Integer Programming Techniques Research Articles

Application of optimized multi-criteria decision-making in an environmental impact assessment study

In Multi-Criteria Decision-Making (MCDM) procedures like Analytical Hierarchy Process (AHP), the aggregate impact of a decision is expressed as a numerical score, with a higher score indicating aggregate positive impact of the decision on various impacted parameters or "impact-factors". In case the aggregate score is unsatisfactory, mitigation measures must be incorporated to lessen the adverse impact of the decision on one or more adversely impacted-factors, thus increasing the score. Incorporation of mitigation measures for each impact-factor is associated with a corresponding cost, which vary with the extent of mitigation proposed. Under the circumstances, questions regarding the extent of mitigation required for each impact-factor in order to obtain, (a) a target aggregate mitigation at minimum mitigation cost, or (b) the maximum aggregate mitigation for a fixed mitigation cost, may be asked. Algorithms incorporating integer-programming techniques have been presented in this paper for the above purpose. These algorithms have been implemented and tested using a typical Environmental Impact Assessment (EIA) problem.

The Role of Integer Programming Techniques in Constraint Programming's Global Constraints

Efforts aimed at combining operations research and constraint programming have become increasingly prominent and successful in the last few years. It is now widely recognized that integration, e.g., inference in the form of constraint propagation and relaxation in the form of linear programming, can yield substantial results. In this paper, we argue the benefits of constraint programming's global constraints as a basis for such an integration and discuss the advantages along with some examples. We illustrate the integration on the global cardinality structure, on piecewise linear functions, on variable subscripts, on the cycle structure and on resource constraints. Each example is completed with a case study.

Knowledge Integration to Overcome Ontological Heterogeneity: Challenges from Financial Information Systems

The shift towards global networking brings with it many opportunities and challenges. In this paper, we discuss key technologies in achieving global semantic interoperability among heterogeneous information systems, including both traditional and web data sources. In particular, we focus on the importance of this capability and technologies we have designed to overcome ontological heterogeneity, a common type of disparity in financial information systems. Our approach to representing and reasoning with ontological heterogeneities in data sources is an extension of the Context Interchange (COIN) framework, a mediator-based approach for achieving semantic interoperability among heterogeneous sources and receivers. We also analyze the issue of ontological heterogeneity in the context of source-selection, and offer a declarative solution that combines symbolic solvers and mixed integer programming techniques in a constraint logic-programming framework. Finally, we discuss how these techniques can be coupled with emerging Semantic Web related technologies and standards such as Web-Services, DAML+OIL, and RuleML, to offer scalable solutions for global semantic interoperability. We believe that the synergy of database integration and Semantic Web research can make significant contributions to the financial knowledge integration problem, which has implications in financial services, and many other e-business tasks.

LINEAR AND INTEGER PROGRAMMING TECHNIQUES FOR COOPERATIVE GAMES

Let Γ = (N, v) be a cooperative game with the player set N and value function v : 2N → R. A solution of the game is in the core if no subset of players could gain advantage by breaking away from the grand coalition of all players. This paper surveys theoretical results on the cores for some cooperative game models. These results proved that the linear program duality characterization of the core is a very powerful tool. We will focus on linear and integer programming techniques applied in this area.

Long Term Production Scheduling Optimisation for a Surface Mining Operation: An Application of MineMax™ Scheduling Software

Since long term production scheduling deals with movement of ore and waste during the life of a mine, it has a significant effect on the cash flow of a mining operation. Therefore, mine planners often seek to optimise the production schedule with respect to a given criterion. The most commonly used criterion in long term scheduling optimisation is to maximise net present value (NPV). The process involves sequencing of ore blocks or parcels to be mined in each period over the life of the mine subject to precedence and other physical constraints imposed by the mining system. The complexity of mine production scheduling in practice entails a computer solution using mathematical programming as the optimisation technique. Linear and mixed integer programming techniques have been used to optimise long term production schedules but most of the computer programs based on these make overly simplifying assumptions and lack the flexibility to handle practical considerations of mine scheduling. MineMax™ scheduling software is applied to long term scheduling for a multielement surface mining operation. MineMax uses mixed integer programming with the branch and bound algorithm as solution strategy. The system allows the planner to generate a mine production schedule in the same manner as manual scheduling, but making use of the interactivity in planning data input, in-built optimisation algorithm and the speed of the personal computer. This study involves investigation into the effects of reblocking and grade intervals on the mining schedule, specifically, the material movement, milling grade and the cash flow over the life of the mine.

Frequency planning and ramifications of coloring

This paper surveys frequency assignment problems coming up in planning wireless communication services. It particularly focuses on cellular mobile phone systems such as GSM, a technology that revolutionizes communication. Traditional vertex coloring provides a conceptual framework for the mathematical modeling of many frequency planning problems. This basic form, however, needs various extensions to cover technical and organizational side constraints. Among these ramifications are $T$-coloring and list coloring. To model all the subtleties, the techniques of integer programming have proven to be very useful. The ability to produce good frequency plans in practice is essential for the quality of mobile phone networks. The present algorithmic solution methods employ variants of some of the traditional coloring heuristics as well as more sophisticated machinery from mathematical programming. This paper will also address this issue. Finally, this paper discusses several practical frequency assignment problems in detail, states the associated mathematical models, and also points to public electronic libraries of frequency assignment problems from practice. The associated graphs have up to several thousand nodes and range from rather sparse to almost complete.

Operating room managers' use of integer programming for assigning block time to surgical groups: a case study.

A common problem at hospitals with fixed amounts of available operating room (OR) time (i.e., "block time") is determining an equitable method of distributing time to surgical groups. Typically, facilities determine a surgical group's share of available block time using formulas based on OR utilization, contribution margin, or some other performance metric. Once each group's share of time has been calculated, a method must be found for fitting each group's allocated OR time into the surgical master schedule. This involves assigning specific ORs on specific days of the week to specific surgical groups, usually with the objective of ensuring that the time assigned to each group is close to its target share. Unfortunately, the target allocated to a group is rarely expressible as a multiple of whole blocks. In this paper, we describe a hospital's experience using the mathematical technique of integer programming to solve the problem of developing a consistent schedule that minimizes the shortfall between each group's target and actual assignment of OR time. Schedule accuracy, the sum over all surgical groups of shortfalls divided by the total time available on the schedule, was 99.7% (SD 0.1%, n = 11). Simulations show the algorithm's accuracy can exceed 97% with > or =4 ORs. The method is a systematic and successful way to assign OR blocks to surgeons. At hospitals with a fixed budget of operating room (OR) time, integer programming can be used by OR managers to decide which surgical group is to be allocated which OR on which day(s) of the week. In this case study, we describe the successful application of integer programming to this task, and discuss the applicability of the results to other hospitals.

A fractional model for locating semi-desirable facilities on networks

In this paper, we address the problem of locating a series of facilities on a network maximizing the average distance to population centers (assumed to be distributed in the plane) per unit transportation cost (a function of the network distances to users). A finite dominating set is constructed, allowing the resolution of the problem by standard integer programming techniques. We also discuss some extensions of the model (including, in particular, the Weber problem with attraction and repulsion in networks), for which ( ε-) dominating sets are derived.

Optimising Life of Mine Production Schedules in Multiple Open Pit Mining Operations A Study of Effects of Production Constraints on NPV

Life of mine scheduling involves sequencing and timing of ore and waste movement during the life of a mine and therefore, has a significant effect on the cash flow of a mining operation. Mine planners often seek to optimise the production schedule with respect to maximise net present value (NPV) of the cash flows. The complexity of mine production scheduling in practice entails a computer solution using mathematical programming as the optimisation technique. Linear and mixed integer programming techniques have been used to optimise long-term production schedules but most of the computer programs based on these make overly simplifying assumptions and lack the flexibility to handle practical considerations of mine scheduling. MineMax™ scheduling software is applied to long term scheduling for a multiple open pit operation. The effects of constraining production and the number of pits on the NPV are analysed. The greater selectivity allowed by unconstrained mine production is offset by increased operational costs resulting in insignificant changes to the NPV. Constraining the number of active pits per period limits the mine planner's ability to find ore of a specified blend. Although it is desirable to produce at constant rate and to limit the number of active pits per period, this strategy places limitations on the grade of ore that can be mined and milled, hence having a detrimental effect on the NPV. This study shows that allowing both the production and number active pits to fluctuate within practical limits improves the NPV of the project.

Optimisation techniques for electrical power systems. Part 1: Mathematical optimisation methods

This is the first tutorial of a three-part series. The series discusses modern optimisation techniques applicable to power system problems and, by considering relevant examples, will explain some of the concepts, issues and terminology in this field. This first part gives an introduction to mathematical programming based methods including linear programming, quadratic programming, nonlinear programming, integer programming, mixed-integer programming, dynamic programming, and Lagrangian decomposition techniques. Practical issues of applying these methods to power systems are discussed.

Reducing redundancy in characteristic rule discovery by using integer programming techniques

The discovery of characteristic rules is a well-known data mining task and has lead to several successful applications. However, because of the descriptive nature of characteristic rules, typically a (very) large number of them is discovered during the mining stage. This makes monitoring and control of these rules, in practice, extremely costly and difficult. Therefore, a selection of the most promising subset of rules is desirable. Some heuristic rule selection methods have been proposed in the literature that deal with this issue. In this paper, we propose an integer programming model to solve the problem of optimally selecting the most promising subset of characteristic rules. Moreover, the proposed technique enables to control a user-defined level of overall quality of the model in combination with a maximum reduction of the redundancy extant in the original ruleset. We use real-world data to empirically evaluate the benefits and performance of the proposed technique against the well-known RuleCover heuristic. Results demonstrate that the proposed integer programming techniques are able to significantly reduce the number of retained rules and the level of redundancy in the final ruleset. Moreover, the results demonstrate that the overall quality in terms of the discriminant power of the final ruleset slightly increases if integer programming methods are used.

Treatment planning for prostate implants using magnetic-resonance spectroscopy imaging

Purpose: Recent studies have demonstrated that magnetic-resonance spectroscopic imaging (MRSI) of the prostate may effectively distinguish between regions of cancer and normal prostatic epithelium. This diagnostic imaging tool takes advantage of the increased choline plus creatine versus citrate ratio found in malignant compared to normal prostate tissue. The purpose of this study is to describe a novel brachytherapy treatment-planning optimization module using an integer programming technique that will utilize biologic-based optimization. A method is described that registers MRSI to intraoperative-obtained ultrasound images and incorporates this information into a treatment-planning system to achieve dose escalation to intraprostatic tumor deposits. Methods: MRSI was obtained for a patient with Gleason 7 clinically localized prostate cancer. The ratios of choline plus creatine to citrate for the prostate were analyzed, and regions of high risk for malignant cells were identified. The ratios representing peaks on the MR spectrum were calculated on a spatial grid covering the prostate tissue. A procedure for mapping points of interest from the MRSI to the ultrasound images is described. An integer-programming technique is described as an optimization module to determine optimal seed distribution for permanent interstitial implantation. MRSI data are incorporated into the treatment-planning system to test the feasibility of dose escalation to positive voxels with relative sparing of surrounding normal tissues. The resultant tumor control probability (TCP) is estimated and compared to TCP for standard brachytherapy-planned implantation. Results: The proposed brachytherapy treatment-planning system is able to achieve a minimum dose of 120% of the 144 Gy prescription to the MRS positive voxels using 125I seeds. The preset dose bounds of 100–150% to the prostate and 100–120% to the urethra were maintained. When compared to a standard plan without MRS-guided optimization, the estimated TCP for the MRS-optimized plan is superior. The enhanced TCP was more pronounced for smaller volumes of intraprostatic tumor deposits compared to estimated TCP values for larger lesions. Conclusions: Using this brachytherapy-optimization system, we could demonstrate the feasibility of MRS-optimized dose distributions for 125I permanent prostate implants. Based on probability estimates of anticipated improved TCP, this approach may have an impact on the ability to safely escalate dose and potentially improve outcome for patients with organ-confined but aggressive prostatic cancers. The magnitude of the TCP enhancement, and therefore the risks of ignoring the MR data, appear to be more substantial when the tumor is well localized; however, the gain achievable in TCP may depend quite considerably on the MRS tumor-detection efficiency.

Applying integer programming to AI planning

Despite the historical difference in focus between AI planning techniques and Integer Programming (IP) techniques, recent research has shown that IP techniques show significant promise in their ability to solve AI planning problems. This paper provides approaches to encode AI planning problems as IP problems, describes some of the more significant issues that arise in using IP for AI planning, and discusses promising directions for future research.

Buffer assignment algorithms on data driven ASICs

Data driven architectures have significant potential in the design of high performance ASICs. By exploiting the inherent parallelism in the application, these architectures can maximize pipelining. The key consideration involved with the design of a data driven ASIC is ensuring that throughput is maximized while a relatively low area is maintained. Optimal throughput can be realized by ensuring that all operands arrive simultaneously at their corresponding operator node. If this condition is achieved, the underlying data flow graph is said to be balanced. If the initial data flow graph is unbalanced, buffers must be inserted to prevent the clogging of the pipeline along the shorter paths. A novel algorithm for the assignment of buffers in a data flow graph is proposed. The method can also be applied to achieve wave-pipelining in digital systems under certain restrictions. The algorithm uses a new application of the retiming technique; the number of buffers here is shown to be equal to the minimum number of buffers achieved by integer programming techniques. We also discuss an extension of this algorithm which can further reduce the number of buffers by altering the DFG without affecting functionality or performance. The time complexities of the proposed algorithms are O(V/spl times/E) and O(V/sup 2//spl times/logV), respectively, a considerable improvement over the existing strategies. Also proposed is a novel buffer distribution algorithm that exploits a unique feature of data driven operation. This procedure maximizes throughput by inserting substantially fewer buffers than other techniques. Experimental results show that the proposed algorithms outperform the existing methods.

Workshop scheduling using practical (inaccurate) data Part 3: A framework to integrate job releasing, routing and scheduling functions to create a robust predictive schedule

A comprehensive simulation study conducted by the authors investigated the robustness of a predictive scheduling system in a dynamic and stochastic environment. The results revealed that to improve the robustness of a scheduling system, besides using a robust scheduling method with a frequent rescheduling policy, the shop load should be well controlled and kept balanced. Integrating the planning and the scheduling functions has been shown to achieve this objective. This paper discusses the effects of the planning i.e. job releasing and routing and the scheduling functions in creating a robust schedule and a framework to integrate the above functions is proposed. This system consists of a planning module that is concerned with job releasing and routing decisions and a scheduling module that provides the detailed scheduling. A mathematical model using the integer programming technique is use to demonstrate a solution for the planning module. In addition, a heuristic algorithm is used to solve the scheduling problem. It is shown that, in terms of shop load balance level and job delivery time, the proposed system performs better than a benchmark loading strategy on the basis of minimum processing cost.

A novel traffic signal control formulation

A novel traffic signal control formulation is developed through a mixed integer programming technique. The formulation considers dynamic traffic, uses dynamic traffic demand as input, and takes advantage of a convergent numerical approximation to the hydrodynamic model of traffic flow. As inherent from the underlying hydrodynamic model, this formulation covers the whole range of the fundamental relationships between speed, flow, and density. Kinematic waves of the stop-and-go traffic associated with traffic signals are also captured. Because of this property, one does not need to tune or switch the model for the different traffic conditions. It “automatically” adjusts to the different traffic conditions. We applied the model to three demand scenarios in a simple network. The results seemed promising. This model produced timing plans that are consistent with models that work for unsaturated conditions. In gridlock conditions, it produced a timing plan that was better than conventional queue management practices.

Optimization of Scheduling of Cleaning in Heat Exchanger Networks Subject to Fouling: Sugar Industry Case Study

Fouling of heat exchangers in the food industry results in frequent cleaning and an operational problem in scheduling production and cleaning periods. The complexity of the problem increases when a network involving more than one exchanger is involved, and requires a solution using integer programming techniques. A new modelling formulation has been developed to solve the resulting MINLP problem and provides near-optimal results. Application of the technique is illustrated with a case study of the raw juice preheat train in a sugar refinery featuring a network of 11 exchangers. Data reconciliation of plant information was used to generate linear fouling models for the simulation and the solver results are compared with current operating practice.

Dependent-chance integer programming applied to capital budgeting

This paper attempts to model capital budgeting problems by a new technique of dependent-chance integer programming as well as dependent-chance multiobjective programming and goal programming. Some examples are provided to illustrate the potential applications in the area of capital budgeting. A stochastic simulation based genetic algorithm is also designed to solve both chance constrained integer programming and dependent-chance integer programming models.

Plant-wide optimal waste management

Synthesis of optimal waste treatment policies on a plant wide level is a formidable challenge due to (i) the knowledge necessary to do selection of treatment steps and (ii) the combinatorial complexity of the resulting problem space. This paper presents a hybrid methodology for an automatic synthesis of feasible alternatives, the superstructure generation, followed by rigorous combinatorial optimization. In step one, evaluation of waste properties against regulatory limits as well as a relaxed set of technology selection criteria gives rise to a tree of feasible treatment options. In step two, rigorous integer programming techniques expose optimal waste management policies with best trade-off between different levels of environmental, ecological and logistic constraints. Results of the application of the methodology onto a case study from the pharmaceutical industry are discussed. These figures demonstrate clearly the huge degree of flexibility that can be obtained by systematic waste management using computerized methods.

OPTIMIZATION OF A WOOD DRYER KILN USING THE MIXED INTEGER PROGRAMMING TECHNIQUE: A CASE STUDY

When wood is to be utilized as a raw material for furniture, buildings etc., it must be dried from approximately 100% to 6% moisture content. This is achieved at least partly in a drying kiln. Heat for this purpose is provided by electrical means, or by steam from boilers fired with wood chips or oil. By making a close examination of monitored values from an actual drying kiln it has been possible to optimize the use of steam and electricity using the so called mixed integer programming technique Owing to the operating schedule for the drying kiln it has been necessary to divide the drying process in very short lime intervals i.e., a number of minutes. Since a drying cycle takes about two or three weeks, a considerable mathematical problem is presented and this has to be solved.