Juho Rantala · International Journal of Forest Engineering · 2004
Abstract In this paper, the applicability of linear programming (LP) in management of seedling transportation was compared to that of mixed integer programming (MIP). In the LP model, presented in an earlier paper, a linear objective function was used as a surrogate for the actual objective function, which is intrinsically nonlinear. In the LP model, transportation costs were determined per seedling, whereas in the MIP model they were based on vehicle loads. When the number of transported seedlings within a certain period decreased, for instance, due to planting through the growth period, the computational accuracy of the LP model was clearly lower than that of the MIP model. Despite that, differences in allocation of orders between these two models were small. Thus, in the actual business situation of Finnish nursery companies, standard LP seems to be an adequate tool for management of seedling transportation. From the standpoint of cost-efficient seedling business, planting through the growth period increased optimal transportation costs markedly. In addition to the seedling business, these results can be utilized in other types of business dealing with analogous transportation problems.
Cited by 6
Ray Pörn, Tapio Westerlund · Computer-aided chemical engineering/Computer aided chemical engineering · 2000
Cited by 6
Zhongqi Zhao, Lei Fan, Yuanxiong Guo et al. · 2024
Benders' decomposition (BD) algorithm constitutes a powerful mathematical programming method of solving mixed-integer linear programming (MILP) problems with a specific block structure. Nevertheless, BD still needs to solve an NP-hard quasi-integer programming master problem (MAP), which motivates us to harness the popular variational quantum algorithm (VQA) to assist BD. More specifically, we choose the popular quantum approximate optimization algorithm (QAOA) of the VQA family. We transfer the BD's MAP into a digital quantum circuit associated with a physically tangible problem-specific ansatz; and then solve it with the aid of a state-of-the-art digital quantum computer. Next, we evaluate the computational results and discuss the feasibility of the proposed algorithm. The hybrid approach advocated, which utilizes both classical and digital quantum computers, is capable of tackling many practical MILP problems in communication and networking, as demonstrated by a pair of case studies.
Cited by 5
Matthew G. Earl, Raffaello D’Andrea · arXiv (Cornell University) · 2005
We present methods to synthesize cooperative strategies for multi-vehicle control problems using mixed integer linear programming. Complex multi-vehicle control problems are expressed as mixed logical dynamical systems. Optimal strategies for these systems are then solved for using mixed integer linear programming. We motivate the methods on problems derived from an adversarial game between two teams of robots called RoboFlag. We assume the strategy for one team is fixed and governed by state machines. The strategy for the other team is generated using our methods. Finally, we perform an average case computational complexity study on our approach.
Cited by 0Open access
Ray Wai Man Kong, Ning Ding, Theodore Ho Tin Kong · ArXiv.org · 2025
This applied research article explores the application of Mixed-Integer Linear Programming (MILP) to address line-balancing challenges in the garment industry, focusing on optimizing production processes under multiple constraints. By integrating MILP with Lean Methodology principles, the study demonstrates significant improvements in operational efficiency and cost-effectiveness. The case study, conducted in collaboration with Prof Dr Ray WM Kong, highlights the successful implementation of MILP using IBM CPLEX Studio to optimize production order quantities across online and offline operations. The results reveal a remarkable reduction in labour costs, exceeding 50%, while effectively managing resource capacity and demand constraints. This study not only validates the theoretical underpinnings of MILP in resolving line-balancing issues but also underscores its practical applicability in modernizing garment production. The findings contribute valuable insights into the potential of advanced optimization techniques to enhance competitiveness and sustainability in the garment industry. This abstract succinctly captures the essence of the research, emphasizing the methodology, results, and significance of the study.
Cited by 0Open access
Alimo, Shahrouz R · JPL Data · 2023
NASA’s Deep Space Network (DSN) is a globally-spanning communications network responsible for supporting the interplanetary spacecraft missions of NASA and other international users. The DSN is a highly utilized asset, and the large demand for its’ services makes the assignment of DSN resources a daunting computational problem. In this paper, we cast the this challenging scheduling task as a Mixed-Integer Linear Programming (MILP) optimization. We offer a novel randomization technique which is capable solving the resulting MILP formulation for large large-scale instances of the DSN scheduling. A real-world DSN dataset is utilized to demonstrate the effectiveness of the proposed MILP model and randomization approach.
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Shizu Sakakubara, Yuusuke Kounoike, Yuji Shinano et al. · Lecture notes in computer science · 2007
Cited by 4
Longquan Yong, M Aiai · 2009
Abstract—We formulate the NP-hard absolute value equation as linear complementary problem when the singular values of A exceed one, and we proposed a mixed integer linear programming method to absolute value equation problem. The effectiveness of the method is demonstrated by its ability to solve random problems. Index Terms—absolute value equation; linear complementary problem; mixed integer linear programming. I.
Cited by 3
Ralf Östermark · Kybernetes · 2009
Purpose – To discuss a new parallel algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.
Cited by 3
Fransiska Mulyani, Ag. Gatot Bintoro · UAJY Repository (University of Southampton) · 2014
Logistik bencana merupakan kegiatan penting dalam penanganan bencana. Kegiatan ini sering digunakan sebagai salah satu indikator keberhasilan penanganan bencana. Perbaikan penanganan bencana selalu dilakukan dari waktu ke waktu baik secara konsep maupun pelaksanaan.Hasil penelitian yang berkaitan dengan logistik bencana masihsulit untuk diimplementasikan. Penelitian ini berkaitan dengan pengembangan model distribusi logistik bencana supaya dapat lebih implementatatif. Model distribusi dikembangkan dengan menggunakan Mixed Integer Linear Programming. Model yang dikembangkan berhasil menentukan rute, alokasi barang bantuan, serta alokasi kendaraan yang optimal dengan waktu komputasi yang cepat
Cited by 1Open access
Ronkainen, Onni · Osuva (University of Vaasa) · 2024
ABSTRACT: This paper explores optimization in tactical production planning within resource-constrained environments, where medium- to short-term decisions are essential for operational efficien-cy. Optimizing production planning under these conditions can confer competitive ad-vantages and improve resource utilization, supporting sustainability and green development goals. Through a theoretical framework, this research identifies effective methodologies suitable for case company for enhancing tactical production planning with a focus on profita-bility. Guided by this framework, a simulation model based on mixed-integer linear pro-gramming (MILP) was developed and tested using historical production data from a case company. Simulation tool was developed with Microsoft Excel, with OpenSolver add-on. Simulation tool was developed in collaboration with the case company and targeted to be a usable tool in production planning. MILP was chosen based on findings in theoretical frame-work and empirical analysis as simulation tool was developed further and new requirements emerged. The model aims to maximize profitability by improving allocation of production volumes to more profitable period. Tool will generate optimized production plans that in-crease profit per tonne produced, while still fulfilling certain production restrictions and re-quirements. Performance was assessed by comparing the simulation model's suggested plans to actual historical production plans over a three-year period. Results demonstrate the model’s potential for profitability improvements, while the simulation tool requires further development to fully cover all characteristics of the production environment. Based on these findings, the paper provides recommendations for future research, along with suggestions for further enhancing the simulation tool. TIIVISTELMÄ: Tämän tutkielman tarkoituksena on perehtyä taktisen tuotannonsuunnittelun optimointiin resurssi rajoitteisessa ympäristössä, missä keskipitkän ja lyhyen aikavälin päätöksillä on merkit-tävä vaikutus operatiiviseen tehokkuuteen. Tällaisessa ympäristössä tuotannon suunnittelun optimointi voi tuoda kilpailuetua, parantaa resurssien käytön tehokkuutta, sekä tukea ympä-ristön kannalta kestävää kehitystä. Teoreettisen viitekehyksen avulla tutkielma esittelee yrityk-seen sovellettavia keinoja parantaa tuotannon suunnittelun tehokkuutta, etenkin tuottavuu-den saralla. Teoreettiseen tutkimukseen pohjautuen, empiirisessä osiossa esitellään tuotannon suunnitteluun soveltuva simulaatiotyökalu, joka hyödyntää mixed-integer-pohjaista lineaaris-ta optimointia. Työkalu kehitettiin käyttäen Microsoft Excel -ohjelmistoa, jossa lisäksi oli Open-Solver -lisäosa. Simulaatiotyökalu on kehitetty yhteistyössä yrityksen edustajien kanssa, tarkoi-tuksena kehittää työkalu tuotannon suunnittelun tueksi. Mixed-integer optimointi valittiin mallin pohjaksi teoreettisen viitekehyksen, sekä empiirisen tutkimuksen pohjalta, kun huomat-tiin kriittiset tarpeet työkalun kehityksessä. Malli pyrkii parantamaan tonni -kohtaista katetta allokoimalla tarvittavat tuotantomäärät tuottavammille aikakausille, samalla kun tuotannon muut tarpeet ja rajoitteet täytetään. Simulaation suorituskykyä testattiin vertailemalla työka-lun ehdottamia optimoituja tuotantosuunnitelmia yrityksen historiallisiin tuotantosuunnitel-miin ja niiden kannattavuuteen kolmen vuoden ajanjaksolla. Tulokset osoittavat, että esitetyllä mallilla on potentiaalia tuottavuuden parantamisen näkökulmasta. Esitetty simulaatiotyökalu itsessään tarvitsee lisää kehitystä, jotta se pystyisi huomioimaan kaikki tuotantoympäristölle ominaiset tekijät. Tutkielman tulosten perusteella annetaan ehdotukset jatkotutkimuksia var-ten, sekä kehitystarpeet suunnitteluun soveltuvan simulaatiotyökalun parantamiseksi.
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Nathan Adelgren, Akshay Gupte · INFORMS journal on computing · 2021
We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, checking node fathoming, presolve, and duality gap measurement. Our branch-and-bound is predominantly a decision space search method because the branching is performed on the decision variables, akin to single objective problems, although we also sometimes split gaps and branch in the objective space. The various algorithms are implemented using a data structure for storing Pareto sets. Computational experiments are carried out on literature instances and on a new set of instances that we generate using a benchmark library (MIPLIB2017) for single objective problems. We also perform comparisons against the triangle splitting method from literature, which is an objective space search algorithm. Summary of Contribution: Biobjective mixed-integer optimization problems have two linear objectives and a mixed-integer feasible region. Such problems have many applications in operations research, because many real-world optimization problems naturally comprise two conflicting objectives to optimize or can be approximated in such a manner and are even harder than single objective mixed-integer programs. Solving them exactly requires the computation of all the nondominated solutions in the objective space, whereas some applications may also require finding at least one solution in the decision space corresponding to each nondominated solution. This paper provides an exact algorithm for solving these problems using the branch-and-bound method, which works predominantly in the decision space. Of the many ingredients of this algorithm, some parts are direct extensions of the single-objective version, but the main parts are newly designed algorithms to handle the distinct challenges of optimizing over two objectives. The goal of this study is to improve solution quality and speed and show that decision-space algorithms perform comparably to, and sometimes better than, algorithms that work mainly in the objective-space.
Cited by 3Open access
Bodo Rosenhahn · Lecture notes in computer science · 2023
Cited by 2
P. Radhakrishnan · 2008
An endeavour is made in this paper to present a novel implicit branch and bound method for mixed integer linear programming problems. The integer variables are driven to their non-basic variables, which can be fixed, at either lower or upper bound, remaining non-basic variables as such. The concept of twin models is exploited to get more number of nodes to get the optimal solution. This method eliminates non-optimal solutions and thus reduces the number of iterations. A different and simple method of adding a new constraint is formulated. Many typical test problems are solved on a micro computer to highlight the efficacy of this method. The accuracy obtained was good. The fact that it required many branching to solve even a small model is a strong evidence of its invulnerability to round off error. Its memory requirement is also modest. It is highly effective in solving a very large class of integer programming models, mixed integer, pure integer and the special class involving only binary variables. This does not add any new constraints to the original constraint set, since it merely manipulates upper and lower bounds on the integer variables. Hence, it can be said that it is immune to round-off errors. Experience indicates that the use of surrogate constraint is effective in improving the computation time. The solution time varies almost exponentially with the number of variables. So problems up to 100 variables can be solved in a reasonable amount of computation time. The most important advantages are its immunity to round off errors and its modest memory requirement in comparison with other methods like branch and bound and cutting plane method.
Cited by 0
André Rossi, Marc Sevaux · HAL (Le Centre pour la Communication Scientifique Directe) · 2008
International audience
Cited by 4
Sridhar, Srinath, Lam, Fumei, Blelloch, Guy et al. · KiltHub Repository · 2018
Reconstruction of phylogenetic trees is a fundamental problem in computational biology. While excellent heuristic methods are available for many variants of this problem, new advances in phylogeny inference will be required if we are to be able to continue making effective use of the rapidly growing stores of variation data now being gathered. In this paper, we present two integer linear programming (ILP) formulations for finding the most parsimonious phylogenetic tree from a set of binary variation data. One method uses a flow-based formulation that can produce exponential numbers of variables and constraints in the worst case. The method has, however, proven to be extremely efficient in practice on data sets that are well beyond the reach of the available provably efficient methods, solving several large mtDNA and Y-chromosome instances within a few seconds and giving provably optimal results in times competitive with fast heuristics that cannot guarantee optimality. An alternative formulation establishes that the problem can be solved with a polynomial-sized ILP. We further present a Web server that was developed based on the exponential-sized ILP that performs fast maximum parsimony inferences and serves as a front end to a database of precomputed phylogenies spanning the human genome.
Cited by 0Open access
Rossi, Roberto, Prestwich, Steven D., Tarim, S. Armagan · arXiv (Cornell University) · 2025
We develop a novel mathematical programming approximation framework to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select a subset of these items to be included into their knapsack. We study both "static" and "dynamic" variants of this problem: in the static setting, the decision about which items should be included in the knapsack is taken at the outset, before any random item value or weight is revealed; in the dynamic setting, items are received sequentially, and the decision about a particular item is made by taking into account previously observed values and weights. The knapsack has a given capacity, and if the total realised weight exceeds this capacity then a penalty cost is incurred for each unit of excess capacity utilised. The goal is to maximise the expected net profit. We tackle the case of normally distributed item weights and we show that our approach extends seamlessly to the case in which item weights are correlated and follow a multivariate normal distribution. In addition, we show our approach represents an effective heuristic for the case in which item weights follow generic probability distributions. In an extensive computational study we demonstrate that our models are near-optimal and more scalable than other state-of-the-art approaches.
Cited by 0Open access
B. Bank · Lecture notes in control and information sciences · 2005
Cited by 5
Rossi, Roberto, Prestwich, Steven D., Tarim, S. Armagan · ArXiv.org · 2025
We develop a novel mathematical programming approximation framework to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select a subset of these items to be included into their knapsack. We study both "static" and "dynamic" variants of this problem: in the static setting, the decision about which items should be included in the knapsack is taken at the outset, before any random item value or weight is revealed; in the dynamic setting, items are received sequentially, and the decision about a particular item is made by taking into account previously observed values and weights. The knapsack has a given capacity, and if the total realised weight exceeds this capacity then a penalty cost is incurred for each unit of excess capacity utilised. The goal is to maximise the expected net profit. We tackle the case of normally distributed item weights and we show that our approach extends seamlessly to the case in which item weights are correlated and follow a multivariate normal distribution. In addition, we show our approach represents an effective heuristic for the case in which item weights follow generic probability distributions. In an extensive computational study we demonstrate that our models are near-optimal and more scalable than other state-of-the-art approaches.
Cited by 0Open access
AG Richards, JP How, T Schouwenaars et al. · Bristol Research (University of Bristol) · 2001
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