Comparative Statics,Informativeness, and the Interval Dominance Order

We identify a new way to order functions, called the interval dominance order, that generalizes both the single crossing property and a standard condition used in statistical decision theory. This allows us to provide a unified treatment of the major theorems on monotone comparative statics with and without uncertainty, the comparison of signal informativeness, and a non‐Bayesian theorem on the completeness of increasing decision rules. We illustrate the concept and results with various applications, including an application to optimal stopping time problems where the single crossing property is typically violated.     

Strategyproof Assignment by Hierarchical Exchange

We give a characterization of the set of group‐strategyproof, Pareto‐optimal, and reallocation‐proof allocation rules for the assignment problem, where individuals are assigned at most one indivisible object, without any medium of exchange. Although there are no property rights in the model, the rules satisfying the above criteria imitate a trading procedure with individual endowments, in which individuals exchange objects from their hierarchically determined endowment sets in an iterative manner. In particular, these assignment rules generalize Gale's top trading cycle procedure, the classical rule for the model in which each individual owns an indivisible good.     

A minimized-rule based approach for improving data currency

Repairing obsolete data items to the up-to-date values faces great challenges in the area of improving data quality. Previous methods of data repairing are based on either quality rules or statistical techniques, but both of the two types of methods have their limitations. To overcome the shortages of the previous methods, this paper focuses on combining quality rules and statistical techniques to improve data currency. (1) A new class of currency repairing rules (CRR for short) is proposed to express both domain knowledge and statistical information. Domain knowledge is expressed by the rule pattern, and the statistical information is described by the conditional probability distribution corresponding to each rule. (2) The problem of generating minimized CRRs is studied in both static and dynamic world. In the static world, the problem of generating minimized CRR patterns is proved to be NP-hard, and two approximate algorithms are provided to solve the problem. In dynamic world, methods are provided to update the CRRs without recomputing the whole CRR set in case of data being changed. In some special cases, the updates can be finished in \(O(1)\) time. In both cases, the methods for learning conditional probabilities for each CRR pattern are provided. (3) Based on the CRRs, the problems of finding optimal repairing plans with and without cost budget is studied, and methods are provided to solve them. (4) The experiments based on both real and synthetic data sets show that the proposed methods are efficient and effective.     

MODIFIED STEPPING-STONE METHOD AS A TEACHING AID FOR CAPACITATED TRANSPORTATION PROBLEMS

This paper extends the standard stepping-stone method to the case of capacitated transportation problems. The purpose is to offer an alternative to network-oriented or simplex-based methods (such as the out-of-kilter and upper-bounding techniques) often used in handling the capacitated transportation problem but generally beyond the scope of introductory decision sciences courses. The proposed procedure is based on the simple stepping-stone method and requires only a few modifications in the cost/assignment matrix and some alterations in the pivoting rules. As such, it is much easier to understand and apply than the above-mentioned solution algorithms. It therefore can serve as an effective tool for teaching capacitated transportation problems. Two numerical examples illustrate applications of the proposed method, procedures for sensitivity analysis, and comparisons with linear programming.     

Inference on Causal Effects in a Generalized Regression Kink Design

We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. We characterize a broad class of models in which a sharp “Regression Kink Design” (RKD or RK Design) identifies a readily interpretable treatment‐on‐the‐treated parameter (Florens, Heckman, Meghir, and Vytlacil (2008)). We also introduce a “fuzzy regression kink design” generalization that allows for omitted variables in the assignment rule, noncompliance, and certain types of measurement errors in the observed values of the assignment variable and the policy variable. Our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. Using a kink in the unemployment benefit formula, we apply a fuzzy RKD to empirically estimate the effect of benefit rates on unemployment durations in Austria.     

Approximation Algorithms for the Multiple Knapsack Problem with Assignment Restrictions

Motivated by a real world application, we study the multiple knapsack problem with assignment restrictions (MKAR). We are given a set of items, each with a positive real weight, and a set of knapsacks, each with a positive real capacity. In addition, for each item a set of knapsacks that can hold that item is specified. In a feasible assignment of items to knapsacks, each item is assigned to at most one knapsack, assignment restrictions are satisfied, and knapsack capacities are not exceeded. We consider the objectives of maximizing assigned weight and minimizing utilized capacity.We focus on obtaining approximate solutions in polynomial computational time. We show that simple greedy approaches yield 1/3-approximation algorithms for the objective of maximizing assigned weight. We give two different 1/2-approximation algorithms: the first one solves single knapsack problems successively and the second one is based on rounding the LP relaxation solution. For the bicriteria problem of minimizing utilized capacity subject to a minimum requirement on assigned weight, we give an (1/3,2)-approximation algorithm.     

Estimating the Effects of a Time‐Limited Earnings Subsidy for Welfare‐Leavers

In the Self Sufficiency Project (SSP) welfare demonstration, members of a randomly assigned treatment group could receive a subsidy for full‐time work. The subsidy was available for 3 years, but only to people who began working full time within 12 months of random assignment. A simple optimizing model suggests that the eligibility rules created an “establishment” incentive to find a job and leave welfare within a year of random assignment, and an “entitlement” incentive to choose work over welfare once eligibility was established. Building on this insight, we develop an econometric model of welfare participation that allows us to separate the two effects and estimate the impact of the earnings subsidy on welfare entry and exit rates among those who achieved eligibility. The combination of the two incentives explains the time profile of the experimental impacts, which peaked 15 months after random assignment and faded relatively quickly. Our findings suggest that about half of the peak impact of SSP was attributable to the establishment incentive. Despite the extra work effort generated by SSP, the program had no lasting impact on wages and little or no long‐run effect on welfare participation.     

The Effects of Learning,Forgetting, and Relearning on Decision Rule Performance in Multiproject Scheduling

Product development occurs in multiproject environments where preemption is often allowed so that critical projects can be addressed immediately. Because product development is characterized by time-based competition, there is pressure to make decisions quickly using heuristics methods that yield fast project completion. Preemption heuristics are needed both to choose activities for preemption and then to determine which resources to use to restart preempted activities. Past research involving preemption has ignored any completion time penalty due to the forgetting experienced by project personnel during preemption and the resulting relearning time required to regain lost proficiency. The purpose of this research is to determine the impact of learning, forgetting, and relearning (LFR) on project completion time when preemption is allowed. We present a model for the LFR cycle in multiproject development environments. We test a number of priority rules for activity scheduling, activity preemption, and resource assignment subsequent to preemption, subject to the existence of the LFR cycle, for which a single type of knowledge worker resource is assigned among multiple projects. The results of the simulation experiments clearly demonstrate that LFR effects are significant. The tests of different scheduling, preemption, and resource reassignment rules show that the choice of rule is crucial in mitigating the completion time penalty effects of the LFR cycle, while maintaining high levels of resource utilization. Specifically, the worst performing rules tested for each performance measure are those that attempt to maintain high resource utilization. The best performing rules are based on activity criticality and resource learning.     

The Nonparametric Identification of Treatment Effects in Duration Models

This paper analyzes the specification and identification of causal multivariate duration models. We focus on the case in which one duration concerns the point in time a treatment is initiated and we are interested in the effect of this treatment on some outcome duration. We define “no anticipation of treatment” and relate it to a common assumption in biostatistics. We show that (i) no anticipation and (ii) randomized treatment assignment can be imposed without restricting the observational data. We impose (i) but not (ii) and prove identification of models that impose some structure. We allow for dependent unobserved heterogeneity and we do not exploit exclusion restrictions on covariates. We provide results for both single‐spell and multiple‐spell data. The timing of events conveys useful information on the treatment effect.     

A Case Study of De-randomization Methods for Combinatorial Approximation Algorithms

We study three different de-randomization methods that are often applied to approximate combinatorial optimization problems. We analyze the conditional probabilities method in connection with randomized rounding for routing, packing and covering integer linear programming problems. We show extensions of such methods for non-independent randomized rounding for the assignment problem. The second method, the so-called random walks is exemplified with algorithms for dense instances of some NP problems. Another often used method is the bounded independence technique; we explicit this method for the sparsest cut and maximum concurrent flow problems.     

Statistical Treatment Rules for Heterogeneous Populations

An important objective of empirical research on treatment response is to provide decision makers with information useful in choosing treatments. This paper studies minimax‐regret treatment choice using the sample data generated by a classical randomized experiment. Consider a utilitarian social planner who must choose among the feasible statistical treatment rules, these being functions that map the sample data and observed covariates of population members into a treatment allocation. If the planner knew the population distribution of treatment response, the optimal treatment rule would maximize mean welfare conditional on all observed covariates. The appropriate use of covariate information is a more subtle matter when only sample data on treatment response are available. I consider the class of conditional empirical success rules; that is, rules assigning persons to treatments that yield the best experimental outcomes conditional on alternative subsets of the observed covariates. I derive a closed‐form bound on the maximum regret of any such rule. Comparison of the bounds for rules that condition on smaller and larger subsets of the covariates yields sufficient sample sizes for productive use of covariate information. When the available sample size exceeds the sufficiency boundary, a planner can be certain that conditioning treatment choice on more covariates is preferable (in terms of minimax regret) to conditioning on fewer covariates.     

随机抽样算法在多项目调度中的应用

针对资源约束下的多项目调度问题,扩展了单项目进度生产机制,并在此基础上设计了多项目调度的随机抽样算法。通过对比分析,说明不同的任务优先规则对随机抽样算法具有不同的影响,其中采用MINSLK等优先规则的随机抽样算法能够有效地缩短项目平均工期。与其他多项目调度启发式算法的比较和统计检验,说明随机抽样算法显著优于这些常用的启发式算法。     

Customer Order Scheduling in a General Job Shop Environment*

The primary objective of this study is to examine the performance of order-based dispatching rules in a general job shop, where the environmental factors are shop utilization and due date tightness. An order is defined as a collection of jobs that are shipped as a group—an order—to the customer, only on completion of the last job of the order. We specifically compare dispatching rules from past job-based studies to some rules adapted to encompass order characteristics. Standard flow time and tardiness measures are used, but in addition, we introduce measures that combine average performance with variation in an attempt to capture the performance of a majority of the orders processed in the shop. Of the 16 dispatching rules tested, our results show that four of the simple rules dominate the others. We also found that order-based rules perform better than their job-based counterparts. The study makes use of multivariate statistical analysis, in addition to the usual univariate tests, which can provide additional insight to managers using multiple criteria in their decision process.     

自动化立体仓库中的储位分配及存取路径优化

储位分配和存取作业路径优化是仓储管理中的两个重要决策问题。本文研究如何在自动化立体仓库中对这两个问题进行同时决策。提出了一个混合整数规划模型对该问题进行优化建模,设计开发了一个基于有向连接图的两阶段优化算法对问题求初始解,并利用禁忌搜索算法对所求得的解进行改进。算法第一阶段解决储位分配问题,在此基础上第二阶段利用Hungarian算法对堆垛机的存取作业路径优化问题进行求解。最后利用实例对算法效率和精度进行分析评价,计算结果验证了算法的有效性。     

SCAT AND SPAT: LARGE-SCALE COMPUTER-BASED OPTIMIZATION SYSTEMS FOR THE PERSONNEL ASSIGNMENT PROBLEM

The personnel assignment problem involves the assignment of people to tasks, projects, etc., in a manner that maximizes a measure of aggregate utility for the assignees subject to several assignment constraints. In addition to computationally efficient solution algorithms, the effective implementation of mathematical models to solve the personnel assignment problem must include data processing systems with comprehensive error checking/resolution procedures, end user reports, documentation, and training. This paper summarizes two successful computer-based systems for solving large-scale personnel assignment problems that frequently occur in university settings. SCAT, the Student-Company Assignment Technique, assigns students to job interview slots. SPAT, the Student-Project Assignment Technique, assigns students to project teams in an MBA field project course. The SCAT and SPAT approaches can be generalized to a wide variety of personnel assignment problems in university, industry, government, and military settings.     

Novel quadratic programming approach for time series clustering with biomedical application

Fundamental problems in data mining mainly involve discrete decisions based on numerical analyses of data (e.g., class assignment, feature selection, data categorization, identifying outlier samples). These decision-making problems in data mining are combinatorial in nature and can naturally be formulated as discrete optimization problems. One of the most widely studied problems in data mining is clustering. In this paper, we propose a new optimization model for hierarchical clustering based on quadratic programming and later show that this model is compact and scalable. Application of this clustering technique in epilepsy, the second most common brain disorder, is a case point in this study. In our empirical study, we will apply the proposed clustering technique to treatment problems in epilepsy through the brain dynamics analysis of electroencephalogram (EEG) recordings. This study is a proof of concept of our hypothesis that epileptic brains tend to be more synchronized (clustered) during the period before a seizure than a normal period. The results of this study suggest that data mining research might be able to revolutionize current diagnosis and treatment of epilepsy as well as give a greater understanding of brain functions (and other complex systems) from a system perspective. This work was partially supported by the NSF grant CCF 0546574 and Rutgers Research Council grant-202018.     

MULTIDIMENSIONAL ASSIGNMENT PROBLEMS

Each of the many two-dimensional variations of the classical assignment problem has at least one counterpart in higher dimensions. This paper is a tutorial on these higher dimensional assignment models and their applications. It is a synthesis of a vast literature scattered throughout a great variety of journal articles and other miscellaneous sources. We have attempted to make the paper a complete bibliography with the emphasis on topics important to practitioners of decision sciences. These topics include original results by the authors, most notably, a polynomial solution approach for a class of multidimensional assignment problems which often arise in scheduling applications.     

Due Date Assignment,Job Order Release,and Sequencing Interaction in Job Shop Scheduling*

Depending on the techniques employed, the due date assignment, release, and sequencing procedures in job shop scheduling may depend on one another. This research investigates the effects of these interactions with a simulation model of a dynamic five-machine job shop in which early shipments are prohibited. Performance of the system is measured primarily in terms of the total cost (work-in-process cost, finished goods holding cost, and late penalty) incurred by the shop, but a number of non-cost performance measures are also reported. The results support existence of a three-way interaction between the due date, release, and sequencing procedures as well as interaction between shop utilization and procedure combination. Statistical tests are used to identify those rules that perform best both overall and in combination with other rules.     

DEMOCRATIC MECHANISMS

We introduce democratic mechanisms as a set of rules that must obey liberal democracy's fundamental principles of equal voting and agenda rights. We show that an appropriate combination of three rules may yield efficient provision of public projects: first, flexible and double majority rules, where the size of the majority depends on the proposal, and taxed and non‐taxed individuals need to support the proposal; second, flexible agenda costs, where the agenda‐setter has to pay a certain amount of money if his proposal does not generate enough supporting votes; third, a ban on subsidies. We highlight that universal equal treatment with regard to taxation is undesirable. Finally, we illustrate how simple constitutions involving fixed super majority rules yield socially desirable outcomes if the agenda‐setter is benevolent. (JEL: D62, D72, H40)