surprisingly, the conventional result can even be completely reversed such that the manufacturers benefit from a certain level of substitutability for some demand patterns. Assuming linear demand, we further isolate the important role of the bargaining power balance and the alternative of agency selling format in moderating the competition effect. For example, as the retailer gains more bargaining power, the (negative) demand effect can overshadow the (positive) competition effect such that a higher degree of substitutability can actually hurt the retailer. Our findings provide valuable implications for persuasive advertising and category management.

Strategic rationing in Stackelberg games

This paper examines Stackelberg price-quantity competition with imperfectly substitutable products. Under general cost and demand conditions, we establish existence of a subgame-perfect Nash equilibrium and provide a full characterization of the set of subgame-perfect Nash equilibria. In each equilibrium, the leader rations part of its clientele. Assuming linear demand and cost functions, first- and second-mover advantages are shown to critically depend on the degree of spillover demand, i.e., how many of the unserved customers visit the follower. We identify the presence of a spillover demand paradox. The leader may be the bigger firm and make more profit, but only when a sufficiently large part of its unmet demand shifts to the follower.

Competitive contract design in a retail supply chain under demand uncertainty

AbstractThis article studies the design of contracts involving a single retailer and multiple competing manufacturers who supply substitutable products. We consider a retail context in which contracts with manufacturers are negotiated relatively infrequently and signed before the demand environment is known, and the retail prices are determined when the demand is known. We develop a Stackelberg model to study the retailer's product selection and pricing decisions and the manufacturers' contract design decisions. We show that it is optimal for each manufacturer to offer a contract with nonlinear prices so that total payments are the total production cost plus a fixed additional cost. In the case of two manufacturers this result allows us to characterize an equilibrium in which the retailer's choice maximizes the supply chain profit, each manufacturer makes a profit equal to its marginal contribution to the supply chain, and the retailer takes the remaining profit. We also find that while increasing demand correlation always benefits the retailer, it benefits the manufacturers only when the production costs are convex. In an extension it is found that our equilibrium continues to hold when the retailer's reservation profit is below a threshold, but the competition dynamics may change when the reservation profit is above the threshold. Finally, we show that the equilibrium results remain true for the case with more than two manufacturers under a submodularity property, which holds in the case of quadratic costs and linear demand.