Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale

A repeated, discrete time, heterogeneous Cournot duopoly game with bounded rational and adaptive players adjusting the quantities of production is subject of investigation. Linear inverse demand function and quadratic cost functions reflecting decreasing returns to scale are assumed. The game is modeled with a system of two difference equations. Evolution of outputs over time is obtained by iteration of a two dimensional nonlinear map. Existing equilibria and their stability are analyzed. In face of diseconomies of scale, bounded rational and adaptive duopolists are shown to experience a decrease in the latitude of their output adjustment decisions with respect to the market stability compared to constant returns to scale and ceteris paribus. Chaotic dynamics is confirmed to depend mainly on the adjustment behavior of the bounded rational player, who if overshoots leaves the adaptive player with limited opportunities to stabilize the market again, hence industries facing diseconomies of scale are found to be less stable than those with constant marginal costs. Complexity of the dynamical system is examined by means of numerical simulations, where the paper extends the results of other authors who considered analogous games assuming linear cost functions. Intermittent transition to chaos and attractor merging crisis are shown among others.     

Transport economies of scale and firm location

This paper studies the impact of economies of scale in transportation on a firm’s location decision. We relate the location problem to weighted Fermat problems and ramified optimal transportation problems and analyze how transport technologies affect the firm’s transportation and location choices. It is found that in general when the level of transport economies of scale is high, the firm locates its factory in the interior of the Weber triangle with a branching transport structure. Two examples are constructed to illustrate how interactions between transport technology and production technology would affect the firm’s input purchase and factory location.     

Computing economies of vertical integration,economies of scope and economies of scale using partial frontier nonparametric methods

So far, in the nonparametric literature only full frontier nonparametric methods have been applied to search for economies of scope and scale, particularly the data envelopment analysis method (DEA). However, these methods present some drawbacks that might lead to biased results. This paper proposes a methodology based on more robust partial frontier nonparametric methods to look for scope and scale economies. Through this methodology it is possible to assess the robustness of these economies, and in particular to assess the influence that extreme data or outliers might have on them. The influence of the imposition of convexity on the production set of firms was also investigated. This methodology was applied to the water utilities that operated in Portugal between 2002 and 2008. There is evidence of economies of vertical integration and economies of scale in drinking water supply utilities and in water and wastewater utilities operating mainly in the retail segment. Economies of scale were found in water and wastewater utilities operating exclusively in the wholesale, and in some of these utilities diseconomies of scope were also found. The proposed methodology also allowed us to conclude that the existence of some smaller utilities makes the minimum optimal scales go down.     

Location of slaughterhouses under economies of scale

The facility location problem described in this paper comes from an industrial application in the slaughterhouse industry of Norway. Investigations show that the slaughterhouse industry experiences economies of scale in the production facilities. We examine a location-allocation problem focusing on the location of slaughterhouses, their size and the allocation of animals in the different farming districts to these slaughterhouses. The model is general and has applications within other industries that experience economies of scale.We present an approach based on linearization of the facility costs and Lagrangean relaxation. We also develop a greedy heuristic to find upper bounds. We use the method to solve a problem instance for the Norwegian Meat Co-operative and compare our results to previous results achieved using standard branch-and-bound in commercial software.     

Strategic design of distribution systems with economies of scale in transportation

We formulate and analyze a strategic design model for multi-product multi-echelon distribution systems where there are significant economies of scale in the transportation movements. The key design decisions considered are: the number and locations of distribution centers (DC's) in the system, the number and locations of consolidation centers (CC's), the inventory levels of the various products to be held at the distribution centers, and the routing of shipments (through a consolidation center or direct) between plants and distribution centers. A heuristic solution method is developed that can efficiently find near-optimal solutions. The quality of solutions to a series of test problems is evaluated---by comparison to exact solutions created by enumeration in small tests, and by comparison to lower bounds developed for larger test problems. In the problems for which exact solutions are available, the heuristic solution is within 1% of optimal. The computational procedure appears to hold substantial promise for effective solution of large distribution system design problems.     

Location and allocation for distribution systems with transshipments and transportion economies of scale

Locating transshipment facilities and allocating origins and destinations to transshipment facilities are important decisions for many distribution and logistic systems. Models that treat demand as a continuous density over the service region often assume certain facility locations or a certain allocation of demand. It may be assumed that facility locations lie on a rectangular grid or that demand is allocated to the nearest facility or allocated such that each facility serves an equal amount of demand. These assumptions result in suboptimal distribution systems. This paper compares the transportation cost for suboptimal location and allocation schemes to the optimal cost to determine if suboptimal location and allocation schemes can produce nearly optimal transportation costs. Analytical results for distribution to a continuous demand show that nearly optimal costs can be achieved with suboptimal locations. An example of distribution to discrete demand points indicates the difficulties in applying these results to discrete demand problems.     

Estimating scale economies in non-convex production models

The literature on nonparametric frontier technologies lacks a method for the measurement of scale economies in non-convex settings. This paper proposes a general procedure which is based on the minimization of the ray average cost and requires the solution of a single programming problem. Our approach allows for multiple optima to introduce the case of global sub-constant scale economies, and it also permits the estimation of scale economies at a local level. The empirical application investigates the role of replicability and the relationship between global and local indicators. It also points out the managerial implications for companies operating in the Italian public transit industry.     

Discrete facility location with nonlinear diseconomies in fixed costs

A discrete facility location problem is formulated where the total fixed cost for establishing the facilities includes a component that is a nonlinear function of the number of facilities being established. Some theoretical properties of the solution are derived when this fixed cost is a convex nondecreasing function of the number of facilities. Based on these properties an efficient bisection heuristic is developed where at each iteration, the classical uncapacitated facility location and/or m-median subproblems are solved using available efficient heuristics.     

Compact bidding languages and supplier selection for markets with economies of scale and scope

Combinatorial auctions have been used in procurement markets with economies of scope. Preference elicitation is already a problem in single-unit combinatorial auctions, but it becomes prohibitive even for small instances of multi-unit combinatorial auctions, as suppliers cannot be expected to enumerate a sufficient number of bids that would allow an auctioneer to find the efficient allocation. Auction design for markets with economies of scale and scope are much less well understood. They require more compact and yet expressive bidding languages, and the supplier selection typically is a hard computational problem. In this paper, we propose a compact bidding language to express the characteristics of a supplier’s cost function in markets with economies of scale and scope. Bidders in these auctions can specify various discounts and markups on overall spend on all items or selected item sets, and specify complex conditions for these pricing rules. We propose an optimization formulation to solve the resulting supplier selection problem and provide an extensive experimental evaluation. We also discuss the impact of different language features on the computational effort, on total spend, and the knowledge representation of the bids. Interestingly, while in most settings volume discount bids can lead to significant cost savings, some types of volume discount bids can be worse than split-award auctions in simple settings.     

Supply chain design considering economies of scale and transport frequencies

In this paper we consider a 3-echelon, multi-product supply chain design model with economies of scale in transport and warehousing that explicitly takes transport frequencies into consideration. Our model simultaneously optimizes locations and sizes of tank farms, material flows, and transport frequencies within the network. We consider all relevant costs: product cost, transport cost, tank rental cost, tank throughput cost, and inventory cost. The problem is based on a real-life example from a chemical company. We show that considering economies of scale and transport frequencies in the design stage is crucial and failing to do so can lead to substantially higher costs than optimal. We solve a wide variety of problems with branch-and-bound and with the efficient solution heuristics based on iterative linearization techniques we develop. We show that the heuristics are superior to the standard branch-and-bound technique for large problems like the one of the chemical company that motivated our research.     

Choice of item pricing feedback schemes for multiple unit reverse combinatorial auctions

Recently, interest in combinatorial auctions has extended to include trade in multiple units of heterogeneous items. Combinatorial bidding is complex and iterative auctions are used to allow bidders to sequentially express their preferences with the aid of auction market information provided in the form of price feedbacks. There are different competing designs for the provision of item price feedbacks; however, most of these have not been thoroughly studied for multiple unit combinatorial auctions. This paper focuses on addressing this gap by evaluating several feedback schemes or algorithms in the context of multiple unit auctions. We numerically evaluate these algorithms under different scenarios that vary in bidder package selection strategies and in the degree of competition. We observe that auction outcomes are best when bidders use a naïve bidding strategy and competition is strong. Performance deteriorates significantly when bidders strategically select packages to maximize their profit. Finally, the performances of some algorithms are more sensitive to strategic bidding than others.     

Multi-unit auctions with complementarities: Issues of efficiency in electricity auctions

In this paper, we analyze the ability of different auction structures to induce the efficient dispatch in a one-shot framework where generators know their own and competitors' costs with certainty. In particular, we are interested in identifying which, if any, rules in an auction structure yield only the efficient dispatch in equilibrium. We find that a critical component to a successful auction design is the way in which demand is bundled and hence the way bids are defined. While an auction mechanism which allows for more than one winner in an auction may support inefficient dispatches in equilibrium, we find that an auction where there is exactly one winner per lot, where the lots are formed to capture the cost structure of generation plants, and all lots are auctioned simultaneously, supports only efficient dispatches in equilibrium.     

An algorithm for optimizing network flow capacity under economies of scale

The problem of optimally allocating a fixed budget to the various arcs of a single-source, single-sink network for the purpose of maximizing network flow capacity is considered. The initial vector of arc capacities is given, and the cost function, associated with each arc, for incrementing capacity is concave; therefore, the feasible region is nonconvex. The problem is approached by Benders' decomposition procedure, and a finite algorithm is developed for solving the nonconvex relaxed master problems. A numerical example of optimizing network flow capacity, under economies of scale, is included.This research was supported by the National Science Foundation, Grant No. GK-32791.     

Technical efficiency and economies of scale: A non-parametric analysis of REIT operating efficiency

This study measures technical efficiency and economies of scale for real estate investment trusts (REITs) by employing data envelopment analysis (DEA), a linear-programming technique. Using data from the National Association of Real Estate Investment Trusts (NAREITs) for the years 1992–1996, we find that REITs are technically inefficient, and the inefficiencies are a result of both poor input utilization and failure to operate at constant returns to scale. With respect to scale inefficiency, most REITs are operating at increasing returns to scale, suggesting that REITs could improve performance through expansion. Moreover, we employ regression analysis to determine what characteristics influence the efficiency measures obtained. The results show that internal REIT management is positively related to all measures of efficiency. Increasing leverage is negatively related to REIT input utilization. Finally, increasing REIT diversification across property types enhances scale efficiency (SE) but reduces input usage efficiency.     

All-pay auctions with risk-averse players

We study independent private-value all-pay auctions with risk-averse players. We show that: (1) Players with low values bid lower and players with high values bid higher than they would bid in the risk neutral case. (2) Players with low values bid lower and players with high values bid higher than they would bid in a first-price auction. (3) Players’ expected utilities in an all-pay auction are lower than in a first-price auction. We also use perturbation analysis to calculate explicit approximations of the equilibrium strategies of risk-averse players and the seller’s expected revenue. In particular, we show that in all-pay auctions the seller’s expected payoff in the risk-averse case may be either higher or lower than in the risk neutral case.     

Large auctions with risk-averse bidders

We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as ${n\longrightarrow \infty }We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as n? ￥{n\longrightarrow \infty } with risk-averse bidders is strictly below the risk-neutral limit. Therefore, these auction mechanisms are not revenue equivalent to large k-price auctions even to leading-order as n? ￥{n\longrightarrow \infty }.     

All-pay auctions with pre- and post-bidding options

Motivated by the emergence of online penny or pay-to-bid auctions, in this study, we analyze the operational consequences of all-pay auctions competing with fixed list price stores. In all-pay auctions, bidders place bids, and highest bidder wins. Depending on the auction format, the winner pays either the amount of their bid or that of the second-highest bid. All losing bidders forfeit their bids, regardless of the auction format. Bidders may visit the store, both before and after bidding, and buy the item at the fixed list price. In a modified version, we consider a setting where bidders can use their sunk bid as a credit towards buying the item from the auctioneer at a fixed price (different from the list price). We characterize a symmetric equilibrium in the bidding/buying strategy and derive optimal list prices for both the seller and auctioneer to maximize expected revenue. We consider two situations: (1) one firm operating both channels (i.e. fixed list price store and all-pay auction), and (2) two competing firms, each operating one of the two channels.