Efficiently gap-filling reaction networks

We present an efficient polynomial-time approximation scheme (EPTAS) for the problem of scheduling jobs on parallel uniform machines that improves all previously known EPTAS for the problem. Our algorithm uses a Mixed Integer Linear Program (MILP) formulation for a relaxed version of the problem. We simplify the MILP by repeatedly removing carefully selected sets of jobs and machines until all integer variables have been removed. Then, we build up the solution through the use of a dynamic programming approach, enumeration, and linear program solving. Notable about our approach is that our algorithm only uses an LP solver, different from previous EPTAS approaches where MILP solvers are necessary.

Supply chain network design and operation: Systematic decision-making for centralized, distributed, and mobile biofuel production using mixed integer linear programming (MILP) under uncertainty

Combined MILP-constraint programming approach for the optimal scheduling of multistage batch processes

Combinatorial optimization problem arise typically in the form of a mixed-integer linear program $$ \max \left\{ {cx + dy:Ax + Dy \leqslant b,x \geqslant 0 and integer, y \geqslant 0} \right\}, $$ (MIP) where A is any m x n matrix of reals, b is a column vector with m real components and c and d are real row vectors of length n and p, respectively. If n = 0 then we have a linear program. If p = 0 then we have a pure integer program. The variables x that must be integer-valued are the integer variables of the problem, the variables y the real or flow variables. There are frequently explicit upper bounds on either the integer or real variables or both. In many applications the integer variables model yes/no decisions, i.e., they assume only the values of zero or one. In this case the problem (MIP) is a mixed zero-one or a zero-one linear program depending on p > or p = 0KeywordsExtreme PointIdeal FormulationMixed Integer Linear ProgramInteger SolutionLinear Programming RelaxationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Faster integer-feasibility in mixed-integer linear programs by branching to force change

In this paper, we present an algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems involving (i) 0-1 integer variables, and, (ii) more than one parameter, bounded between lower and upper bounds, present on the right hand side (RHS) of constraints. The solution is approached by decomposing the mp-MILP into two subproblems and then iterating between them. The first subproblem is obtained by fixing integer variables, resulting in a multiparametric linear programming (mp-LP) problem, whereas the second subproblem is formulated as a mixed integer linear programming (MILP) problem by relaxing the parameters as variables.

A computational comparison of cargo prioritization and terminal allocation problem models

Purpose – This paper aims to address the problem of optimal allocation of demand of items among candidate suppliers to maximize the purchase value of items. The purchase value of the items directly relates to cost and quality of raw materials purchased from the supplier. In an increasingly competitive environment, firms are paying more attention to selecting the right suppliers for procurement of raw materials and component parts for their products. The present research work focuses on this issue of supply chain management. Design/methodology/approach – This present research work devises a hybrid algorithm for multi-period demand allocation among the suppliers. The customer demand is allocated by using a hybrid algorithm based on the technique for order preference by similarity to ideal solution (TOPSIS), fuzzy set theory and the mixed linear integer programming (MILP) approaches. Findings – The supply chain network is witnessing a changing business environment due to government policies aimed at promoting new small manufacturing enterprises (small and medium-sized enterprises) for intermediate parts and components. Hence, the managers have an option to select a new group of suppliers and allocate the optimal multi-period demand among the new group of suppliers to maximize their purchase value. In this context, the proposed hybrid model would be beneficial for the managers to operate their supply chain effectively and efficiently. The present research work will be helpful for the managers who are interested to reconfigure their supply chain under the failure of any supply chain partner or in a changing business environment. The model provides flexibility to the managers for evaluation of the different available alternatives to take a decision of optimal demand allocation among the suppliers. The proposed hybrid (fuzzy, TOPSIS and MILP) model provides more objective information for supplier evaluation and demand allocation among suppliers in a supply chain. The managers can use the proposed model to the analysis of other management decision-making problems. Originality/value – This present research work devises a hybrid algorithm for multi-period demand allocation among the suppliers. This hybrid algorithm prioritizes the suppliers and then allocates the multi-period demand among the suppliers. The customer demand is allocated by using a hybrid algorithm based on the technique for order preference by similarity to ideal solution (TOPSIS), fuzzy set theory and the mixed linear integer programming (MILP) approaches.

Algorithms and computer-based tools for analyzing infeasible linear and nonlinear programs have been developed in recent years, but few such tools exist for infeasible mixed-integer or integer linear programs. One approach that has proven especially useful for infeasible linear programs is the isolation of an Irreducible Infeasible Set of constraints (IIS), a subset of the constraints defining the overall linear program that is itself infeasible, but for which any proper subset is feasible. Isolating an IIS from the larger model speeds the diagnosis and repair of the model by focussing the analytic effort. This paper describes and tests algorithms for finding small infeasible sets in infeasible mixed-integer and integer linear programs; where possible these small sets are IISs.

Mixed-integer linear programming (MILP) can be used for a variety of optimization problems. However, it is limited to relatively small-scale problems, because its computation time increases dramatically with the number of integer variables. Decomposition methods have been presented to derive good feasible solutions of MILP problems. The objective of this paper is to propose a strategy for partitioning variables in using a decomposition method presented by the authors. The strategy proposed here is to decompose an original MILP problem into the smallest MILP subproblems, each of which has a single integer variable, and enables one to assume the values of part of integer variables efficiently to obtain a reduced MILP master problem. A single-period operational planning problem of a simplified heat supply system is investigated analytically to show the meaning and validity of the strategy. A multi-period operational planning problem of a practical heat supply system is also investigated numerically to show the validity and effectiveness of the decomposition method into which the strategy is incorporated.

Power gating is a very effective technique to reduce the subthreshold leakage by using sleep transistors to turn off the functional blocks or cells when they are not used. When the sleep transistors are turned on, the power grid may experience a huge current surge which may violate the integrity of the power grid. This paper addresses this problem by formulating the wakeup scheduling of sleep transistors as an exact mixed integer linear program (MILP). Since the resulting MILP is hard, we propose a very efficient yet near optimal algorithm by successively relaxing the MILP to a sequence of linear program (LP) problems. The results obtained on the ISCAS benchmarks indicate that our proposed algorithm obtains a near optimal solution with a speedup of 15× on average compared to the MILP. The proposed algorithm has a runtime complexity which is linear in practice.

The demand for hydrogen in refineries is growing due to its importance as a sulfur capture element. Therefore, hydrogen management is critical for fulfilling demands as efficiently as possible. Through mathematical modeling, hydrogen network management can be better performed. Cost-efficient Mixed-Integer Linear Programming (MILP) and Mixed-Integer Nonlinear Programming (MINLP) optimization models for (re)designing were proposed and implemented in GAMS with two case studies. Linear programming has the limitation of no stream mixing allowed; therefore, to overcome this limitation, an algorithm-based procedure called the Virtual Compressor Approach was proposed. Based on the MILP optimal solution obtained, the streams and compressors were merged. As a result, the number of compressors was reduced, along with the inherent investment costs. An operational cost reduction of more than 28% (example 1) and 26% (example 2) was obtained with a linear model. The optimal MILP solution after rearranging compressors was then provided as a good starting point to the MINLP. The operating costs were decreased by more than 31% (example 1) and 32% (example 2). Most of the cost reduction was obtained only with the usage of the MILP model. Besides, a higher level of cost reduction was only obtained when the linear model was used as the starting point.

Using submodularity in solving the robust bandwidth packing problem with queuing delay guarantees

Previous article Next article Complementarity Theorems for Linear ProgrammingA. C. WilliamsA. C. Williamshttps://doi.org/10.1137/1012015PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Frank Eugene Clark, Mathematical Notes: Remark on the Constraint Sets in Linear Programming, Amer. Math. Monthly, 68 (1961), 351–352 MR1531192 0109.38204 CrossrefISIGoogle Scholar[2] A. J. Goldman, Resolution and separation theorems for polyhedral convex setsLinear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N. J., 1956, 41–51, in [4] MR0089113 0072.37505 Google Scholar[3] A. J. Goldman and , A. W. Tucker, Theory of linear programmingLinear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N.J., 1956, 53–97, in [4] MR0101826 0072.37601 Google Scholar[4] H. W. Kuhn and , A. W. Tucker, Linear Inequalities and Related Systems, Princeton University Press, Princeton, 1956 0072.37502 Google Scholar[5] A. C. Williams, Boundedness relations for linear constraint sets, Linear Algebra and Appl., 3 (1970), 129–141 10.1016/0024-3795(70)90009-1 MR0266612 0201.22003 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Sparse solutions to an underdetermined system of linear equations via penalized Huber loss6 November 2020 | Optimization and Engineering, Vol. 22, No. 3 Cross Ref Dynamic Non-diagonal Regularization in Interior Point Methods for Linear and Convex Quadratic Programming26 February 2019 | Journal of Optimization Theory and Applications, Vol. 181, No. 3 Cross Ref Necessary and Sufficient Conditions for Noiseless Sparse Recovery via Convex Quadratic SplinesMustafa Ç Pinar12 February 2019 | SIAM Journal on Matrix Analysis and Applications, Vol. 40, No. 1AbstractPDF (416 KB)A labeling algorithm for the sensitivity ranges of the assignment problemApplied Mathematical Modelling, Vol. 35, No. 10 Cross Ref Bibliography15 August 2011 Cross Ref Sensitivity Analysis and Dynamic Programming15 February 2011 Cross Ref Bibliography Cross Ref Condition measures and properties of the central trajectory of a linear programMathematical Programming, Vol. 83, No. 1-3 Cross Ref New characterizations of ℓ1 solutions to overdetermined systems of linear equationsOperations Research Letters, Vol. 16, No. 3 Cross Ref Limiting behavior of weighted central paths in linear programmingMathematical Programming, Vol. 65, No. 1-3 Cross Ref Stability of linearly constrained convex quadratic programsJournal of Optimization Theory and Applications, Vol. 64, No. 1 Cross Ref Marginal values in mixed integer linear programmingMathematical Programming, Vol. 44, No. 1-3 Cross Ref A theory of linear inequality systemsLinear Algebra and its Applications, Vol. 106 Cross Ref Boundedness relations in linear semi-infinite programmingAdvances in Applied Mathematics, Vol. 8, No. 1 Cross Ref A Variable-Complexity Norm Maximization ProblemO. L. Mangasarian and T. -H. Shiau17 July 2006 | SIAM Journal on Algebraic Discrete Methods, Vol. 7, No. 3AbstractPDF (698 KB)Simple computable bounds for solutions of linear complementarity problems and linear programs26 February 2009 Cross Ref On polyhedral extension of some LP theoremsMathematical Programming, Vol. 30, No. 1 Cross Ref Polyhedral extensions of some theorems of linear programmingMathematical Programming, Vol. 24, No. 1 Cross Ref Optimal simplex tableau characterization of unique and bounded solutions of linear programsJournal of Optimization Theory and Applications, Vol. 35, No. 1 Cross Ref Projection and Restriction Methods in Geometric Programming and Related Problems Cross Ref Representation of Convex Sets Cross Ref Projection and restriction methods in geometric programming and related problemsJournal of Optimization Theory and Applications, Vol. 26, No. 1 Cross Ref The complementary unboundedness of dual feasible solution sets in convex programmingMathematical Programming, Vol. 12, No. 1 Cross Ref Theorems on the dimension of convex setsLinear Algebra and its Applications, Vol. 12, No. 1 Cross Ref On the primal and dual constraint sets in geometric programmingJournal of Mathematical Analysis and Applications, Vol. 32, No. 3 Cross Ref Volume 12, Issue 1| 1970SIAM Review History Submitted:23 December 1968Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1012015Article page range:pp. 135-137ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

Estimating aspiration levels from discrete choices - computational techniques and experiences