Complexity analysis of an assignment problem with controllable assignment costs and its applications in scheduling

We extend the classical linear assignment problem to the case where the cost of assigning agent j to task i is a multiplication of task i’s cost parameter by a cost function of agent j. The cost function of agent j is a linear function of the amount of resource allocated to the agent. A solution for our assignment problem is defined by the assignment of agents to tasks and by a resource allocation to each agent. The quality of a solution is measured by two criteria. The first criterion is the total assignment cost and the second is the total weighted resource consumption. We address these criteria via four different problem variations. We prove that our assignment problem is NP-hard for three of the four variations, even if all the resource consumption weights are equal. However, and somewhat surprisingly, we find that the fourth variation is solvable in polynomial time. In addition, we find that our assignment problem is equivalent to a large set of important scheduling problems whose complexity has been an open question until now, for three of the four variations.     

Recent developments in Dual Resource Constrained (DRC) system research

Real world manufacturing systems are usually constrained by both machine and human resources. Human operators are often the constraining resource and transfer between workstations to process jobs when required. This kind of system is known as a Dual Resource Constrained (DRC) system and presents additional technical challenges which must be considered during planning and scheduling. These technical challenges can be categorised into the five main dimensions of job release mechanisms, job dispatching, worker flexibility, worker assignment and transfer costs. This paper aims to provide an overview of recent developments in DRC research concerned with each of these areas and also discusses some possible approaches to solving the resource scheduling problem in a DRC system. The focus is on materials published after 1995 and up to 2009. Previous reviews on DRC systems are commented on and followed by a review of recent works associated with each of the five dimensions of DRC system research. Advancements made and new methodologies proposed are discussed and future research directions are identified.     

Resource constraint scheduling with a fractional shared resource

We consider a scheduling problem motivated by mining in remote off-grid areas. In this model, mines have pre-assigned mineral processing jobs and their own machine for executing these jobs. Each job also needs a certain amount of electricity in order to get completed. The electricity, on the other hand, is of limited supply and must be shared between the mines. We present a mathematical formulation of the problem and a Lagrangian relaxation based heuristic. Computational results which compares our heuristic with genetic algorithm and simulated annealing are also presented.     

基于统一价格拍卖的初始排污权分配方法

针对初始排污权总量分配的实际问题,基于统一价格拍卖的思想提出了一种具有激励性的可变总量的分配方法,分别给出了排污企业对称和排污企业非对称两种情形下的线性均衡报价策略,并证明了该方法的可行性和有效性,从而为建设排污权分配和交易制度提供了理论依据和方法参考.     

Trade-offs between target hardening and overarching protection

Defenders concerned about protecting multiple targets can either protect them individually (through target hardening), or collectively (through overarching protections such as border security, public health, emergency response, or intelligence). Decision makers may find it relatively straightforward to choose which targets to harden, but are likely to find it more difficult to compare seemingly incommensurate forms of protection - e.g., target hardening, versus a reduction in the likelihood of weapons being smuggled across the border. Unfortunately, little previous research has addressed this question, and fundamental research is needed to provide guidance and practical solution approaches. In this paper, we first develop a model to optimally allocate resources between target hardening and overarching protection, then investigate the factors affecting the relative desirability of target hardening versus overarching protection, and finally apply our model to a case study involving critical assets in Wisconsin. The case study demonstrates the value of our method by showing that the optimal solution obtained using our model is in some cases substantially better than the historical budget allocation.     

煤炭码头船货匹配下泊位动态分配多目标优化模型及算法

本文针对输出型煤炭码头船货匹配下泊位动态分配问题,构建了堆场-取装线-泊位-船舶联合分配优化数学模型,并设计了采用仿真推演策略解码的遗传算法求解。首先,综合考虑船舶、泊位、堆场、取装线、煤种、航道开放时间和装船作业规则等要素,以船舶在港时间最短和作业效率最大为目标建立了相应的多约束多目标优化模型。然后,综合多目标优化、遗传算法以及仿真推演技术,设计了相应的遗传算法求解,包括:组合式编码、采用仿真推演策略的解码方法,追加了具有合法性检查的染色体生成算法,设计了采用多种策略的遗传操作等。最后实例表明,本算法的执行效率高而且优化效果好。     

On the population monotonicity of independent set games

An independent set game is a cooperative game dealing with profit sharing in the maximum independent set problem. A population monotonic allocation scheme is a rule specifying how to share the profit of each coalition among its participants such that every participant is better off when the coalition expands. In this paper, we provide a necessary and sufficient characterization for independent set games admitting population monotonic allocation schemes. Moreover, our characterization can be verified efficiently.     

基于风险-均值分析的供应商选择与订单分配集成优化模型与求解

针对不确定环境下具有不同供应合约的供应商选择与订单分配问题,本文构建了基于风险-均值分析的模糊两阶段多周期集成优化模型。与传统的该问题研究并未充分考虑供应商选择与订单分配两阶段决策的交互影响不同,在该模型中,第一阶段供应商选择的评价目标依赖于后期实际运营中的订单分配决策;并考虑未来需求和实际运营成本的不确定性,引入在险价值和期望值两种决策准则对供应商选择方案的绩效进行评价。提出了该模型的分析求解方法,在险价值得以精确评估,期望值被控制在确定的误差范围内,并可以达到足够的精度要求。     

Bandwidth allocation for guaranteed versus best effort service categories

Modern communication networks evolve towards integration of guaranteed-performance and best-effort service types. The coexistence of these two service types offers substantial benefits, such as resource sharing between service classes, and the ability of the user to select an appropriate service class according to its individual requirements and preferences. Notwithstanding, such interaction gives rise to more complicated system behavior and related performance issues, which need to be explored and understood in order to allow efficient network operation. In this paper we examine potential congestion phenomena, which arise due to the combined effect of bandwidth sharing and user migration between service classes. We propose a simplified fluid model for session flow, consisting of two coupled queues with state-dependent flows, which captures the essential ingredients of service-class interaction. Our analysis shows that the system might exhibit bistable behavior, in the sense that transient congestion may stir the system from a stable and efficient operating point to an inefficient and congested one. We identify conditions which give rise to bistability, and propose a call admission control scheme which prevents the system from getting trapped in a congested-type equilibrium, while not interfering with normal system operation. This revised version was published online in June 2006 with corrections to the Cover Date.     

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.