This paper presents the effect of implementing interruptible loads (ILs) from the demand side for reserve allocation in an electricity supply system. A unit commitment (UC) objective function is used to incorporate th...
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This paper presents the effect of implementing interruptible loads (ILs) from the demand side for reserve allocation in an electricity supply system. A unit commitment (UC) objective function is used to incorporate the energy/reserve providers and to schedule energy and reserves simultaneously. An innate IL reliability modelling methodology is explicitly presented. A thermal unit system with demand-side participation is traversed by varying the size of the ILs, the reserve offer prices, and the value of lost load (VOLL). A penalty cost is imposed on IL service providers whose loads are supposed to be interrupted when initiated but fail to respond and grid service providers who are responsible for the maintenance of under-frequency relays (UFRs) and circuit-breakers (CBs) connected to ILs. The objective of this penalty cost proposal is to achieve a better and healthier energy supply system. The results in this paper provide useful insight into how the Demand Side Management and penalty scheme is capable of maintaining and/or improving the operation of the electricity supply system. (c) 2012 Elsevier Ltd. All rights reserved.
There are two distinct strengthening methods for disjunctive cuts with some integer variables;they differ in the way they modularize the coefficients. In this paper, we introduce a new variant of one of these methods,...
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There are two distinct strengthening methods for disjunctive cuts with some integer variables;they differ in the way they modularize the coefficients. In this paper, we introduce a new variant of one of these methods, the monoidal cut strengthening procedure, based on the paradox that sometimes weakening a disjunction helps the strengthening procedure and results in sharper cuts. We first derive a general result that applies to cuts from disjunctions with any number of terms. It defines the coefficients of the cut in a way that takes advantage of the option of adding new terms to the disjunction. We then specialize this result to the case of split cuts for mixedinteger programs with some binary variables, in particular Gomory mixedinteger cuts, and to intersection cuts from multiple rows of a simplex tableau. In both instances we specify the conditions under which the new cuts have smaller coefficients than the cuts obtained by either of the two currently known strengthening procedures. (C) 2011 Elsevier B.V. All rights reserved.
This paper addresses a scheduling problem for a two-stage assembly shop in a machinery factory. At stage one, all parts of jobs are assembled simultaneously on a batch machine with a common processing time and a const...
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This paper addresses a scheduling problem for a two-stage assembly shop in a machinery factory. At stage one, all parts of jobs are assembled simultaneously on a batch machine with a common processing time and a constant batch setup time. Then the assembled jobs are moved to the second stage to perform system integration with different processing times on a discrete machine. On both machines, a family setup time is required when the processing switches from one family to a different one. The objective is to minimize the weighted sum of makespan, total completion time and total tardiness. A mixed integer programming (MIP) model is developed for solving small-size problems, and three heuristics are proposed for solving medium- and large- size problems. Computational experiments show that RFBFS, a full batch family sorting heuristic combining with rolling horizon scheduling strategy, is better than the other two heuristics in terms of solution quality. Real-life implementation also shows that the performance of RFBFS is significantly better than the current method. (c) 2012 Elsevier B.V. All rights reserved.
As is well known, the computational complexity in the mixed integer programming (MW) problem is one of the main issues in model predictive control (MPC) of hybrid systems such as mixed logical dynamical systems. Thus ...
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As is well known, the computational complexity in the mixed integer programming (MW) problem is one of the main issues in model predictive control (MPC) of hybrid systems such as mixed logical dynamical systems. Thus several efficient MIP solvers such as multi-parametric MIP solvers have been extensively developed to cope with this problem. On the other hand, as an alternative approach to this issue, this paper addresses how a deterministic finite automaton, which is a part of a hybrid system, should be expressed to efficiently solve the MIP problem to which the MPC problem is reduced. More specifically, a modeling method to represent a deterministic finite automaton in the form of a linear state equation with a smaller set of binary input variables and binary linear inequalities is proposed. After a motivating example is described, a derivation procedure of a linear state equation with linear inequalities representing a deterministic finite automaton is proposed as three steps;modeling via an implicit system, coordinate transformation to a linear state equation, and state feedback binarization. Various significant properties on the proposed modeling are also presented throughout the proofs on the derivation procedure. (C) 2012 Elsevier Ltd. All rights reserved.
The n-step mixedinteger rounding (MIR) inequalities of Kianfar and Fathi (Math Program 120(2):313-346, 2009) are valid inequalities for the mixed-integer knapsack set that are derived by using periodic n-step MIR fun...
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The n-step mixedinteger rounding (MIR) inequalities of Kianfar and Fathi (Math Program 120(2):313-346, 2009) are valid inequalities for the mixed-integer knapsack set that are derived by using periodic n-step MIR functions and define facets for group problems. The mingling and 2-step mingling inequalities of Atamturk and Gunluk (Math Program 123(2):315-338, 2010) are also derived based on MIR and they incorporate upper bounds on the integer variables. It has been shown that these inequalities are facet-defining for the mixedinteger knapsack set under certain conditions and generalize several well-known valid inequalities. In this paper, we introduce new classes of valid inequalities for the mixed-integer knapsack set with bounded integer variables, which we call n-step mingling inequalities (for positive integer n). These inequalities incorporate upper bounds on integer variables into n-step MIR and, therefore, unify the concepts of n-step MIR and mingling in a single class of inequalities. Furthermore, we show that for each n, the n-step mingling inequality defines a facet for the mixedinteger knapsack set under certain conditions. For n = 2, we extend the results of Atamturk and Gunluk on facet-defining properties of 2-step mingling inequalities. For n a parts per thousand yen 3, we present new facets for the mixedinteger knapsack set. As a special case we also derive conditions under which the n-step MIR inequalities define facets for the mixedinteger knapsack set. In addition, we show that n-step mingling can be used to generate new valid inequalities and facets based on covers and packs defined for mixedinteger knapsack sets.
We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular,...
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We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.
Let L be a family of lattice-free polyhedra in R-m containing the splits. Given a polyhedron P in Rm+n, we characterize when a valid inequality for P boolean AND (Z(n) x R-n) can be obtained with a finite number of di...
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Let L be a family of lattice-free polyhedra in R-m containing the splits. Given a polyhedron P in Rm+n, we characterize when a valid inequality for P boolean AND (Z(n) x R-n) can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L. We also characterize the lattice-free polyhedra M such that all the disjunctive cuts corresponding to M can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L for every polyhedron P. Our results imply interesting consequences, related to split rank and to integral lattice-free polyhedra, that extend recent research findings.
The production scheduling of a real-world multistage food process is considered in this work. An efficient mixed integer programming (MIP) continuous-time model is proposed to address the production problem under stud...
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The production scheduling of a real-world multistage food process is considered in this work. An efficient mixed integer programming (MIP) continuous-time model is proposed to address the production problem under study. The overall mathematical framework relies on an efficient modeling approach of the sequencing decisions, the integrated modeling of all production stages, and the inclusion of a set of strong tightening constraints. The simultaneous optimization of all processing stages aims at facilitating the interaction among the different departments of the production facility. Moreover, an alternative MIP-based solution strategy is proposed for dealing with large-scale food processing scheduling problems. Although this method may no guarantee global optimality, it favors low computational requirements and solutions of very good quality. Several problem instances are solved to reveal the salient computational performance and the practical benefits of the proposed MIP formulation and solution strategy. (c) 2011 Elsevier Ltd. All rights reserved.
Work-related musculoskeletal disorders (WMSDs) are common occupational diseases among assembly workers due to repetitive motions or heavy workloads. The conventional approaches to decreasing WMSDs in assembly workers ...
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Work-related musculoskeletal disorders (WMSDs) are common occupational diseases among assembly workers due to repetitive motions or heavy workloads. The conventional approaches to decreasing WMSDs in assembly workers usually focus on individual assembly work at the station level. These approaches, however, do not pay enough attention to work allocation at the whole assembly line level such as balancing ergonomic burdens among workers by proper work assignment. This paper presents a methodology that can be used to integrate ergonomic measures of upper extremities into assembly line design problems. Linear models are developed to link work-worker assignment to the upper extremity ergonomic measures based on a guideline from American Conference of Governmental Industrial Hygienists. These linear models allow ergonomic and productivity measures to be integrated as a mixed-integerprogramming model. The case studies of this paper show the new model can effectively balance and control exposure levels in the upper extremity while not significantly decreasing line efficiency. This research shows the potential to reduce the need of numerous task adjustments for ergonomic improvement after initial assembly line design in conventional trial-and-error based assembly task adjustment. Furthermore, these linearization methods can be generalized in order to incorporate other ergonomic measures in tabulated forms into assembly line design problems. (C) 2011 Elsevier Ltd. All rights reserved.
We show how the performance of general purpose mixed integer programming (MIP) solvers, can be enhanced by using the Semi-Lagrangian Relaxation (SLR) method. To illustrate this procedure we perform computational exper...
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We show how the performance of general purpose mixed integer programming (MIP) solvers, can be enhanced by using the Semi-Lagrangian Relaxation (SLR) method. To illustrate this procedure we perform computational experiments on large-scale instances of the Uncapacitated Facility Location (UFL) problems with unknown optimal values. CPLEX solves 3 out of the 36 instances. By combining CPLEX with SLR, we manage to solve 18 out of the 36 instances and improve the best known lower bound for the other instances. The key point has been that, on average, the SLR approach, has reduced by more than 90% the total number of relevant UFL variables.
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