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Presented is an integer-programming approach to item pool design that can be used to calculate an optimal blueprint for an item pool to support an existing testing program. The results are optimal in the sense that they minimize the efforts involved in actually producing the items as revealed by current item writing patterns. Also presented is an adaptation of the models for use as a set of monitoring tools in item pool management. The approach is demonstrated empirically for an item pool designed for the Law School Admission Test. (Contains 2 tables and 30 references.) (Author/SLD)

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen and Azizo\u{g}lu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen and Azizo\u{g}lu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.

The Army is reducing and reshaping its force structure to adapt to the nation's changing defense needs and budget constraints. In response to these changes, Army Materiel Command (AMC) will submit facility realignment and closure recommendations in FY93 and FY95. This thesis develops a bi-criteria mixed integer programming model with the objectives of minimizing operating costs and maximizing a measure of military value to assist AMC in the generation of alternative realignments. Realignment of depot maintenance, research and development, test and evaluation, and administrative function are considered on 32 AMC installations. An extensive empirical study demonstrates the applicability of the developed approach.

The Army is reducing and reshaping its force structure to adapt to the nation's changing defense needs and budget constraints. In response to these changes, Army Materiel Command (AMC) will submit facility realignment and closure recommendations in FY93 and FY95. This thesis develops a bi-criteria mixed integer programming model with the objectives of minimizing operating costs and maximizing a measure of military value to assist AMC in the generation of alternative realignments. Realignment of depot maintenance, research and development, test and evaluation, and administrative function are considered on 32 AMC installations. An extensive empirical study demonstrates the applicability of the developed approach.

Bibliography: pt. 1, p. 46-47; pt. 2, p. 48

Bibliography: p. 41-42

This article is from PLoS ONE , volume 9 . Abstract In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at “http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html.”

Igor Ferst https://www.pyohio.org/2019/presentations/86 How do airlines choose which planes service which routes? How does a hospital optimize the shift schedule for hundreds of doctors and nurses? How do you choose the optimal location for a group of fulfillment centers, or oil derricks, or cell towers? These kinds of problems (and many others!) can be solved with integer linear programming (ILP), a powerful and decades-old framework for solving optimization problems. In this talk we will give a brief introduction to ILP and describe it's uses, strengths, and weaknesses. We will also show how to solve a real-world vehicle routing problem using Google's open-source python library for ILP. Trigger warning: this talk will contain high-school level math. Integer linear programming (ILP) is a powerful framework for solving optimization problems related to scheduling, resource allocation, vehicle routing, and many other areas. This talk will give a brief introduction to ILP and show how to solve a real-world vehicle routing problem using Google's open-source python library for ILP. === https://pyohio.org A FREE annual conference for anyone interested in Python in and around Ohio, the entire Midwest, maybe even the whole world. Produced by NDV: https://youtube.com/channel/UCQ7dFBzZGlBvtU2hCecsBBg?sub_confirmation=1 Sun Jul 28 14:30:00 2019 at Hays Cape

Bibliography: l. 19-20

This is an introductory survey of integer programming, its theory, methodology and applications, for the Encyclopedia of Statistical Sciences. (Author)

This report gives documentation for the computer code HEUR for finding good approximate solutions to integer linear programming problems using Hillier's heuristic procedure. A listing of the program with sample input and output is included. (Author)

Special Operations Forces (SOF) are frequently employed to conduct missions not within the limited boundaries of unilateral special operations. These operations often involve cooperation with general purpose forces (GPF) and are often under their command. This thesis argues that these cooperative efforts are better examined as integrated operations rather than special or conventional operations. These operations require SOF to conduct specialized tasks facilitating the introduction of follow-on GPF to complete the mission. This thesis develops a theory of integrated operations by examining six operations, previously considered under conventional wisdom as either special or conventional. It rejects much of the myth which surrounds these operations and offers a revisionist interpretation of the necessary and sufficient conditions for success in these endeavors. The thesis then goes on to compare cases of these special units using organizational theory to determine the sources of integration. The cases examined indicate a causal relationship between organizational factors related to command and training and a special units ability to integrate with GPF. The thesis concludes by recommending the realignment of select SOF in the current force structure to better meet the challenges of future integrated operations.

Special Operations Forces (SOF) are frequently employed to conduct missions not within the limited boundaries of unilateral special operations. These operations often involve cooperation with general purpose forces (GPF) and are often under their command. This thesis argues that these cooperative efforts are better examined as integrated operations rather than special or conventional operations. These operations require SOF to conduct specialized tasks facilitating the introduction of follow-on GPF to complete the mission. This thesis develops a theory of integrated operations by examining six operations, previously considered under conventional wisdom as either special or conventional. It rejects much of the myth which surrounds these operations and offers a revisionist interpretation of the necessary and sufficient conditions for success in these endeavors. The thesis then goes on to compare cases of these special units using organizational theory to determine the sources of integration. The cases examined indicate a causal relationship between organizational factors related to command and training and a special units ability to integrate with GPF. The thesis concludes by recommending the realignment of select SOF in the current force structure to better meet the challenges of future integrated operations.

We give an exact algorithm for the 0-1 Integer Linear Programming problem with a linear number of constraints that improves over exhaustive search by an exponential factor. Specifically, our algorithm runs in time $2^{(1-\text{poly}(1/c))n}$ where n is the number of variables and cn is the number of constraints. The key idea for the algorithm is a reduction to the Vector Domination problem and a new algorithm for that subproblem.

Bibliography: pt. 1, p. 46-47; pt. 2, p. 48

This paper discussed the merit of mixed-integer linear programming (MILP)- based approach against Lagrangian relaxation (LR)-based approach in solving generation and transmission maintenance scheduling problem. MILP provides a straightforward solution by formulating coupling constraints equations so that these sub-problems can be solved simultaneously without involving multipliers. In LR-based approach, generation and transmission maintenance scheduling, and security-constrained unit commitment have been solved individually and the integration was realized through a series of multipliers which has caused computational burden to the system. Numerical case studies were evaluated on the 6-bus system. A comparative study is carried out between the MILP and LR approaches. Simulation results indicate that the maintenance schedule derived by the proposed MILP approach outperforms the LR in terms of operational cost savings and gap tolerance. The operating cost could be saved up to 5% and the gap tolerance achieved is 0.01% as compared to 0.14% by LR.

An algorithm for the solution of integer linear programming problems is presented and programmed in Fortran IV for use off digital computers. The program incorporates an optional feature which provides all existing alternative optimal solutions. Solutions, computation times, and iteration requirements for each of thirteen test problems are summarized and discussed.

We present a new combinatorial market maker that operates arbitrage-free combinatorial prediction markets specified by integer programs. Although the problem of arbitrage-free pricing, while maintaining a bound on the subsidy provided by the market maker, is #P-hard in the worst case, we posit that the typical case might be amenable to modern integer programming (IP) solvers. At the crux of our method is the Frank-Wolfe (conditional gradient) algorithm which is used to implement a Bregman projection aligned with the market maker's cost function, using an IP solver as an oracle. We demonstrate the tractability and improved accuracy of our approach on real-world prediction market data from combinatorial bets placed on the 2010 NCAA Men's Division I Basketball Tournament, where the outcome space is of size 2^63. To our knowledge, this is the first implementation and empirical evaluation of an arbitrage-free combinatorial prediction market on this scale.

We study the combinatorial FIFO Stack-Up problem, where bins have to be stacked-up from conveyor belts onto pallets. Given k sequences of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. The FIFO Stack-Up problem asks whether there is some processing of the sequences of bins such that at most p stack-up places are used. In this paper we strengthen the hardness of the FIFO Stack-Up by considering practical cases and the distribution of the pallets onto the sequences. We introduce a digraph model for this problem, the so called decision graph, which allows us to give a breadth first search solution. Further we apply methods to solve hard problems to the FIFO Stack-Up problem. In order to evaluate our algorithms, we introduce a method to generate random, but realistic instances for the FIFO Stack-Up problem. Our experimental study of running times shows that the breadth first search solution on the decision graph combined with a cutting technique can be used to solve practical instances on several thousands of bins of the FIFO Stack-Up problem. Further we analyze two integer programming approaches implemented in CPLEX and GLPK. As expected CPLEX can solve the instances much faster than GLPK and our pallet solution approach is much better than the bin solution approach.

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.

Bibliography: leaves 30-31

A parametric integer linear program (PILP) may be defined as a family of closely related integer linear programs (ILP). Within this definition the author incorporates not only continuous scalar parameterizations but also finite parameterizations. These may include an ILP with a finite number of objective functions or right hand sides or constraint matrices or any combination of these. A general framework for PILP is presented. It begins by outlining the need for PILP algorithms. Basic solution methodologies are explained and two rudimentary approaches for the PILP are stated. Theoretical properties for special parameterizations are proved, and techniques for improving algorithmic efficiency are discussed. The framework concludes with an examination of underlying factors which intimately relate to the scheduling of solution priorities in a PILP algorithm.

The focus of this project is new computational tools for mixed-integer programming (MIP). During the course of this project we have studied and obtained results on the following topics. 1. Dual heuristics for integer programs in order to rapidly improve dual bounds. 2. Choosing good branching variables in branch-and-bound algorithms for MIP. 3. Machine Learning in solving MIPs.4. Parallel Processing in Solving MIPS. The new algorithms are computational tested and, in many cases, outperform existing algorithms. This research has been presented at several conferences and has and will appear in archival journals.

We show that in a knapsack feasibility problem an integral vector $p$, which is short, and near parallel to the constraint vector gives a branching direction with small integer width. We use this result to analyze two computationally efficient reformulation techniques on low density knapsack problems. Both reformulations have a constraint matrix with columns reduced in the sense of Lenstra, Lenstra, and Lov\'asz. We prove an upper bound on the integer width along the last variable, which becomes 1, when the density is sufficiently small. In the proof we extract from the transformation matrices a vector which is near parallel to the constraint vector $a.$ The near parallel vector is a good branching direction in the original knapsack problem, and this transfers to the last variable in the reformulations.

We accomplished our objectives, successfully implementing the Neighborhood Covering Heuristic (NCH) for solving the mixed integer programming problems. NCH is a unique, proprietary approach with several ground-breaking advantages. We completed a series of comparisons between NCH and the standard Branch and Bound (BAB) approach. Using the tunable parameters available within NCH, we created ten variants. We randomly generated sets of MIP problems, where the numbers of integer and binary variables, and constraints were varied in a systematic way. Then we applied both BAB and our ten variants of NCH to each of the generated problems. We obtained several significant results. First, when other parameters are fixed, the number of integer and binary variables in a random MIP problem does not have an exponential impact on the time required to find a feasible solution using NCH. Second, the performance data show that NCH produces feasible solutions significantly faster than BAB. Moreover the variance in time to produce a feasible solution is smaller in NCH. This reduction in variance and the resulting greater predictability of time to first solution will be extremely attractive to logistic companies, consultants, and useful directly in the Navy COMPASS program specifically and for Navy optimization needs in general.

Radiotherapy represents an important phase of treatment for a large number of cancer patients. It is essential that resources used to deliver this treatment are employed effectively. This paper presents a new integer linear programming model for real-world radiotherapy treatment scheduling and analyses the effectiveness of using this model on a daily basis in a hospital. Experiments are conducted varying the days on which schedules can be created. Results obtained using real-world data from the Nottingham University Hospitals NHS Trust, UK, are presented and show how the proposed model can be used with different policies in order to achieve good quality schedules.

This paper presents algorithms for solving multiobjective integer programming problems. The algorithm uses Barvinok's rational functions of the polytope that defines the feasible region and provides as output the entire set of nondominated solutions for the problem. Theoretical complexity results on the algorithm are provided in the paper. Specifically, we prove that encoding the entire set of nondominated solutions of the problem is polynomially doable, when the dimension of the decision space is fixed. In addition, we provide polynomial delay algorithms for enumerating this set. An implementation of the algorithm shows that it is useful for solving multiobjective integer linear programs.

This paper presents an efficient algorithm for solving a class of quadratic integer programming problems. These problems include discrete versions of the quadratic placement problem and the squared Euclidean distance problem. The algorithm solves a finite sequence of minimum cut problems, or equivalently maximum flow problems, on a graph with n + 2 vertices where n is the number of variables in the problem. (Author)

This paper presents an efficient algorithm for solving a class of quadratic integer programming problems. These problems include discrete versions of the quadratic placement problem and the squared Euclidean distance problem. The algorithm solves a finite sequence of minimum cut problems, or equivalently maximum flow problems, on a graph with n + 2 vertices where n is the number of variables in the problem. (Author)

Contents: Resource Decomposition: A Conceptual Outline; Branching in the Rudimentary Branch-and-Bound Algorithm; Computing Bounds: Single Linking Constraint Case; Computing Bounds: Multiple Linking Constraints Case; Computational Results; and Conclusions, Extensions, and Areas for Future Research.

A nonlinear integer programming model for expanding the transportation system of an underdeveloped country is presented. The model uses integer 0-1 decision variables. The basic model has linear constraints and a nonlinear objective function. Some special situations and extensions to the model are presented. The benefits being maximized in the objective function are discussed, as are the problems of parameterization and suboptimization. A solution procedure for the model is suggested, but an efficient algorithm is not available for solving the model. Some areas for future research are also suggested.

The report presents a synthesis of the Balasian implicit enumeration approach to integer linear programming with the approach typified by Land and Doig and by Roy, Bertier, and Nghiem. This synthesis results from the use of an imbedded linear program to compute surrogate constraints that are as 'strong' as possible in a sense slightly different from that originally used by Glover. A very simple implicit enumeration algorithm fitted with optional imbedded linear programming machinery was implemented and tested extensively on an IBM 7044 computer. Use of the imbedded linear program dramatically reduced solution time in virtually every case and sufficied to render the tested algorithm superior to the other five implicit enumeration algorithms for which comparable published experience was available. Existing evidence suggests that the present approach should permit the routine solution of practical integer problems involving hundreds of variables.

The Marine Corps has long been successful in assigning its available personnel to vacant billets. However, by our research, the Marine Corps has not been as successful in minimizing assignment costs when moving a Marine to another permanent duty station. With increased pressure on cost savings due to shrinking budgets, the importance of cost minimizing efforts is becoming more significant. This thesis examines the Marine Corps personnel assignment process and proposes a methodology for optimizing the allocation of Marine Corps personnel that minimizes assignment costs while taking into account constraints such as military occupational specialty, billet vacancies, duty station preference, and seniority. Optimization is achieved by incorporating an integer programming model into the personnel assignment process. The model is tested by contrasting the results of the actual assignments of a 15-Marine sample with the results of simulated optimization assignments of the same sample. The findings of this thesis show that the proposed methodology is both valid and feasible, and that it could yield significant monetary savings for the Marine Corps.

A scenario where multiple air vehicles are required to prosecute geographically dispersed targets is considered. Furthermore, multiple tasks are to be successively performed on each target, i.e. the targets must be classified, attacked, and verified as destroyed. The optimal, e.g. minimum time, performance of these tasks requires cooperation amongst the vehicles such that critical timing constraints are satisfied, that is, a target must be classified before it can be attacked, and an air vehicle is sent to a target area to verify its destruction only after the target has been attacked. In this paper, the optimal task assignment/scheduling problem is posed as a mixed integer linear program (MILP). The solution of the MILP assigns all tasks to the vehicles and performs the scheduling in an optimal manner, including staged departure times. Coupled tasks involving timing and task order constraints are automatically addressed. When the air vehicles have sufficient endurance. the existence of a solution is guaranteed.

Three algorithms are developed that may be based exclusively on hyperspherically deduced cuts. The algorithms only apply, therefore, to problems structured so that these cuts are valid. The algorithms are shown to be finite.

Lecture from a Business Mathematics course (2005 - 6) by KIT

This dissertation considers optimization problems in which similar decisions need to be made repeatedly over many successive periods. These problems have wide applications including manpower planning, scheduling, production planning and control, capacity expansion, and equipment replacement/modemization. In reality these decision problems usually extend over an indeterminate horizon, but it is common practice to model them using a finite horizon. Unfortunately, an artificial finite horizon may adversely influence optimal decisions, a difficulty commonly referred to as the end effects problem. Past research into end effects has focused on theoretical issues associated with solving (or approximately solving) infinite-horizon extensions of finite-horizon problems. This dissertation derives equivalent finite-horizon formulations for a small class of infinite-horizon problem structures. For a larger class of problems, it also develops finite-horizon approximations which bound the infinite- horizon optimal solution, thereby quantifying the influence of end effects. For linear programs, extensions of these approximations quantify the end effects of fixed initial period decisions over a functional range of future infinite-horizon conditions.

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In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.

Relay Observation Scheduling of Global Distributed Telescope Array Based on Integer Programming 后印本 作者： Junhan Ju, Ce Yu, Yi Hu, Yajie Zhang, Chao Sun and Jizeng Wei 1 作者单位： 1. Junhan Ju, Ce Yu, Yi Hu, Yajie Zhang, Chao Sun and Jizeng Wei 提交时间： 2025-02-25 10:58:35 摘要: Certain transients require regular observations over several days at intervals of hours or shorter, which cannot be accomplished by telescopes at a single site. The deployment of globally distributed telescopes at geographic locations of different longitudes enables the periodic monitoring of transients through relay observation. However, the simultaneous relay observation of numerous targets requires a telescope array of multiple telescopes that can be efficiently coordinated, and an automated scheduler for the array. This paper proposes IPROS, an integer programming model relay observation scheduler for a telescope array, that accounts for the entire process of relay observation and is consistent with the practical scenarios. We introduce the integer programming mathematical model for the relay observation scheduling problem with the telescope array, upon which the scheduler is based. Additionally, we propose an algorithm to provide a comprehensive formulation of the optimization objective of minimizing cadence deviation in the model. Experimental results demonstrate that the relay observation scheduler based on the integer programming model can effectively address the telescope array relay observation problem. It shows superiority over a scheduler with non-specific consideration of relay observation in the modeling and a scheduler based on greedy thought. 分类： 天文学 >> 天文学 期刊： Research in Astronomy and Astrophysics 投稿状态： 已在期刊出版 引用： ChinaXiv:202502.00295 (或此版本 ChinaXiv:202502.00295V1 ) DOI:https://doi.org/10.1088/1674-4527/ad9429 CSTR:32003.36.ChinaXiv.202502.00295 推荐引用方式： Junhan Ju, Ce Yu, Yi Hu, Yajie Zhang, Chao Sun and Jizeng Wei.Relay Observation Scheduling of Global Distributed Telescope Array Based on Integer Programming.Research in Astronomy and Astrophysics:https://chinaxiv.org/abs/202502.00295.[ChinaXiv:202502.00295V1] 版本历史 [V1] 2025-02-25 10:58:35 ChinaXiv:202502.00295V1 下载全文

IMPROVEMENT IN THE EXISTING AREA OF INTEGER PROGRAMMING CODES IN THE EASY GENERATION OF EFFICIENT CUTTING HYPERPLANES IS STUDIED. In this analysis the problem is approached by using a triangular canonical form. In part 1 an algorithm is given based on Gomory's all-integer integer programming algorithm, which constitutes a first step in this direction. This procedure is a practical analog of a deepest cut method discussed in the second part of the analysis. A brief outline and flow diagram for the algorithm are given; finally the algorithm and the deepest cut problem are illustrated by examples.

The study was concerned with the essential question of how to address multiperiod inventory problems characterized by not unrealistic conditions for which modeling and solution procedures have not been developed. The research placed special emphasis on the application of deterministic mixed-integer programming models to multiperiod inventory problems characterized by changing costs and beta-distributed demands. The special concern for the mixed-integer programming model was prompted by the realization that, among all of the easy- to-use deterministic inventory models, the mixed-integer programming formulation is the only model that is amenable to the additional constraints and multiple- objective criteria that coincide with broadly conceived statements of inventory control. Through the combined usage of mixed-integer programming and computer simulation techniques, a method was developed whereby a first-period reorder policy that minimizes expected total inventory cost over a multiperiod planning horizon can be identified with a nominal investment in computer processing time. The analysis led to the conclusion that first-period policies obtained by using the mixed-integer programming model with expectations as periodic demand inputs are generally adequate under the conditions specified in the research and compare favorably with policies obtained from commonly used inventory models. (Author)

The study was concerned with the essential question of how to address multiperiod inventory problems characterized by not unrealistic conditions for which modeling and solution procedures have not been developed. The research placed special emphasis on the application of deterministic mixed-integer programming models to multiperiod inventory problems characterized by changing costs and beta-distributed demands. The special concern for the mixed-integer programming model was prompted by the realization that, among all of the easy- to-use deterministic inventory models, the mixed-integer programming formulation is the only model that is amenable to the additional constraints and multiple- objective criteria that coincide with broadly conceived statements of inventory control. Through the combined usage of mixed-integer programming and computer simulation techniques, a method was developed whereby a first-period reorder policy that minimizes expected total inventory cost over a multiperiod planning horizon can be identified with a nominal investment in computer processing time. The analysis led to the conclusion that first-period policies obtained by using the mixed-integer programming model with expectations as periodic demand inputs are generally adequate under the conditions specified in the research and compare favorably with policies obtained from commonly used inventory models. (Author)

In this paper, we consider a method of computing minimal models in circumscription using integer programming in propositional logic and first-order logic with domain closure axioms and unique name axioms. This kind of treatment is very important since this enable to apply various technique developed in operations research to nonmonotonic reasoning. Nerode et al. (1995) are the first to propose a method of computing circumscription using integer programming. They claimed their method was correct for circumscription with fixed predicate, but we show that their method does not correctly reflect their claim. We show a correct method of computing all the minimal models not only with fixed predicates but also with varied predicates and we extend our method to compute prioritized circumscription as well.

Includes bibliographical references (leaves 23-25)

Includes bibliographical references (leaves 23-25)

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