A modification of a mixed integer linear programming (MILP) model to avoid the computational complexity

2015 ◽  
Vol 235 (1) ◽  
pp. 599-623 ◽  
Author(s):  
H. Hasan Örkcü ◽  
Mehmet Güray Ünsal ◽  
Hasan Bal
Keyword(s):  
Linear Programming ◽  
Computational Complexity ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Mixed Integer ◽  
Milp Model

scholarly journals Optimising the selection of food items for FFQs using Mixed Integer Linear Programming

2014 ◽  
Vol 18 (1) ◽  
pp. 68-74 ◽  
Author(s):  
Johanna C Gerdessen ◽  
Olga W Souverein ◽  
Pieter van ‘t Veer ◽  
Jeanne HM de Vries
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Selection Process ◽  
Saturated Fat ◽  
Mixed Integer ◽  
Monounsaturated Fat ◽  
Food Items ◽  
Milp Model ◽  
Selection Of

AbstractObjectiveTo support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible.DesignSelection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy, total protein, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, total carbohydrates, mono- and disaccharides, dietary fibre and potassium.ResultsThe food lists generated by the MILP model have good performance in terms of length, coverage and R2 (explained variance) of all nutrients. MILP-generated food lists were 32–40 % shorter than a benchmark food list, whereas their quality in terms of R2 was similar to that of the benchmark.ConclusionsThe results suggest that the MILP model makes the selection process faster, more standardised and transparent, and is especially helpful in coping with multiple nutrients. The complexity of the method does not increase with increasing number of nutrients. The generated food lists appear either shorter or provide more information than a food list generated without the MILP model.

scholarly journals Spillways Scheduling for Flood Control of Three Gorges Reservoir Using Mixed Integer Linear Programming Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Maoyuan Feng ◽  
Pan Liu
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Three Gorges Reservoir ◽  
Flood Control ◽  
Mixed Integer ◽  
Piecewise Linear Approximation ◽  
Three Gorges ◽  
Reservoir Storage ◽  
Milp Model

This study proposes a mixed integer linear programming (MILP) model to optimize the spillways scheduling for reservoir flood control. Unlike the conventional reservoir operation model, the proposed MILP model specifies the spillways status (including the number of spillways to be open and the degree of the spillway opened) instead of reservoir release, since the release is actually controlled by using the spillway. The piecewise linear approximation is used to formulate the relationship between the reservoir storage and water release for a spillway, which should be open/closed with a status depicted by a binary variable. The control order and symmetry rules of spillways are described and incorporated into the constraints for meeting the practical demand. Thus, a MILP model is set up to minimize the maximum reservoir storage. The General Algebraic Modeling System (GAMS) and IBM ILOG CPLEX Optimization Studio (CPLEX) software are used to find the optimal solution for the proposed MILP model. The China’s Three Gorges Reservoir, whose spillways are of five types with the total number of 80, is selected as the case study. It is shown that the proposed model decreases the flood risk compared with the conventional operation and makes the operation more practical by specifying the spillways status directly.

Optimizing a Pipeline Operation by Constraint Logic Programming (CLP) and Mixed Integer Linear Programming (MILP)

2004 ◽  
Author(s):  
L. Magata˜o ◽  
L. V. R. Arruda ◽  
F. Neves
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Logic Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Constraint Logic Programming ◽  
Mixed Integer ◽  
Pipeline System ◽  
Liquefied Petroleum Gas ◽  
Milp Model

This paper addresses the problem of developing an optimization structure to aid the operational decision-making in a real-world pipeline scenario. The pipeline connects an inland refinery to a harbor, conveying different types of products (gasoline, diesel, kerosene, alcohol, liquefied petroleum gas, jet fuel, etc). The scheduling of activities has to be specified in advance by a specialist, who must provide low cost operational procedures. The specialist has to take into account issues concerning product availability, tankage constraints, pumping sequencing, flow rate determination, and a series of operational requirements. Thus, the decision-making process is hard and error-prone due to the diversity of aspects to be considered. Nevertheless, the developed optimization structure can aid the specialist in solving the pipeline scheduling task with improved efficiency. Such optimization structure has its core in a novel mathematical approach, which uses Constraint Logic Programming (CLP) and Mixed Integer Linear Programming (MILP) technologies in an integrated CLP-MILP model. In particular, the integration of CLP and MILP technologies has been recognized as an emerging discipline for achieving the best that CLP and MILP can contribute to solve scheduling problems [1]. The scheme used for integrating CLP and MILP is double modeling [1], and the combined CLP-MILP model is implemented and solved by using a commercial tool [2]. Illustrative instances demonstrate that the optimization structure is able to define new operational points to the pipeline system, providing significant cost saving.

scholarly journals Mixed-Integer Linear Programming Model by Linear Approximation for a Strike Package-to-Target Assignment Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Heungseob Kim
Keyword(s):  
Linear Programming ◽  
Linear Approximation ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Programming Model ◽  
Mixed Integer ◽  
Piecewise Linear Approximation ◽  
Heterogeneous Vehicle Routing Problem ◽  
Target Assignment ◽  
Milp Model

This study deals with an aircraft-to-target assignment (ATA) problem considering the modern air operation environment, such as the strike package concept, multiple targets for a sortie, and the strike packages’ survivability. For the ATA problem, this study introduces a novel mathematical model in which a heterogeneous vehicle routing problem (HVRP) and a weapon-to-target assignment (WTA) problem are conceptually integrated. The HVRP generates the flight routes for strike packages because this study confirms that the survivability of a strike package depends on the path, and the WTA problem evaluates the likelihood of successful target destruction of assigned weapons. Although the first version of the model is developed as a mixed-integer nonlinear programming (MINLP) model, this study attempts to convert it to a mixed-integer linear programming (MILP) model using the logarithmic transformation and piecewise linear approximation methods. For an ATA problem, this activity could provide an opportunity to use the excellent existing algorithms for searching the optimal solution of LP models. To maximize the operational effectiveness, the MILP model simultaneously determines the following for each strike package: (a) composition type, (b) targets, (c) flight route, (d) types, and (e) quantity of weapons for each target.

scholarly journals Optimization of Flow Shop Scheduling in Precast Concrete Component Production via Mixed-Integer Linear Programming

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhansheng Liu ◽  
Zisheng Liu ◽  
Meng Liu ◽  
Jingjing Wang
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Production Scheduling ◽  
Delay Time ◽  
Mixed Integer Linear Programming ◽  
Production Cost ◽  
Storage Time ◽  
Precast Concrete ◽  
Mixed Integer ◽  
Milp Model

The increasing number of prefabrication projects has increased the demand for precast concrete (PC) components. The production cost of PC components significantly affects the development of the precast industry and the progress of prefabrication projects. To reduce the production cost, both the delivery delay time and component storage time must be reduced. Flow-arrangement optimization is generally performed using the genetic algorithm. However, this method cannot always yield a perfect optimal solution. Moreover, the traditional optimization model does not consider the impact of the overtime hours of workers on the project costs. In this study, a mixed-integer linear programming (MILP) model was developed to optimize the production scheduling by minimizing the storage and delay times. The total delay time for the components was reduced by 55.3%, from 3.8 to 1.7 h, and the total storage time for finished components was reduced by 20.3%, from 6.4 to 5.1 h. Then, the use of the MILP model was extended to optimize the production scheduling by minimizing overtime. Finally, the feasibility and effectiveness of MILP were verified by comparing the results. The total overtime decreased by approximately 24.5%, from 11.5 to 9.3 h. It has been demonstrated that the proposed MILP model can achieve a better production sequence with less overtime. The findings of this research can be deployed in optimizing efficiency in the real-life scheduling of production sequence.

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