On the core of cost-revenue games: Minimum cost spanning tree games with revenues

In this paper, we analyze cost sharing problems arising from a general service by explicitly taking into account the generated revenues. To this cost-revenue sharing problem, we associate a cooperative game with transferable utility, called cost-revenue game. By considering cooperation among the agents using the general service, the value of a coalition is defined as the maximum net revenues that the coalition may obtain by means of cooperation. As a result, a coalition may profit from not allowing all its members to get the service that generates the revenues. We focus on the study of the core of cost-revenue games. Under the assumption that cooperation among the members of the grand coalition grants the use of the service under consideration to all its members, it is shown that a cost-revenue game has a nonempty core for any vector of revenues if, and only if, the dual game of the cost game has a large core. Using this result, we investigate minimum cost spanning tree games with revenues. We show that if every connection cost can take only two values (low or high cost), then, the corresponding minimum cost spanning tree game with revenues has a nonempty core. Furthermore, we provide an example of a minimum cost spanning tree game with revenues with an empty core where every connection cost can take only one of three values (low, medium, or high cost).     

Competition through capacity investment under asymmetric existing capacities and costs

This paper discusses the way that different operational characteristics including existing capacity, scale economies, and production policy have an important influence on the capacity outcomes when firms compete in the market place. We formulate a game-theoretical model where each firm has an existing capacity and faces both fixed and variable costs in purchasing additional capacity. Specifically, the firms simultaneously (or sequentially) make their expansion decisions, and then simultaneously decide their production decisions with these outputs being capacity constrained. We also compare our results with cases where production has to match capacity. By characterizing the firms’ capacity and production choices in equilibrium, our analysis shows that the operational factors play a crucial role in determining what happens. The modeling and analysis in the paper gives insight into the way that the ability to use less production capacity than has been built will undermine the commitment value of existing capacity. If a commitment to full production is not possible, sinking operational costs can enable a firm to keep some preemptive advantage. We also show that the existence of fixed costs can introduce cases where there are either no pure strategy equilibrium or multiple equilibria. The managerial implications of our analysis are noted in the discussion. Our central contribution in this paper is the innovative integration of the strategic analysis of capacity expansion and well-known (s,S)$(s\text{,}S)$ policy in operations and supply chain theory.     

Polynomial cases of the economic lot sizing problem with cost discounts

In this paper we study the economic lot sizing problem with cost discounts. In the economic lot sizing problem a facility faces known demands over a discrete finite horizon. At each period, the ordering cost function and the holding cost function are given and they can be different from period to period. There are no constraints on the quantity ordered in each period and backlogging is not allowed. The objective is to decide when and how much to order so as to minimize the total ordering and holding costs over the finite horizon without any shortages. We study two different cost discount functions. The modified all-unit discount cost function alternates increasing and flat sections, starting with a flat section that indicates a minimum charge for small quantities. While in general the economic lot sizing problem with modified all-unit discount cost function is known to be NP-hard, we assume that the cost functions do not vary from period to period and identify a polynomial case. Then we study the incremental discount cost function which is an increasing piecewise linear function with no flat sections. The efficiency of the solution algorithms follows from properties of the optimal solution. We computationally test the polynomial algorithms against the use of CPLEX.     

中缅原油管道贯通对进口原油海上运输成本的影响分析

研究了中缅原油管道贯通对我国进口原油海上运输成本的影响.首先分析了我国的主要原油进口地、进口量和海上运输航线等信息,然后选择了三种不同型号油轮,并调查了其载重量、航速、日租金等数据.以不同型号油轮的运输航次及各条航线上的实际运输量为决策变量,总租金(总运输成本)最小化为目标函数,分别建立了中缅原油管道贯通前后我国进口原油海上运输问题的数学模型,并分别给出了求解方法.最后,根据实际统计数据进行计算,分别求出了中缅原油管道贯通前后我国原油海上运输的总成本,结果显示,中缅原油管道贯通后我国进口原油的海上运输成本将降低4.95%.     

Optimizing cost flows by edge cost and capacity upgrade

We examine a network upgrade problem for cost flows. A budget can be distributed among the arcs of the network. An investment on each single arc can be used either to decrease the arc flow cost, or to increase the arc capacity, or both. The goal is to maximize the flow through the network while not exceeding bounds on the budget and on the total flow cost.

The problems are NP-hard even on series-parallel graphs. We provide an approximation algorithm on series-parallel graphs which, for arbitrary δ,>0, produces a solution which exceeds the bounds on the budget and the flow cost by factors of at most 1+δ and 1+, respectively, while the amount of flow is at least that of an optimum solution. The running time of the algorithm is polynomial in the input size and 1/(δ). In addition we give an approximation algorithm on general graphs applicable to problem instances with small arc capacities.     

Spying on the cost structure of naive bidding competitors via linear programming models

A linear programming model is constructed which enables a firm to estimate its competitor's cost structure when the competitor adheres to a non-randomized strategy. The existence of the model makes randomized bidding prudent apart from game theory considerations. The need for increased curriculum attention to optimal bidding is highlighted.     

作业成本法数学模型的创新

随着企业产品价格竞争愈演愈烈，成本的合理分配、计算日显重要，但在间接费用的分摊上，传统成本会计对成本信息反映失真的局限性日益显露，会计理论界和实务界开始寻求一种新的准确的成本计算方法，作业成本法应运而生。本将由作业成本法基本原理推导出其数学模型，并将对其数学模型进一步改进，建立比较数学模型。使作业成本法向实际应用更进一步。     

Compensatory transfers in two-player decision problems

This paper presents an axiomatic characterization of a family of solutions to two-player quasi-linear social choice problems. In these problems the players select a single action from a set available to them. They may also transfer money between themselves.The solutions form a one-parameter family, where the parameter is a non-negative number, t.The solutions can be interpreted as follows: Any efficient action can be selected. Based on this action, compute for each player a “best claim for compensation”. A claim for compensation is the difference between the value of an alternative action and the selected efficient action, minus a penalty proportional to the extent to which the alternative action is inefficient. The coefficient of proportionality of this penalty is t. The best claim for compensation for a player is the maximum of this computed claim over all possible alternative actions. The solution, at the parameter value t, is to implement the chosen efficient action and make a monetary transfer equal to the average of these two best claims. The characterization relies on three main axioms. The paper presents and justifies these axioms and compares them to related conditions used in other bargaining contexts. In Nash Bargaining Theory, the axioms analogous to these three are in conflict with each other. In contrast, in the quasi-linear social choice setting of this paper, all three conditions can be satisfied simultaneously.This work was supported by the Division of Research at the Harvard Business School. Thanks are due to the Cowles Foundation for Research in Economics at Yale University for its kind hospitality during the Spring of 2002. I have received helpful advice and comments from Youngsub Chun, Ehud Kalai, Herve Moulin, Al Roth, Ilya Segal, Adam Szeidl, Richard Zeckhauser, and other members of the Theory Seminars at Harvard, MIT, Princeton, Rice and Northwestern.     

The opportunity cost of mean–variance choice under estimation risk

Mean–variance portfolio choice is often criticized as sub-optimal in the more general expected utility framework. It is argued that the expected utility framework takes into consideration higher moments ignored by mean variance analysis. A body of research suggests that mean–variance choice, though arguably sub-optimal, provides very close-to-expected utility maximizing portfolios and their expected utilities, basing its evaluation on in-sample analysis where mean–variance choice is sub-optimal by definition. In order to clarify this existing research, this study provides a framework that allows comparing in-sample and out-of-sample performance of the mean variance portfolios against expected utility maximizing portfolios. Our in-sample results confirm the results of earlier studies. On the other hand, our out-of-sample results show that the expected utility model performs worse. The out-of-sample inferiority of the expected utility model is more pronounced for preferences and constraints under which in-sample mean variance approximations are weakest. We argue that, in addition to its elegance and simplicity, the mean–variance model extracts more information from sample data because it uses the covariance matrix of returns. The expected utility model may reach its optimal solution without using information from the covariance matrix.