HMIP Model for a Territory Design Problem with Capacity and Contiguity Constraints

2011 ◽  
pp. 226-257
Author(s):  
Fabian Lopez
Keyword(s):  
Design Problem ◽  
Large Scale ◽  
Research Work ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Territory Design ◽  
New Strategy ◽  
Activity Measures ◽  
Np Hard Problem ◽  
Cut Generation

Small geographic basic units (BU) are grouped into larger geographic territories on a Territory Design Problem (TDP). Proposed approach to solve a TDP is presented through a study case developed on a large soft drinks company which operates in the city of Monterrey, México. Each BU of our TDP is defined by three activity measures: (1) number of customers, (2) sales volume and (3) workload. Some geographic issues about contiguity and compactness for the territories to be constructed are considered. An optimal solution is obtained when the constructed territories are well balanced taking into consideration each activity measure simultaneously. In particular, contiguity is hard to be represented mathematically. All previous research work indicates that this NP-Hard problem is not suitable for solving on large-scale instances. A new strategy which is based on a hybrid-mixed integer programming (HMIP) approach is developed. Specifically, our implementation is based on a Cut-Generation Strategy. We take advantage from territory centers obtained through a relaxation of a P-median based model. This model has a very high degree of connectivity. Thus, small number of iterations to find connected solutions is required. The authors detail out their methodology and then they proceed to its computational implementation. Experimental results show the effectiveness of our method in finding near-optimal solutions for very large instances up to 10,000 BU’s in short computational times (less than 10 minutes). Nowadays, this model is being used by the firm with important economical benefits.

A Heuristic Algorithm for Solving a Large-scale Real-world Territory Design Problem

Omega ◽  
2021 ◽  
pp. 102442
Author(s):  
Lin Zhou ◽  
Lu Zhen ◽  
Roberto Baldacci ◽  
Marco Boschetti ◽  
Ying Dai ◽  
...  
Keyword(s):  
Heuristic Algorithm ◽  
Real World ◽  
Design Problem ◽  
Large Scale ◽  
Territory Design

scholarly journals Robust Optimization Model for Bi-objective Emergency Medical Service Design Problem with Demand Uncertainty

2019 ◽  
Vol 20 (2) ◽  
pp. 95
Author(s):  
Diah Chaerani ◽  
Siti Rabiatul Adawiyah ◽  
Eman Lesmana
Keyword(s):  
Robust Optimization ◽  
Emergency Medical Service ◽  
Design Problem ◽  
Medical Service ◽  
Optimal Solution ◽  
Service Design ◽  
Mixed Integer ◽  
Worst Case ◽  
Robust Counterpart ◽  
Emergency Medical

Bi-objective Emergency Medical Service Design Problem is a problem to determining the location of the station Emergency Medical Service among all candidate station location, the determination of the number of emergency vehicles allocated to stations being built so as to serve medical demand. This problem is a multi-objective problem that has two objective functions that minimize cost and maximize service. In real case there is often uncertainty in the model such as the number of demand. To deal the uncertainty on the bi-objective emergency medical service problem is using Robust Optimization which gave optimal solution even in the worst case. Model Bi-objective Emergency Medical Service Design Problem is formulated using Mixed Integer Programming. In this research, Robust Optimization is formulated for Bi-objective Emergency Medical Service Design Problem through Robust Counterpart formulation by assuming uncertainty in demand is box uncertainty and ellipsoidal uncertainty set. We show that in the case of bi-objective optimization problem, the robust counterpart remains computationally tractable. The example is performed using Lexicographic Method and Branch and Bound Method to obtain optimal solution. 

scholarly journals Some Computational Insights on the Optimal Bus Transit Route Network Design Problem

2012 ◽  
Vol 47 (3) ◽  
Author(s):  
Wei (David) Fan ◽  
Randy B. Machemehl
Keyword(s):  
Network Design ◽  
Design Problem ◽  
Large Scale ◽  
Network Design Problem ◽  
Mixed Integer ◽  
Research Experiences ◽  
Bus Transit ◽  
Route Network ◽  
Transit Route ◽  
Demand Aggregation

The objective of this paper is to present some computational insights based on previous extensive research experiences on the optimal bus transit route network design problem (BTRNDP) with zonal demand aggregation and variable transit demand. A multi-objective, nonlinear mixed integer model is developed. A general meta-heuristics-based solution methodology is proposed. Genetic algorithms (GA), simulated annealing (SA), and a combination of the GA and SA are implemented and compared to solve the BTRNDP. Computational results show that zonal demand aggregation is necessary and combining metaheuristic algorithms to solve the large scale BTRNDP is very promising.

Study and Application on Real Time Optimum Operation for Plant Units

2005 ◽  
Author(s):  
Yanfen Liao ◽  
Jiejin Cai ◽  
Xiaoqian Ma
Keyword(s):  
Power Plant ◽  
Large Scale ◽  
Unit Commitment ◽  
Operating Cost ◽  
Target Function ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Coal Consumption ◽  
Allocation Model ◽  
Load Demand

The optimum unit commitment is to determine an optimal scheme which can minimize the system operating cost during a period while the load demand, operation constrains of the individual unit are simultaneously satisfied. Since it is characterized as a nonlinear, large scale, discrete, mixed-integer combinatorial optimization problem with constrains, it is always hard to find out the theoretical optimal solution. In this paper, a method combining the priority-order with dynamic comparison is brought out to obtain an engineering optimal solution, and is validated in a power plant composed of three 200MW and two 300MW units. Through simulating the on-line running datum from the DCS system in the power plant, the operating cost curves are obtained in different units, startup/shut-down mode and load demand. According to these curves, an optimum unit commitment model is established based on equal incremental rate principle principle. Make target function be minimum gross coal consumption, the results show that compared with the duty-chief-mode that allocates the load based on operators’ experience, the units’ mean gross coal consumption rate is reduced about 0.5g/(kW·h) when operating by this unit commitment model, and its economic profit is far more than the load economic allocation model that doesn’t considered the units’ start-up/shut-down.

scholarly journals Optimizing Painting Sequence Scheduling Based on Adaptive Partheno-Genetic Algorithm

Processes ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1714
Author(s):  
Jun Yang ◽  
Tong Sun ◽  
Xiuxiang Huang ◽  
Ke Peng ◽  
Zhongxiang Chen ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Programming Problem ◽  
Large Scale ◽  
Scheduling Algorithm ◽  
Real Life ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Rule Based ◽  
Multi Objective ◽  
Color Changes

In this paper, we formulate and solve a novel real-life large-scale automotive parts paint shop scheduling problem, which contains color arrangement restrictions, part arrangement restrictions, bracket restrictions, and multi-objectives. Based on these restrictions, we construct exact constraints and two objective functions to form a large-scale multi-objective mixed-integer linear programming problem. To reduce this scheduling problem’s complexity, we converted the multi-objective model into a multi-level objective programming problem by combining the rule-based scheduling algorithm and the adaptive Partheno-Genetic algorithm. The rule-based scheduling algorithm is adopted to optimize color changes horizontally and bracket replacements vertically. The adaptive Partheno-Genetic algorithm is designed to optimize production based on the rule-based scheduling algorithm. Finally, we apply the model to the actual optimization problem that contained 829,684 variables and 137,319 constraints, and solved this problem by Python. The proposed method solves the optimal solution, consuming 575 s.

scholarly journals UAV Task Allocation Based on Clone Selection Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiaopan Zhang ◽  
Xingjun Chen
Keyword(s):  
Task Allocation ◽  
Large Scale ◽  
Optimal Solution ◽  
Allocation Problem ◽  
Network Technology ◽  
Selection Algorithm ◽  
Intelligent Optimization ◽  
Optimization Control ◽  
Np Hard Problem ◽  
Multi Uav

With the continuous development of computer and network technology, the large-scale and clustered operations of drones have gradually become a reality. How to realize the reasonable allocation of UAV cluster combat tasks and realize the intelligent optimization control of UAV cluster is one of the most challenging difficulties in UAV cluster combat. Solving the task allocation problem and finding the optimal solution have been proven to be an NP-hard problem. This paper proposes a CSA-based approach to simultaneously optimize four objectives in multi-UAV task allocation, i.e., maximizing the number of successfully allocated tasks, maximizing the benefits of executing tasks, minimizing resource costs, and minimizing time costs. Experimental results show that, compared with the genetic algorithm, the proposed method has better performance on solving the UAV task allocation problem with multiple objectives.

scholarly journals A Hybrid Approach Using an Artificial Bee Algorithm with Mixed Integer Programming Applied to a Large-Scale Capacitated Facility Location Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Guillermo Cabrera G. ◽  
Enrique Cabrera ◽  
Ricardo Soto ◽  
L. Jose Miguel Rubio ◽  
Broderick Crawford ◽  
...  
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Large Scale ◽  
Location Problem ◽  
Hybrid Approach ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Mixed Integer ◽  
Capacitated Facility Location Problem ◽  
Capacitated Facility Location

We present a hybridization of two different approaches applied to the well-known Capacitated Facility Location Problem (CFLP). The Artificial Bee algorithm (BA) is used to select a promising subset of locations (warehouses) which are solely included in the Mixed Integer Programming (MIP) model. Next, the algorithm solves the subproblem by considering the entire set of customers. The hybrid implementation allows us to bypass certain inherited weaknesses of each algorithm, which means that we are able to find an optimal solution in an acceptable computational time. In this paper we demonstrate that BA can be significantly improved by use of the MIP algorithm. At the same time, our hybrid implementation allows the MIP algorithm to reach the optimal solution in a considerably shorter time than is needed to solve the model using the entire dataset directly within the model. Our hybrid approach outperforms the results obtained by each technique separately. It is able to find the optimal solution in a shorter time than each technique on its own, and the results are highly competitive with the state-of-the-art in large-scale optimization. Furthermore, according to our results, combining the BA with a mathematical programming approach appears to be an interesting research area in combinatorial optimization.

scholarly journals Incorporating Location Aspects in Process Integration Methodology

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3338 ◽  
Author(s):  
Hür Bütün ◽  
Ivan Kantor ◽  
François Maréchal
Keyword(s):  
Large Scale ◽  
Process Integration ◽  
Optimal Solution ◽  
Economic Feasibility ◽  
Mixed Integer ◽  
Industrial Plants ◽  
Pressure Steam ◽  
The Cost ◽  
Business As Usual ◽  
The Impact

The large potential for waste resource and heat recovery in industry has been motivating research toward increasing efficiency. Process integration methods have proven to be effective tools in improving industrial sites while decreasing their resource and energy consumption; however, location aspects and their impact are generally overlooked. This paper presents a method based on process integration, which considers the location of plants. The impact of the locations is included within the mixed integer linear programming framework in the form of heat losses, temperature and pressure drop, and piping cost. The objective function is selected as minimisation of the total cost of the system excluding piping cost and ϵ -constraints are applied on the piping cost to systematically generate multiple solutions. The method is applied to a case study with industrial plants from different sectors. First, the interaction between two plants and their utility integration are illustrated, depending on the piping cost limit which results in the heat pump and boiler on one site being gradually replaced by excess heat recovered from the other plant. Then, the optimisation of the whole system is carried out, as a large-scale application. At low piping cost allowances, heat is shared through high pressure steam in above-ground pipes, while at higher piping cost limits the system switches toward lower pressure steam sharing in underground pipes. Compared to the business-as-usual operation of the sites, the optimal solution obtained with the proposed method leads to 20% reduction in the overall cost of the system, including the piping cost. Further reduction in the cost is possible using a state of the art method but the technical and economic feasibility is not guaranteed. Thus, the present work provides a tool to find optimal industrial symbiosis solutions under different investment limits on the infrastructure between plants.

Strategic-Level Robust Optimal Design Method of Product Family and Supply Chain Network

2018 ◽  
Author(s):  
Masato Toi ◽  
Kana Sawai ◽  
Yutaka Nomaguchi ◽  
Kikuo Fujita
Keyword(s):  
Supply Chain ◽  
Design Problem ◽  
Design Method ◽  
Product Family ◽  
Optimal Solution ◽  
Computational Method ◽  
Mixed Integer ◽  
Mathematical Framework ◽  
Integer Programming Problem ◽  
Supply Chain Network

Manufacturing firms must meet a wide variety of customer needs flexibly and effectively. Thus, simultaneous design of the product family and the supply chain network is required. This design problem must be assessed in terms of strategic-level decision making under uncertainties without any detailed and fixed information on the design conditions. We therefore propose a mathematical framework by considering the optimal profitability and robustness against destructive incidences. This paper discusses the design problem structure and formulates it as a mixed-integer programming problem. A computational method is configured for solving the optimization problem, in which only profitability is considered as the objective. A procedure to assess the robustness of the profitability-oriented optimal solution is proposed by evaluating the Pareto optimality among the nominal optimal solution and its competitive solutions. A case study of a coffee maker product family design problem is demonstrated to verify the proposed framework.

scholarly journals An Extended Stochastic Goal Mixed Integer Programming for Optimal Portfolio Selection in the Amman Stock Exchange

2019 ◽  
Vol 10 (2) ◽  
pp. 36
Author(s):  
Rula Hani Salman AlHalaseh ◽  
Aminul Islam ◽  
Rosni Bakar
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Portfolio Selection ◽  
Large Scale ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Financial Instrument ◽  
Main Challenge ◽  
Time Period ◽  
Future Time Period

This paper optimally solves the portfolio selection problem that consists of multi assets in a continuous time period to achieve the optimal trade-off between multi-objectives. In this paper, the Stochastic Goal Mixed Integer programming of Stoyan (2009) is extended. The empirical contributions of this research presented on extending the SGMIP model by adding information as a new factor that selects the portfolio elements. The information element used as a portfolio managing characteristics to see whether it is applicable for different problems. The data was collected on a daily basis for all the parameters of the individual stock. Brownian motion formula was used to predict the stock price in the future time period. SP framework used to capture numerous sources of uncertainty and to formulate the portfolio problem. The main challenge of this model is that it contains additional real-world objective and multi types of financial assets, which form a Mixed Integer Programming (MIP). This large-scale problem solved using Optimising Programming Language (OPL) and decomposition algorithm to improve the memory allocation and CPU time. A fascinating result was obtained from the portfolio algorithm design. The ESGMIP portfolio outperforms the Index portfolio return. Under uncertain environment, the availability of information rationalized the diversity when the dynamic portfolio invested in one financial instrument (stocks), and tend to be diversifiable when invested in more than one financial instrument (stock and bond). This work presents a novel extended SGMIP model to reach an optimal solution.

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