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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

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

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

We present a bounding technique for use in implicit enumeration algorithms for solving the integer linear programming problem with binary variables. The main assumptions used by this technique are the associated linear program, obtained by dropping the integrality constraints on the variables, possesses a unique optimal solution, this optimal solution is not binary, and a good feasible solution to the original problem is available. An alternative to the last assumption which is weaker is also presented. We show that joint bounds can be obtained on the values of a subset of the variables. In addition we given an efficient method to implement this bounding technique. Finally, a class of problems particularly well-suited to this bounding procedure is specified. (Author)

Bibliography: p. 91

A computer code, FEASBL, is developed to maximize a non-linear objective function over a convex feasible region. The feasible region is defined by a set of non-linear and linear constraints on the variables. FEASBL can solve problems involving up to fifty variables with a feasible region formed by up to fifty non-linear constraints, and fifty linear constraints. FEASBL uses a feasible direction method as its solution algorithm.

We consider the problem of finding an n-agent joint-policy for the optimal finite-horizon control of a decentralized Pomdp (Dec-Pomdp). This is a problem of very high complexity (NEXP-hard in n >= 2). In this paper, we propose a new mathematical programming approach for the problem. Our approach is based on two ideas: First, we represent each agent's policy in the sequence-form and not in the tree-form, thereby obtaining a very compact representation of the set of joint-policies. Second, using this compact representation, we solve this problem as an instance of combinatorial optimization for which we formulate a mixed integer linear program (MILP). The optimal solution of the MILP directly yields an optimal joint-policy for the Dec-Pomdp. Computational experience shows that formulating and solving the MILP requires significantly less time to solve benchmark Dec-Pomdp problems than existing algorithms. For example, the multi-agent tiger problem for horizon 4 is solved in 72 secs with the MILP whereas existing algorithms require several hours to solve it.

We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' property, and we show that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. LP decoding performance is illustrated for the (11,6,5) ternary Golay code with ternary PSK modulation over AWGN, and in this case it is shown that the LP decoder performance is comparable to codeword-error-rate-optimum hard-decision based decoding.

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

Geoffrion's structured modeling provides a very promising framework for the development of future model management systems (MMS). This thesis presents a prototype that converts a mathematical representation of simple LP models to Geoffrion's structured modeling representations. The general procedures presented could be extended to convert an LP model represented in any precisely defined mathematical language. This would allow the development of integrated modeling environments based upon the structured modeling framework which could accept input in a number of common LP language formats. Keywords: Modeling; Linear programming; Model management systems; Structured modeling; Mathematical modeling.

We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some recent concentration of measure results. The linear programming inequality may be of independent interest.

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F2 Decison Making 2- Limiting Factor And Linear Programming

2 v. 27 cm

It is known that the Mizuno-Todd-Ye predictor-corrector primaldual Newton interior-point method generates a duality-gap sequence which converges quadratically to zero, and this is accomplished with an iteration complexity of O (square root of n L).

Over the last decade, much attention has been focused on the development of automated letter mail processing systems for postal sorting. Optical character readers and bar-code sorters have begun to augment mechanized processing that has been in use since the mid-1960s. Continuing automated mail processing programs are aimed at minimizing growth in labor costs, which at $30. 5 billion accounted for 83 percent of the total United States Postal Service (USPS) operating costs in fiscal year 1988. Simulation and mixed integer linear programming (MILP) models are developed in this thesis with the objective of assisting postal managers is designing automated systems for the general mail facilities. GMFs) of the USPS. The simulation model utilizes a probabilistic structure to channel processed mail between stations. Processing equipment and associated personnel are modelled as resources. The arrival process can accurately model daily input mail profiles and variability, as well as seasonal loads and secular trends such as changes in mail address quality. Such a detailed probabilistic model provides a realistic test of proposed equipment selections and resources schedules for strategic planning and operations management. A simulation model of a specific medium-sized GMF is constructed using the SLAMII simulation language.

This paper presents a new interior-point algorithm for linear programming where the constraints are all expressed as inequalities. Along with the concept of minimum-weight basis, the algorithm features a novel mechanism for finding search directions. Unlike other interior-point methods which implicity or explicitly involve optimization over ellipsoids for their direction-finding schemes, the one reported here uses boxes. The corresponding subproblems are simple linear programs having closed form solutions. It is shown that the iterates generated by the algorithm converge to an extreme point of the feasible region. When this point is nondegenerate, it is optimal and reached within finitely any steps. The methodology introduced here also gives rise to a polyhedral subdivision of the problem's feasible region and in fact to the entire space of decision variables.

Under present arrangements the number of large scale transportation routing problems arising out of SPCC redistribution actions is relatively small. A sample indicates that less than five percent of these problems are of sufficient size and complexity to merit sophisticated computa tional treatment. For these purposes a problem was considered to be sizable if it involved no less than seven activities, no less than three consignees and no less than three consignors. However, it is possible to effect worthwhile savings in transportation outlay on these larger redistribution problems. Even approximative techniques which involve no more complex calcu lations thanhe present rules can save about two percent on transportation mileage in the average redistribution problem. This is a rela tively small figure but considering the large snnual outlay on redistribution transportation cost the absolute dollar saving is likely to be considerable. Most of the calculations were based on straightforward mileage tables rather than transportation cost tables or the proximity tables currently in use by SPCC.

For the problem of minimizing the integral f(x)dx from limits of 0 to 1 subject to the constraints - f(x) xg(y) f(x) if 0 x y 1, - f(x) xg(y) - x + y f(x) if 0 y x 1, solutions are given to prove both that they satisfy the constraints and that they have the extremizing property. The problem arose in an elastico-plastic, structural-design context.

Postoptimality analysis and parametric optimization techniques are fully developed aspects of linear programming. In the context of integer linear programming, however, these aspects have barely begun to be developed. The purpose of this paper is to take stock of what is known about this topic and to lay the foundation for future progress. Our conceptual starting point is the notion that, in practical applications, typically one is faced not with a single numerical integer linear program to solve but rather with an entire family of numerical problems of interest. The members of the family may all have the same structure but differ as to the values of one or more coefficients, or they may even have different (but related) structures. The scope of this paper is limited to be first mentioned case.

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. (KAR) P. 2

The report is concerned with methods of approximating the chance- constrained set S = (x such that/Pr(A x=or B)=or alpha) when the underlying distribution, F(.) of the random variate (A, B) is non-normal. The resulting sets are completely distribution-free in that no assumptions are made about the form of F(.) or any of its parameters. The concept employed is the distribution- free tolerance region. This is a sample based region containing 100 alpha percent of the population, at a confidence level, beta. The elements of the distribution-free sets satisfy the chance-constraint, Pr(Ax = or B) =or alpha with a confidence of at least beta. Furthermore, the sample size required to attain this level of confidence is readily available in tabular or graphical form. The superiority of the distribution-free approach over existing chance- constrained methods is demonstrated using simulated gamma variates.

This report examines the role played by several kinds of ceiling points in solving the pure, general integer linear programming problem (ILP). While no assumptions are made concerning the structure or signs of the data of the problem, it is assumed that the feasible region for (ILP) is non-empty and bounded. A ceiling point with respect to a single constraint maybe thought of as an integer solution on or close to the boundary of the feasible region defined by the constraint. The definition of a ceiling point with respect to a single constraint is extended to take multiple constraints into consideration simultaneously, defining what is called a feasible ceiling point. It is shown that the set all feasible ceiling points contains at least one optimal solution for (ILP). A related class of solutions called feasible 1-ceiling points is also characterized and shown to contain all optimal solutions for (ILP). Moreover, 1- ceiling points are computationally easier to identify than ordinary ceiling points and may be sought with respect to one constant at a time. It is also demonstrated that solving (ILP) requires only enumerating feasible 1-ceiling points with respect to a subset of all functional constraints. Keywords: Integer variables; Enumeration algorithms.

The statistical technique, "Zero-One Linear Programming," that has successfully been used to create multiple tests with similar characteristics (e.g., item difficulties, test information and test specifications) in the area of educational measurement, was deemed to be a suitable method for creating multiple sets of matched samples to be used as control groups in the quasi-experimental design of "non-randomized comparison group pretest-posttest." Compared to the existing propensity-score matching method, this method does not require any statistical models and assumptions and can handle the covariate of the pretest score more appropriately. If the measurement error of the pretest-score mean of the treatment group is ignored, this method will generate a unique matched sample once the criteria for attempting to create two similar groups are determined. Otherwise, multiple sets of similar matched samples can be generated and the performance of the treatment group can be compared with each of the multiple matched samples using an appropriate statistical analysis. Afterwards, the mean of the effect size measure, taking the average of the effect size across replicated comparisons, can then be used to assess the efficacy of any program. This enhances our confidence level to decide whether a program is effective or not, compared to the finding resulting from a single comparison. A description of "Zero-One Linear Programming" and its application to create a matched sample or multiple sets of matched samples is introduced in this paper. (Contains 3 tables and 3 figures.)

This volume was digitized and made accessible online due to deterioration of the original print copy.

Bibliography: leaves 38-39

Linear and Nonlinear Programming by David G.Luenberger and Yinyu Ye

Linear and Nonlinear Programming by David G.Luenberger and Yinyu Ye

Linear programming techniques for solving administrative and planning problems are discussed. The simplex method is advanced as the most practical way of solving the mathematical problem. The value of the IBM 701 calculator as a computational aid is explored. A petroleum blending problem is used to illustrate the power of linear programming as a tool for planning.

A two-step optimization procedure using linear programming is employed to obtain a near-optimal solution to the large-scale, multiple-weapon type allocation problem. Initially, the target system is partitioned into target categories, each of which contains targets of equal worth and similar characteristics. Then, depending upon the requirements of the particular problem addressed, one of three different linear programming models is used to allocate the available supply of weapons among the target categories. Instead of inputing a point value for each target category, as is frequently done in other allocation models, in these models the user indicates a desired ratio of the probability of survival of the various categories. After the allocation of weapons among the categories has been accomplished, an integer programming model is used to assign weapons to individual targets within each category so as to minimize the average probability of survival of the category. These models have been programmed for an IBM 7090 computer at Headquarters Strategic Air Command.

A complete analysis and explicit solution is presented for the problem of linear fractional programming with interval programming constraints whose matrix is of full row rank. The analysis proceeds by simple transformation to canonical form, exploitation of the Farkas-Minkowski lemma and the duality relationships which emerge from the Charnes-Cooper linear programming equivalent for general linear fractional programming. The formulations as well as the proofs and the transformations provided by our general linear fractional programming theory are here employed to provide a substantial simplification for this class of cases. The augmentation developing the explicit solution is presented, for clarity, in an algorithmic format.

Through the use of linear programming techniques, the optimal number and positioning of air and ground ambulances within a theater of operations may be determined to ensure the orderly transport of casualties from the front lines to third echelon medical treatment facilities. The Probabilistic Location Set Covering Problem has been chosen as the core module for a linear programming model to assist in these determinations. The Optimal Placement of Casualty Evacuation Assets (OPTEVAC) model prompts the user to enter the dimensions of the theater, troop deployment nodes, types of evacuation assets available, and preferred locations of medical treatment facilities. The OPTEVAC model then provides output as to the required numbers of air and ground ambulances as well as the optimal positioning of those evacuation assets and ambulance exchange points.

This report develops a hybrid algorithm to solve the binary integer linear programming problem. This problem involves optimizing a linear objective function subject to a set of linear inequalities where, in addition, we require the variables to take on the value 0 or 1. the approach developed is that of implicit enumeration; that is, the set of all possible binary combinations of values for the variables is searched without considering each combination explicitly. This is accomplished by applying a series of tests which when satisfied allow immediate elimination of large subsets of these completions. It is in the choice of tests to be used that this algorithm may be termed a hybrid. Borrowing penalties and pseudocosts as well as binary infeasibility and conditional binary infeasibility tests from previous approaches, the algorithm is built to use each of their strengths. In addition, an existing heuristic procedure is used to generate a good feasible binary point at the outset. Thus, a good initial bound on the optimal function value is available. (Author)

An algorithm is described for determining the optimal solution of parametric linear and quadratic programming problems as an explicit piecewise linear function of the parameter. Each linear function is uniquely determined by an appropriate subset of active constraints. For every critical value of the parameter a new subset has to be determined. A simple rule is given for adding and deleting constraints from this subset. (Author)

In this paper, we consider deterministic models for a stochastic linear program with a constant feasible region and stochastic cost coefficients having multi-variate normal distribution. Relationships among the solutions of these models are examined and it is shown that solving a parametric quadratic program associated with Markowitz's mean-variance model yields solutions to all other models considered for all relevant values of parameters. (Author)

This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are basic semialgebraic sets. When the index set of an LSIPP problem is compact, a convergent hierarchy of semidefinite programming (SDP) relaxations is constructed under the assumption that the Slater condition and the Archimedean property hold. When the index set is noncompact, we use the technique of homogenization to equivalently convert the LSIPP problem into compact case under some generic assumption. Consequently, a corresponding hierarchy of SDP relaxations for noncompact LSIPP problems is obtained. We apply this relaxation approach to the special LSIPP problem reformulated from a polynomial optimization problem. A new SDP relaxation method is derived for solving the class of polynomial optimization problems whose objective polynomials are stably bounded from below on noncompact feasible sets.

In this paper we propose a novel two-step linear optimization model to calculate energy-efficient timetables in metro railway networks. The resultant timetable minimizes the total energy consumed by all trains and maximizes the utilization of regenerative energy produced by braking trains, subject to the constraints in the railway network. In contrast to other existing models, which are NP-hard, our model is computationally the most tractable one being a linear program. We apply our optimization model to different instances of service PES2-SFM2 of line 8 of Shanghai Metro network spanning a full service period of one day (18 hours) with thousands of active trains. For every instance, our model finds an optimal timetable very quickly (largest runtime being less than 13s) with significant reduction in effective energy consumption (the worst case being 19.27%). Code based on the model has been integrated with Thales Timetable Compiler - the industrial timetable compiler of Thales Inc that has the largest installed base of communication-based train control systems worldwide.

Finding the densest sphere packing in $d$-dimensional Euclidean space $\mathbb{R}^d$ is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding theory, discrete geometry, number theory, and biological systems. Numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations, even for the restricted problem of finding the densest lattice sphere packings. In this paper, we apply the Torquato-Jiao packing algorithm, which is a method based on solving a sequence of linear programs, to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19. We show that the TJ algorithm is appreciably more efficient at solving these problems than previously published methods. Indeed, in some dimensions, the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones. We also study the suboptimal local density-maxima solutions (inherent structures or "extreme" lattices) to gain insight about the nature of the topography of the "density" landscape.

We introduce a linear programming method to obtain bounds on the cardinality of codes in Grassmannian spaces for the chordal distance. We obtain explicit bounds, and an asymptotic bound that improves on the Hamming bound. Our approach generalizes the approach originally developed by P. Delsarte and Kabatianski-Levenshtein for compact two-point homogeneous spaces.

This is a brief overview of the life of Leonid Kantorovich (1912--1986) and his contribution to the fields of linear programming and ordered vector spaces.

A new class of entanglement witnesses (EWs) called reduction type entanglement witnesses is introduced, which can detect some multi-qudit entangeled states including PPT ones with Hilbert space of dimension $d_{_{1}}\otimes d_{_{2}}\otimes...\otimes d_{_{n}}$. The novelty of this work comes from the fact that the feasible regions turn out to be convex polygons, hence the manipulation of these EWs reduces to linear programming which can be solved \emph{exactly} by using simplex method. The decomposability and non-decomposability of these EWs are studied and it is shown that it has a close connection with eigenvalues and optimality of EWs. Also using the Jamio\l kowski isomorphism, the corresponding possible positive maps, including the generalized reduction maps of Ref. \cite{Hall1}, are obtained.

Available from National Technical Information Service, Springfield, Va

Zlatar Ski Center has an extremely high potential as a ski resort that could be among the most visited ones in Serbia. What characterizes this center is the proximity of Kokin Brod Lake, the Tara River and the like. Therefore, Zlatar should be considered both as a ski center and in terms of other diversities. The aim of this paper is to analyze the possibility of expanding the capacity of ski resorts by increasing the possible flow of skiers on new ski lifts and ski slopes. The methods used in this paper belong to operational research, specifically, the geometric interpretation of linear programming. It is also shown how to optimize the extended capacities. If the capacities of ski slopes are to be increased, it would initiate greater investment in accommodation capacities in the area of the municipality of Nova Varoš, which would affect its improvement in terms of tourism.

The motivation for this work has been the need for a practical procedure to solve the maximum-weight cut problem (MCP) in undirected graphs. Our primary focus has been on problems arising from considerations in statistical mechanics. These problems are typically posed on grid graphs and some natural variants. There has been significant progress in two areas: solution of the maximum-weight cut problem and development of simplex-based tools for integer programming. Codes developed have been widely used to improve solution time.

The authors discuss interior-point methods for linear programming derived by applying a logarithmic barrier transformation and performing projected Newton steps for a sequence of barrier parameters. Under certain conditions, one of these projected Newton barrier methods is shown to be equivalent to Karmarkar's (1984) projective method for linear programming. Details are given of a specific barrier algorithm and its practical implementation. Numerical results are given for several nontrivial test problems. Additional keywords: tables(data); numerical analysis; iterations; computations; least squares method. (Author)

This report forms the user's guide for Version 1.0 of LSSOL, a set of Fortran 77 subroutines for linearly constrained linear least-squares and convex quadratic programming. The method of LSSOL is of the two-phase, active-set type, and is related to the method used in the package SOL/QPSOL. Two main features of LSSOL are its exploitation of convexity and treatment of singularity. LSSOL may also be used for linear programming, and to find a feasible point with respect to a set of linear inequality constraints. LSSOL treats all matrices as dense, and hence is not intended for large sparse problems. Keywords: Algorithms; Parameters; Optimization; Linear programming; Mathematical software. (Author)

The L sub infinity norm has been widely studied as a criterion for curve fitting problems. This paper presents an algorithm to solve discrete approximation problems in the L sub infinity norm. The algorithm is a special- purpose linear programming dual method which employs a reduced basis and multiple pivots. Results of the computational experience with a computer code version of the algorithm are presented.

A special quadratic assignment problem is shown to be equivalent to a linear programming problem with n cubed constraints and n squared variables where n is the number of elements to be assigned. A labeling algorithm similar to that for the linear transportation problem is presented for solving the problem. An example is presented that deals with ' triangularizing' input-output matrices.