Technology selection and capacity investment under uncertainty

We analyze the problem of technology selection and capacity investment for electricity generation in a competitive environment under uncertainty. Adopting a Nash-Cournot competition model, we consider the marginal cost as the uncertain parameter, although the results can be easily generalized to other sources of uncertainty such as a load curve. In the model, firms make three different decisions: (i) the portfolio of technologies, (ii) each technology’s capacity and (iii) the technology’s production level for every scenario. The decisions related to the portfolio and capacity are ex-ante and the production level is ex-post to the realization of uncertainty. We discuss open and closed-loop models, with the aim to understand the relationship between different technologies’ cost structures and the portfolio of generation technologies adopted by firms in equilibrium. For a competitive setting, to the best of our knowledge, this paper is the first not only to explicitly discuss the relation between costs and generation portfolio but also to allow firms to choose a portfolio of technologies. We show that portfolio diversification arises even with risk-neutral firms and technologies with different cost expectations. We also investigate conditions on the probability and cost under which different equilibria of the game arise.     

Estimating conjectural variations for electricity market models

Agents’ behavior in oligopolistic markets has traditionally been represented by equilibrium models. Recently, several approaches based on conjectural variations equilibrium models have been proposed for representing agents’ behavior in electrical power markets. These models provide insight of market equilibrium sensitivity to agents’ strategies and external variables, and therefore, they are widely applied. Unfortunately, not enough analysis has been done in how these user-supplied parameters, the conjectural variations, should be estimated. This paper proposes a parameter inference procedure based on two stages. The first stage infers historical values of the parameter by fitting the models’ results to historical market data. The second stage is based on a statistical time-series model whose objective is to forecast parameter values in future scenarios. Additionally, results of this procedure’s application to a real-size case are presented.     

Contract design and supply chain coordination in the electricity industry

In this article we propose a model of the supply chain in electricity markets with multiple generators and retailers and considering several market structures. We analyze how market design interacts with the different types of contract and market structure to affect the coordination between the different firms and the performance of the supply chain as a whole. We compare the implications on supply chain coordination and on the players’ profitability of two different market structures: a pool based market vs. bilateral contracts, taking into consideration the relationship between futures and spot markets. Furthermore, we analyze the use of contracts for differences and two-part-tariffs as tools for supply chain coordination. We have concluded that there are multiple equilibria in the supply chain contracts and structure and that the two-part tariff is the best contract to reduce double marginalization and increase efficiency in the management of the supply chain.     

Optimizing revenue in CDMA networks under demand uncertainty

Mathematical programming models for telecommunications network design are prevalent in the literature, but little research has been reported on stochastic models for cellular networks. We present a stochastic revenue optimization model for CDMA networks inspired by bid pricing models from the airline industry. We describe the optimality conditions for the model and develop a supergradient algorithm to solve it. We provide computational results that show the effects of the distribution and variance of demand. Finally, we discuss areas of future research, including a method to optimize the locations of the towers.     

Selection of contract suppliers under price and demand uncertainty in a dynamic market

In this paper, we consider a supply contracting problem in which the buyer firm faces non-stationary stochastic price and demand. First, we derive analytical results to compare two pure strategies: (i) periodically purchasing from the spot market; and (ii) signing a long-term contract with a single supplier. The results from the pure strategies show that the selection of suppliers can be complicated by many parameters, and is particularly affected by price uncertainty. We then develop a stochastic dynamic programming model to incorporate mixed strategies, purchasing commitments and contract cancellations. Computational results show that increases in price (demand) uncertainty favor long-term (short-term) suppliers. By examining the two-way interactions of contract factors (price, demand, purchasing bounds, learning and technology effect, salvage values and contract cancellation), both intuitive and non-intuitive managerial insights in outsourcing strategies are derived.     

Optimal resource allocation for security in reliability systems

Recent results have used game theory to explore the nature of optimal investments in the security of simple series and parallel systems. However, it is clearly important in practice to extend these simple security models to more complicated system structures with both parallel and series subsystems (and, eventually, to more general networked systems). The purpose of this paper is to begin to address this challenge. While achieving fully general results is likely to be difficult, and may require heuristic approaches, we are able to find closed-form results for systems with moderately general structures, under the assumption that the cost of an attack against any given component increases linearly in the amount of defensive investment in that component. These results have interesting and sometimes counterintuitive implications for the nature of optimal investments in security.     

Strategic defense and attack for series and parallel reliability systems

A system of independent components is defended by a strategic defender and attacked by a strategic attacker. The reliability of each component depends on how strongly it is defended and attacked, and on the intensity of the contest. In a series system, the attacker benefits from a substitution effect since attacker benefits flow from attacking any of the components, while the defender needs to defend all components. Even for a series system, when the attacker is sufficiently disadvantaged with high attack inefficiencies, and the intensity of the contest is sufficiently high, the defender earns maximum utility and the attacker earns zero utility. The results for the defender (attacker) in a parallel system are equivalent to the results for the attacker (defender) in a series system. Hence, the defender benefits from the substitution effect in parallel systems. With budget constraints the ratio of the investments for each component, and the contest success function for each component, are the same as without budget constraints when replacing the system values for the defender and attacker with their respective budget constraints.     

Cooperative advertising models in supply chain management: A review

This paper reviews articles on cooperative advertising, a topic which has gained substantial interest in the recent years. Thereby, we first briefly distinguish five different definitions of cooperative advertising which can be found in operations research literature. After that, we concentrate on vertical cooperative advertising, which is the most common object of investigation and is understood as a financial agreement where a manufacturer offers to pay a certain share of his retailer’s advertising expenditures. In total, we identified 58 scientific papers considering mathematical modeling of vertical cooperative advertising. These articles are then analyzed with regard to their general model setting (e.g., the underlying supply chain structure and design of the cooperative advertising program). After that, we explain the different demand and cost functions that are employed, whereupon we distinguish between static and dynamic models. The last dimension of our review is dedicated to the game-theoretic concepts which are mostly used to reflect different forms of distribution of power within the channel.     

Two-settlement electricity markets with price caps and Cournot generation firms

We compare two alternative mechanisms for capping prices in two-settlement electricity markets. With sufficient lead time, forward market prices are implicitly capped by competitive pressure of potential entry that will occur when forward prices rise above some backstop price. Another more direct approach is to cap spot prices through a regulatory intervention. In this paper we explore the implications of these two alternative mechanisms in a two-settlement Cournot equilibrium framework. We formulate the market equilibrium as a stochastic equilibrium problem with equilibrium constraints (EPEC) capturing congestion effects, probabilistic contingencies and horizontal market power. As an illustrative test case, we use the 53-bus Belgian electricity network with representative generator costs but hypothetical demand and ownership structure. Compared to a price-uncapped two-settlement system, a forward cap increases firms’ incentives for forward contracting, whereas a spot cap reduces such incentives. Moreover, in both cases, more forward contracts are committed as the generation resource ownership structure becomes more diversified.     

Integrated risk management for an electricity producer

Electricity suppliers face two sources of risk: uncertainty of spot prices and uncertainty of production costs. Uncertainty in selling the output is usually “solved” by signing forwards and the two sources of risk are dealt with separately. However, managing the integrated risk optimally is the direction we will suggest. We intend to analyse the problem a power producer is confronted to upon acting in a market where spot and forward agreements are available. Since forwards allow to sell production in advance at a given price but do not hedge against cost volatility, the total risk can be reduced by selling also in the spot market. The analysis is further detailed to encompass the spread option inherent in electricity production. We find a benchmark value for forwards to sign and the optimal spot/forward combinations. The analysis is carried out by accounting for market figures for input and output variables in the German market EEX.     

Equilibria of two-sided matching games with common preferences

Problems of matching have long been studied in the operations research literature (assignment problem, secretary problem, stable marriage problem). All of these consider a centralized mechanism whereby a single decision maker chooses a complete matching which optimizes some criterion. This paper analyzes a more realistic scenario in which members of the two groups (buyers–sellers, employers–workers, males–females) randomly meet each other in pairs (interviews, dates) over time and form couples if there is mutual agreement to do so. We assume members of each group have common preferences over members of the other group. Generalizing an earlier model of Alpern and Reyniers [Alpern, S., Reyniers, D.J., 2005. Strategic mating with common preferences. J. Theor. Biol. 237, 337–354], we assume that one group (called males) is r   times larger than the other, r?1$r?1$. Thus all females, but only 1/r$1/r$ of the males, end up matched. Unmatched males have negative utility -c$-c$. We analyze equilibria of this matching game, depending on the parameters r   and c$c$. In a region of (r,c)$(r\text{,}c)$ space with multiple equilibria, we compare these, and analyze their ‘efficiency’ in several respects. This analysis should prove useful for designers of matching mechanisms who have some control over the sex ratio (e.g. by capping numbers of males at a ‘singles event’or by having ‘ladies free’ nights) or the nonmating cost c (e.g. tax benefits to married couples).     

Introducing competition in healthcare services: The role of private care and increased patient mobility

We study the operational implications from competition in the provision of healthcare services, in the context of national public healthcare systems in Europe. Specifically, we study the potential impact of two alternative ways through which policy makers have introduced such competition: (i) via the introduction of private hospitals to operate alongside public hospitals and (ii) via the introduction of increased patient choice to grant European patients the freedom to choose the country they receive treatment at. We use a game-theoretic framework with a queueing component to capture the interactions among the patients, the hospitals and the healthcare funders. Specifically, we analyze two different sequential games and obtain closed form expressions for the patients’ waiting time and the funders’ reimbursement cost in equilibrium. We show that the presence of a private provider can be beneficial to the public system: the patients’ waiting time will decrease and the funders’ cost can decrease under certain conditions. Also, we show that the cross-border healthcare policy, which increases patient mobility, can also be beneficial to the public systems: when welfare requirements across countries are sufficiently close, all funders can reduce their costs without increasing the patients’ waiting time. Our analysis implies that in border regions, where the cost of crossing the border is low, “outsourcing” the high-cost country’s elective care services to the low-cost country is a viable strategy from which both countries’ systems can benefit.     

Opportunistic timing and manipulation in Australian Federal Elections

In many parliamentary systems, election timing is an important decision made by governments in order to maximize their expected remaining life in power. Governments can also introduce policy or economic actions to enhance their popular standing and thus their chance of being re-elected. On the other hand, an oppositions’ natural objective is to gain power, and they will also apply controls through their own policies to reduce the governments’ chance of being re-elected. In this paper we employ a dynamic programming approach to determine the optimal timing for governments and oppositions to best utilize their limited resources. At each decision branch, the optimal control is interpreted as a Nash–Cournot equilibrium of a zero-sum political game which, in certain states, admits mixed strategy solutions. We perform a case study on the Australian Federal Election for House of Representatives.     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

Connectivity-and-hop-constrained design of electricity distribution networks

This paper addresses the problem of designing the configuration of an interconnected electricity distribution network, so as to maximize the minimum power margin over the feeders. In addition to the limitation of feeder power capacity, the distance (as hop count) between any customer and its allocated feeder is also limited for preventing power losses and voltage drops. Feasibility conditions are studied and a complexity analysis is performed before introducing a heuristic algorithm and two integer linear programming formulations for addressing the problem. A cutting-plane algorithm relying on the generation of two classes of cuts for enforcing connectivity and distance requirements respectively is proposed for solving the second integer linear programming formulation. All the approaches are then compared on a set of 190 instances before discussing their performances.     

Ordering policy and coordination of a supply chain with two-period demand uncertainty

We develop a two-period game model of a one-manufacturer and one-retailer supply chain to investigate the optimal decisions of the players, where stock-out and holding costs are incorporated into the model. The demand at each period is stochastic and price sharply drops in mid-life. We assume the retailer has a single order opportunity, and decides how much inventory to keep in the middle of selling season. We show that both the price-protection mid-life and end-of-life returns (PME) scheme and the only mid-life and end-of-life returns (ME) scheme may achieve channel coordination and access a ‘win-win’ situation under some conditions. The larger the lowest expected profit of the retailer, the lower the possibility of ‘win-win’ situation will be. Combined with the analysis of feasible regions for coordination policies, we find that PME scheme is not always better than ME scheme from the perspective of implementable mechanism. Finally, we find that adopting the dispose-down-to (DDT) policy can bring a larger improvement of the expected channel profit in the centralized setting, and it is interesting that by using DDT policy, double marginalization occurs only at Period 1, and however, does not plague the retailer in Period 2.     

Workforce routing and scheduling for electricity network maintenance with downtime minimization

We investigate a combined routing and scheduling problem for the maintenance of electricity networks. In electricity networks power lines must be regularly maintained to ensure a high quality of service. For safety reasons a power line must be physically disconnected from the network before maintenance work can be performed. After completing maintenance work the power line must be reconnected. Each maintenance job therefore consists of multiple tasks which must be performed at different locations in the network. The goal is to assign each task to a worker and to determine a schedule such that the downtimes of power lines and the travel effort of workers are minimized. For solving this problem, we combine a Large Neighborhood Search meta-heuristic with mathematical programming techniques. The method is evaluated on a large set of test instances which are derived from network data of a German electricity provider.     

On channel coordination through revenue-sharing contracts with price and shelf-space dependent demand

This paper deals with the problem of coordinating a vertically separated channel under a consignment contract with revenue sharing. We consider the demand of the downstream player, e.g., the retailer, being price and shelf-space sensitive. Under such a setting, the retailer decides on the revenue-sharing percentage and the slotting fee. And the upstream player, e.g., the manufacturer, decides on the retail price and the size of shelf-space. For each item sold, the retailer deducts an agreed-upon percentage from the selling price and remits the balance to the manufacturer. We model the decision-making of the two firms as a Stackelberg game, and carry out equilibrium analysis for both the centralized and decentralized regimes of the channel, with and without cooperation. In addition, a profit sharing scheme through a two-part slotting allowance is proposed, which leads to Pareto improvements among channel participants. Our analysis reveals that the non-cooperative game tends to set a higher revenue-sharing percentage and lower slotting fee by the retailer, and a higher retail price and less display space by the manufacturer, which leads to a lower channel profit. The consistent bias can be perfectly rectified by the cooperative game through the proposed two-part contractual agreement.     

Improving reliability of a shared supplier with competition and spillovers

Supplier reliability is a key determinant of a manufacturer’s competitiveness. It reflects a supplier’s capability of order fulfillment, which can be measured by the percentage of order quantity delivered in a given time window. A perfectly reliable supplier delivers an amount equal to the order placed by its customer, while an unreliable supplier may deliver an amount less than the amount ordered. Therefore, when suppliers are unreliable, manufacturers often have incentives to help suppliers improve delivery reliability. Suppliers, however, often work with multiple manufacturers and the benefit of enhanced reliability may spill over to competing manufacturers. In this study, we explore how potential spillover influences manufacturers’ incentives to improve supplier’s reliability. We consider two manufacturers that compete with imperfectly substitutable products on Type I service level (i.e., in-stock probability). The manufacturers share a common supplier who, due to variations in production quality or yield, is unreliable. Manufacturers may exert efforts to improve the supplier’s reliability in the sense that the delivered quantity is stochastically larger after improvement. We develop a two-stage model that encompasses supplier improvement, uncertain supply and random demand in a competitive setting. In this complex model, we characterize the manufacturers’ equilibrium in-stock probability. Moreover, we characterize sufficient conditions for the existence of the equilibrium of the manufacturers’ improvement efforts. Finally, we numerically test the impact of market characteristics on the manufacturers’ equilibrium improvement efforts. We find that a manufacturer’s equilibrium improvement effort usually declines in market competition, market uncertainty or spillover effect, although its expected equilibrium profit typically increases in spillover effect.