Applications of data envelopment analysis in education

Non-parametric methods for efficiency evaluation were designed to analyse industries comprising multi-input multi-output producers and lacking data on market prices. Education is a typical example. In this chapter, we review applications of DEA in secondary and tertiary education, focusing on the opportunities that this offers for benchmarking at institutional level. At secondary level, we investigate also the disaggregation of efficiency measures into pupil-level and school-level effects. For higher education, while many analyses concern overall institutional efficiency, we examine also studies that take a more disaggregated approach, centred either around the performance of specific functional areas or that of individual employees.

A nettó jelenérték maximalizálása erőforrás-korlátos projektekben - egy új harmóniakereső metaheurisztika (A harmony search metaheuristic for the resourceconstrained project scheduling problem with discounted cash flows)

Ebben a tanulmányban a szerző egy új harmóniakereső metaheurisztikát mutat be, amely a minimális időtartamú erőforrás-korlátos ütemezések halmazán a projekt nettó jelenértékét maximalizálja. Az optimális ütemezés elméletileg két egész értékű (nulla-egy típusú) programozási feladat megoldását jelenti, ahol az első lépésben meghatározzuk a minimális időtartamú erőforrás-korlátos ütemezések időtartamát, majd a második lépésben az optimális időtartamot feltételként kezelve megoldjuk a nettó jelenérték maximalizálási problémát minimális időtartamú erőforrás-korlátos ütemezések halmazán. A probléma NP-hard jellege miatt az egzakt megoldás elfogadható idő alatt csak kisméretű projektek esetében képzelhető el. A bemutatandó metaheurisztika a Csébfalvi (2007) által a minimális időtartamú erőforrás-korlátos ütemezések időtartamának meghatározására és a tevékenységek ennek megfelelő ütemezésére kifejlesztett harmóniakereső metaheurisztika továbbfejlesztése, amely az erőforrás-felhasználási konfliktusokat elsőbbségi kapcsolatok beépítésével oldja fel. Az ajánlott metaheurisztika hatékonyságának és életképességének szemléltetésére számítási eredményeket adunk a jól ismert és népszerű PSPLIB tesztkönyvtár J30 részhalmazán futtatva. Az egzakt megoldás generálásához egy korszerű MILP-szoftvert (CPLEX) alkalmaztunk. _______________ This paper presents a harmony search metaheuristic for the resource-constrained project scheduling problem with discounted cash flows. In the proposed approach, a resource-constrained project is characterized by its „best” schedule, where best means a makespan minimal resource constrained schedule for which the net present value (NPV) measure is maximal. Theoretically the optimal schedule searching process is formulated as a twophase mixed integer linear programming (MILP) problem, which can be solved for small-scale projects in reasonable time. The applied metaheuristic is based on the "conflict repairing" version of the "Sounds of Silence" harmony search metaheuristic developed by Csébfalvi (2007) for the resource-constrained project scheduling problem (RCPSP). In order to illustrate the essence and viability of the proposed harmony search metaheuristic, we present computational results for a J30 subset from the well-known and popular PSPLIB. To generate the exact solutions a state-of-the-art MILP solver (CPLEX) was used.

Készpénz optimalizálás GLPK program használatával (Cash flow management with GLPK software)

A készpénz-optimalizálás az operációkutatás régóta kutatott területe. Ebben a cikkben valós adatokon mutatok be egy banki készpénz-optimalizálást, melyet lineáris programozási feladatok segítségével végeztem el. A cikkben összehasonlítottam a determinisztikus és a sztochasztikus megközelítéseket is. A hagyományos készpénz-optimalizáción két területen léptem túl: egyrészt vizsgáltam a bankfiók valutagazdálkodását is, másrészről a bankfiókok közötti készpénzszállítás lehetőségét is. A vegyes egészértékű lineáris programozási feladatok megoldására a glpk nevű szabad hozzáférésű szoftvert használtam, így a cikkből képet kaphatunk a megoldó (solver) felhasználhatóságáról és korlátairól is. ___________ In recent years both operational research and quantitative ¯nance have paid much attention to cash management issues. In this paper we present a cash management study which is based on real world data and uses a mixed integer linear programming (MILP) model as the main tool. In the paper we compare deterministic and stochastic approaches. The classical cash management problem is extended in two ways: we considered the possibility of bank offices keeping more than one currency and also investigated the opportunity of cash transports between bank offices. The MILP problem was solved with glpk (GNU Linear Programming Kit), a free software. The reader can also get a feel of how to use this solver.

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as “histogram binning” inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. ^ Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. ^ The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. ^ These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. ^ In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation. ^

Optimization models for selecting bus stops for accessibility improvements for people with disabilities

Bus stops are key links in the journeys of transit patrons with disabilities. Inaccessible bus stops prevent people with disabilities from using fixed-route bus services, thus limiting their mobility. The Americans with Disabilities Act (ADA) of 1990 prescribes the minimum requirements for bus stop accessibility by riders with disabilities. Due to limited budgets, transit agencies can only select a limited number of bus stop locations for ADA improvements annually. These locations should preferably be selected such that they maximize the overall benefits to patrons with disabilities. In addition, transit agencies may also choose to implement the universal design paradigm, which involves higher design standards than current ADA requirements and can provide amenities that are useful for all riders, like shelters and lighting. Many factors can affect the decision to improve a bus stop, including rider-based aspects like the number of riders with disabilities, total ridership, customer complaints, accidents, deployment costs, as well as locational aspects like the location of employment centers, schools, shopping areas, and so on. These interlacing factors make it difficult to identify optimum improvement locations without the aid of an optimization model. This dissertation proposes two integer programming models to help identify a priority list of bus stops for accessibility improvements. The first is a binary integer programming model designed to identify bus stops that need improvements to meet the minimum ADA requirements. The second involves a multi-objective nonlinear mixed integer programming model that attempts to achieve an optimal compromise among the two accessibility design standards. Geographic Information System (GIS) techniques were used extensively to both prepare the model input and examine the model output. An analytic hierarchy process (AHP) was applied to combine all of the factors affecting the benefits to patrons with disabilities. An extensive sensitivity analysis was performed to assess the reasonableness of the model outputs in response to changes in model constraints. Based on a case study using data from Broward County Transit (BCT) in Florida, the models were found to produce a list of bus stops that upon close examination were determined to be highly logical. Compared to traditional approaches using staff experience, requests from elected officials, customer complaints, etc., these optimization models offer a more objective and efficient platform on which to make bus stop improvement suggestions.

Algorithms for scheduling parallel batch processing machines with non-identical job ready times

This research is motivated by a practical application observed at a printed circuit board (PCB) manufacturing facility. After assembly, the PCBs (or jobs) are tested in environmental stress screening (ESS) chambers (or batch processing machines) to detect early failures. Several PCBs can be simultaneously tested as long as the total size of all the PCBs in the batch does not violate the chamber capacity. PCBs from different production lines arrive dynamically to a queue in front of a set of identical ESS chambers, where they are grouped into batches for testing. Each line delivers PCBs that vary in size and require different testing (or processing) times. Once a batch is formed, its processing time is the longest processing time among the PCBs in the batch, and its ready time is given by the PCB arriving last to the batch. ESS chambers are expensive and a bottleneck. Consequently, its makespan has to be minimized. ^ A mixed-integer formulation is proposed for the problem under study and compared to a formulation recently published. The proposed formulation is better in terms of the number of decision variables, linear constraints and run time. A procedure to compute the lower bound is proposed. For sparse problems (i.e. when job ready times are dispersed widely), the lower bounds are close to optimum. ^ The problem under study is NP-hard. Consequently, five heuristics, two metaheuristics (i.e. simulated annealing (SA) and greedy randomized adaptive search procedure (GRASP)), and a decomposition approach (i.e. column generation) are proposed—especially to solve problem instances which require prohibitively long run times when a commercial solver is used. Extensive experimental study was conducted to evaluate the different solution approaches based on the solution quality and run time. ^ The decomposition approach improved the lower bounds (or linear relaxation solution) of the mixed-integer formulation. At least one of the proposed heuristic outperforms the Modified Delay heuristic from the literature. For sparse problems, almost all the heuristics report a solution close to optimum. GRASP outperforms SA at a higher computational cost. The proposed approaches are viable to implement as the run time is very short. ^

A quantitative approach to the organizational design problem

The span of control is the most discussed single concept in classical and modern management theory. In specifying conditions for organizational effectiveness, the span of control has generally been regarded as a critical factor. Existing research work has focused mainly on qualitative methods to analyze this concept, for example heuristic rules based on experiences and/or intuition. This research takes a quantitative approach to this problem and formulates it as a binary integer model, which is used as a tool to study the organizational design issue. This model considers a range of requirements affecting management and supervision of a given set of jobs in a company. These decision variables include allocation of jobs to workers, considering complexity and compatibility of each job with respect to workers, and the requirement of management for planning, execution, training, and control activities in a hierarchical organization. The objective of the model is minimal operations cost, which is the sum of supervision costs at each level of the hierarchy, and the costs of workers assigned to jobs. The model is intended for application in the make-to-order industries as a design tool. It could also be applied to make-to-stock companies as an evaluation tool, to assess the optimality of their current organizational structure. Extensive experiments were conducted to validate the model, to study its behavior, and to evaluate the impact of changing parameters with practical problems. This research proposes a meta-heuristic approach to solving large-size problems, based on the concept of greedy algorithms and the Meta-RaPS algorithm. The proposed heuristic was evaluated with two measures of performance: solution quality and computational speed. The quality is assessed by comparing the obtained objective function value to the one achieved by the optimal solution. The computational efficiency is assessed by comparing the computer time used by the proposed heuristic to the time taken by a commercial software system. Test results show the proposed heuristic procedure generates good solutions in a time-efficient manner.

The order selection and lot sizing problem in the make-to-order environment

This research is motivated by the need for considering lot sizing while accepting customer orders in a make-to-order (MTO) environment, in which each customer order must be delivered by its due date. Job shop is the typical operation model used in an MTO operation, where the production planner must make three concurrent decisions; they are order selection, lot size, and job schedule. These decisions are usually treated separately in the literature and are mostly led to heuristic solutions. The first phase of the study is focused on a formal definition of the problem. Mathematical programming techniques are applied to modeling this problem in terms of its objective, decision variables, and constraints. A commercial solver, CPLEX is applied to solve the resulting mixed-integer linear programming model with small instances to validate the mathematical formulation. The computational result shows it is not practical for solving problems of industrial size, using a commercial solver. The second phase of this study is focused on development of an effective solution approach to this problem of large scale. The proposed solution approach is an iterative process involving three sequential decision steps of order selection, lot sizing, and lot scheduling. A range of simple sequencing rules are identified for each of the three subproblems. Using computer simulation as the tool, an experiment is designed to evaluate their performance against a set of system parameters. For order selection, the proposed weighted most profit rule performs the best. The shifting bottleneck and the earliest operation finish time both are the best scheduling rules. For lot sizing, the proposed minimum cost increase heuristic, based on the Dixon-Silver method performs the best, when the demand-to-capacity ratio at the bottleneck machine is high. The proposed minimum cost heuristic, based on the Wagner-Whitin algorithm is the best lot-sizing heuristic for shops of a low demand-to-capacity ratio. The proposed heuristic is applied to an industrial case to further evaluate its performance. The result shows it can improve an average of total profit by 16.62%. This research contributes to the production planning research community with a complete mathematical definition of the problem and an effective solution approach to solving the problem of industry scale.

Minimizing makespan for hybrid flowshops with batch, discrete processing machines and arbitrary job sizes

This research aims at a study of the hybrid flow shop problem which has parallel batch-processing machines in one stage and discrete-processing machines in other stages to process jobs of arbitrary sizes. The objective is to minimize the makespan for a set of jobs. The problem is denoted as: FF: batch1,sj:Cmax. The problem is formulated as a mixed-integer linear program. The commercial solver, AMPL/CPLEX, is used to solve problem instances to their optimality. Experimental results show that AMPL/CPLEX requires considerable time to find the optimal solution for even a small size problem, i.e., a 6-job instance requires 2 hours in average. A bottleneck-first-decomposition heuristic (BFD) is proposed in this study to overcome the computational (time) problem encountered while using the commercial solver. The proposed BFD heuristic is inspired by the shifting bottleneck heuristic. It decomposes the entire problem into three sub-problems, and schedules the sub-problems one by one. The proposed BFD heuristic consists of four major steps: formulating sub-problems, prioritizing sub-problems, solving sub-problems and re-scheduling. For solving the sub-problems, two heuristic algorithms are proposed; one for scheduling a hybrid flow shop with discrete processing machines, and the other for scheduling parallel batching machines (single stage). Both consider job arrival and delivery times. An experiment design is conducted to evaluate the effectiveness of the proposed BFD, which is further evaluated against a set of common heuristics including a randomized greedy heuristic and five dispatching rules. The results show that the proposed BFD heuristic outperforms all these algorithms. To evaluate the quality of the heuristic solution, a procedure is developed to calculate a lower bound of makespan for the problem under study. The lower bound obtained is tighter than other bounds developed for related problems in literature. A meta-search approach based on the Genetic Algorithm concept is developed to evaluate the significance of further improving the solution obtained from the proposed BFD heuristic. The experiment indicates that it reduces the makespan by 1.93 % in average within a negligible time when problem size is less than 50 jobs.

Solving satisfiability, *implication, and equivalence problems in database systems

Satisfiability, implication and equivalence problems are important and widely-encountered database problems that need to be efficiently and effectively solved. We provide a comprehensive and systematic study of these problems. We consider three popular types of arithmetic inequalities, (X op C), (X op Y), and (X op Y + C), where X and Y are attributes, C is a constant of the domain of X, and op $\in\ \{{<},\ {\le},\ {=},\ {\not=},\ {>},\ {\ge}\}.$ These inequalities are most frequently used in a database system, since the first type of inequalities represents $\theta$-join, the second type represents selection, and the third type is popular in deductive databases. We study the problems under the integer domain and the real domain, as well as under two different operator sets.^ Our results show that solutions under different domains and/or different operator sets are quite different. In this dissertation, we either report the first necessary and sufficient conditions as well as their efficient algorithms with complexity analysis, or provide improved algorithms. ^

Capacity planning methodology for concurrent engineer -to -order operations

This research focuses on developing a capacity planning methodology for the emerging concurrent engineer-to-order (ETO) operations. The primary focus is placed on the capacity planning at sales stage. This study examines the characteristics of capacity planning in a concurrent ETO operation environment, models the problem analytically, and proposes a practical capacity planning methodology for concurrent ETO operations in the industry. A computer program that mimics a concurrent ETO operation environment was written to validate the proposed methodology and test a set of rules that affect the performance of a concurrent ETO operation. ^ This study takes a systems engineering approach to the problem and employs systems engineering concepts and tools for the modeling and analysis of the problem, as well as for developing a practical solution to this problem. This study depicts a concurrent ETO environment in which capacity is planned. The capacity planning problem is modeled into a mixed integer program and then solved for smaller-sized applications to evaluate its validity and solution complexity. The objective is to select the best set of available jobs to maximize the profit, while having sufficient capacity to meet each due date expectation. ^ The nature of capacity planning for concurrent ETO operations is different from other operation modes. The search for an effective solution to this problem has been an emerging research field. This study characterizes the problem of capacity planning and proposes a solution approach to the problem. This mathematical model relates work requirements to capacity over the planning horizon. The methodology is proposed for solving industry-scale problems. Along with the capacity planning methodology, a set of heuristic rules was evaluated for improving concurrent ETO planning. ^

Branch and price solution approach for order acceptance and capacity planning in make -to -order operations

The increasing emphasis on mass customization, shortened product lifecycles, synchronized supply chains, when coupled with advances in information system, is driving most firms towards make-to-order (MTO) operations. Increasing global competition, lower profit margins, and higher customer expectations force the MTO firms to plan its capacity by managing the effective demand. The goal of this research was to maximize the operational profits of a make-to-order operation by selectively accepting incoming customer orders and simultaneously allocating capacity for them at the sales stage. ^ For integrating the two decisions, a Mixed-Integer Linear Program (MILP) was formulated which can aid an operations manager in an MTO environment to select a set of potential customer orders such that all the selected orders are fulfilled by their deadline. The proposed model combines order acceptance/rejection decision with detailed scheduling. Experiments with the formulation indicate that for larger problem sizes, the computational time required to determine an optimal solution is prohibitive. This formulation inherits a block diagonal structure, and can be decomposed into one or more sub-problems (i.e. one sub-problem for each customer order) and a master problem by applying Dantzig-Wolfe’s decomposition principles. To efficiently solve the original MILP, an exact Branch-and-Price algorithm was successfully developed. Various approximation algorithms were developed to further improve the runtime. Experiments conducted unequivocally show the efficiency of these algorithms compared to a commercial optimization solver.^ The existing literature addresses the static order acceptance problem for a single machine environment having regular capacity with an objective to maximize profits and a penalty for tardiness. This dissertation has solved the order acceptance and capacity planning problem for a job shop environment with multiple resources. Both regular and overtime resources is considered. ^ The Branch-and-Price algorithms developed in this dissertation are faster and can be incorporated in a decision support system which can be used on a daily basis to help make intelligent decisions in a MTO operation.^

On Optimizing Compatible Security Policies in Wireless Networks

This paper deals with finding the maximum number of security policies without conflicts. By doing so we can remove security loophole that causes security violation. We present the problem of maximum compatible security policy and its relationship to the problem of maximum acyclic subgraph, which is proved to be NP-hard. Then we present a polynomial-time approximation algorithm and show that our result has approximation ratio for any integer with complexity .

Optimization of waiting time at toll plazas

Toll plazas have several toll payment types such as manual, automatic coin machines, electronic and mixed lanes. In places with high traffic flow, the presence of toll plaza causes a lot of traffic congestion; this creates a bottleneck for the traffic flow, unless the correct mix of payment types is in operation. The objective of this research is to determine the optimal lane configuration for the mix of the methods of payment so that the waiting time in the queue at the toll plaza is minimized. A queuing model representing the toll plaza system and a nonlinear integer program have been developed to determine the optimal mix. The numerical results show that the waiting time can be decreased at the toll plaza by changing the lane configuration. For the case study developed an improvement in the waiting time as high as 96.37 percent was noticed during the morning peak hour.

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as "histogram binning" inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation.