scholarly journals A Redesigned Benders Decomposition Approach for Large-Scale In-Transit Freight Consolidation Operations

2018 ◽  
Vol 11 (2) ◽  
pp. 1-15 ◽  
Author(s):  
Abdulkader S. Hanbazazah ◽  
Luis E. Abril ◽  
Nazrul I. Shaikh ◽  
Murat Erkoc
Keyword(s):  
Large Scale ◽  
Benders Decomposition ◽  
Scale Up ◽  
Third Party ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Due Dates ◽  
Decomposition Approach ◽  
Freight Consolidation ◽  
In Transit

The growth in online shopping and third-party logistics has caused a revival of interest in finding optimal solutions to the large-scale, in-transit freight consolidation problem. Given the shipment date, size, origin, destination, and due dates of multiple shipments distributed over space and time, the problem requires determining when to consolidate some of these shipments into one shipment at an intermediate consolidation point so as to minimize shipping costs while satisfying the due date constraints. In this article, the authors develop a mixed-integer programming formulation for a multi-period freight consolidation problem that involves multiple products, suppliers, and potential consolidation points. Benders decomposition is then used to replace a large number of integer freight-consolidation variables by a small number of continuous variables that reduce the size of the problem without impacting optimality. The results show that Benders decomposition provides a significant scale-up in the performance of the solver. The authors demonstrate their approach using a large-scale case with more than 27.5 million variables and 9.2 million constraints.

scholarly journals Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy

2020 ◽  
Vol 66 (7) ◽  
pp. 3051-3068 ◽  
Author(s):  
Daniel Baena ◽  
Jordi Castro ◽  
Antonio Frangioni
Keyword(s):  
Data Privacy ◽  
Large Scale ◽  
Benders Decomposition ◽  
Mixed Integer ◽  
Master Problem ◽  
Continuous Variables ◽  
Typical Structure ◽  
Disclosure Control ◽  
Current State ◽  
Statistical Disclosure

The cell-suppression problem (CSP) is a very large mixed-integer linear problem arising in statistical disclosure control. However, CSP has the typical structure that allows application of the Benders decomposition, which is known to suffer from oscillation and slow convergence, compounded with the fact that the master problem is combinatorial. To overcome this drawback, we present a stabilized Benders decomposition whose master is restricted to a neighborhood of successful candidates by local-branching constraints, which are dynamically adjusted, and even dropped, during the iterations. Our experiments with synthetic and real-world instances with up to 24,000 binary variables, 181 million (M) continuous variables, and 367M constraints show that our approach is competitive with both the current state-of-the-art code for CSP and the Benders implementation in CPLEX 12.7. In some instances, stabilized Benders provided a very good solution in less than 1 minute, whereas the other approaches found no feasible solution in 1 hour. This paper was accepted by Yinyu Ye, optimization.

Integrated Scheduling for a Multi-Product Pipeline Network With Delivery Due Dates

2018 ◽  
Author(s):  
Ning Xu ◽  
Qi Liao ◽  
Yongtu Liang ◽  
Zhengbing Li ◽  
Haoran Zhang
Keyword(s):  
Time Horizon ◽  
Large Scale ◽  
Mixed Integer ◽  
Market Demand ◽  
Due Dates ◽  
Long Distance ◽  
Decomposition Approach ◽  
Pipeline Network ◽  
Integrated Scheduling ◽  
Product Pipeline

Currently, pipeline is the most effective way to transport large-volume products over long distance. To effectively satisfy market demands for multiple refined products by delivery due dates, the multi-product pipeline network usually transports several refined products in sequence from refineries to certain destinations. The integrated scheduling of multi-product pipeline network, including inventory management, transport routes planning, batch sequence, batch volume, et al., is one of the most strategic problems due to its large-scale, complexity as well as economic significance. This subject has been widely studied during the last decade. However, most researches focus on large-size scheduling models whose computational efficiency greatly decreases for a complex pipeline network or a long time horizon. Aiming at this problem, the paper develops an efficient decomposition approach, which is composed of two mixed integer linear programming (MILP) models. The first model divides the entire time horizon into several intervals according to delivery due dates and optimizes the transport routes and total transport volume during each interval with considering market demand, production campaigns and inventory limits. Then the solved results are used by the second model which sets the objective function as the membership function based on fuzzy delivery due dates. Besides, a series of operational constraints are also considered in the second model to obtain the optimal batch sequence, batch volume, delivery volume and delivery time in each node. Finally, the proposed approach is applied to a Chinese real-world pipeline network that includes 5 complex multi-product pipelines associated with 6 refineries and 2 depots. The results demonstrate that the proposed approach can provide a guideline for long-term pipeline network scheduling with delivery due dates.

The Star Degree Centrality Problem: A Decomposition Approach

2021 ◽  
Author(s):  
Mustafa C. Camur ◽  
Thomas Sharkey ◽  
Chrysafis Vogiatzis
Keyword(s):  
Integer Programming ◽  
Large Scale ◽  
Benders Decomposition ◽  
Open Neighborhood ◽  
Decomposition Algorithm ◽  
Solution Time ◽  
Set Cover ◽  
Degree Centrality ◽  
Decomposition Approach ◽  
Acceleration Techniques

We consider the problem of identifying the induced star with the largest cardinality open neighborhood in a graph. This problem, also known as the star degree centrality (SDC) problem, is shown to be [Formula: see text]-complete. In this work, we first propose a new integer programming (IP) formulation, which has a smaller number of constraints and nonzero coefficients in them than the existing formulation in the literature. We present classes of networks in which the problem is solvable in polynomial time and offer a new proof of [Formula: see text]-completeness that shows the problem remains [Formula: see text]-complete for both bipartite and split graphs. In addition, we propose a decomposition framework that is suitable for both the existing and our formulations. We implement several acceleration techniques in this framework, motivated by techniques used in Benders decomposition. We test our approaches on networks generated based on the Barabási–Albert, Erdös–Rényi, and Watts–Strogatz models. Our decomposition approach outperforms solving the IP formulations in most of the instances in terms of both solution time and quality; this is especially true for larger and denser graphs. We then test the decomposition algorithm on large-scale protein–protein interaction networks, for which SDC is shown to be an important centrality metric. Summary of Contribution: In this study, we first introduce a new integer programming (NIP) formulation for the star degree centrality (SDC) problem in which the goal is to identify the induced star with the largest open neighborhood. We then show that, although the SDC can be efficiently solved in tree graphs, it remains [Formula: see text]-complete in both split and bipartite graphs via a reduction performed from the set cover problem. In addition, we implement a decomposition algorithm motivated by Benders decomposition together with several acceleration techniques to both the NIP formulation and the existing formulation in the literature. Our experimental results indicate that the decomposition implementation on the NIP is the best solution method in terms of both solution time and quality.

scholarly journals Optimal Torpedo Scheduling

2018 ◽  
Vol 63 ◽  
pp. 955-986 ◽  
Author(s):  
Adrian Goldwaser ◽  
Andreas Schutt
Keyword(s):  
Large Scale ◽  
Benders Decomposition ◽  
Steel Production ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Hot Metal ◽  
Rail Network ◽  
Sulfur Level ◽  
First Time ◽  
Resource Capacity

We consider the torpedo scheduling problem in steel production, which is concerned with the transport of hot metal from a blast furnace to an oxygen converter. A schedule must satisfy, amongst other considerations, resource capacity constraints along the path and the locations traversed as well as the sulfur level of the hot metal. The goal is first to minimize the number of torpedo cars used during the planning horizon and second to minimize the time spent desulfurizing the hot metal. We propose an exact solution method based on Logic based Benders Decomposition using Mixed-Integer and Constraint Programming, which optimally solves and proves, for the first time, the optimality of all instances from the ACP Challenge 2016 within 10 minutes. In addition, we adapted our method to handle large-scale instances and instances with a more general rail network. This adaptation optimally solved all challenge instances within one minute and was able to solve instances of up to 100,000 hot metal pickups.

scholarly journals Micro Grid Energy Management using DE Algorithm with BDC theorem

2019 ◽  
Vol 8 (4S2) ◽  
pp. 334-338
Keyword(s):  
Power Plants ◽  
Large Scale ◽  
Benders Decomposition ◽  
Reactive Power ◽  
Differential Evolution Algorithm ◽  
Decomposition Theorem ◽  
Drop Out ◽  
Mixed Integer ◽  
De Algorithm ◽  
Micro Grid

this paper evaluates combination of DE algorithm and benders decomposition theorem of VMG is used to solving the large scale mixed integer programming problems. DE algorithm is implemented in Village area Micro grids. Village area micro grid and the required load is calculated regarding the sold out power or purchase power with the help of DE algorithm. Differential evolution algorithm is applied in the village area micro grid and measure the real power, reactive power of various power plants. . In this DE algorithm is implemented in village area micro grid and the survey period is two years. Final survey shows which month produce more power and sold out power in nearest city area electricity board, But in power shortage in village area micro grid ,it purchase the power from nearest electricity board.DE algorithm determine the one month power survey and benders decomposition determine the individual value of the power plants. But the benders decomposition theorem is not accept the non linearity items. To overcome this problem BDCT and DEA is implemented in village area micro grid. This combination is used to maintain the drop out voltage of any power plants.

Solving an Integrated Sales-Leasing Problem With Remanufacturing and Inventory Shortage Using Differential Evolution

2018 ◽  
Vol 9 (3) ◽  
pp. 1-26
Author(s):  
Masoud Rabbani ◽  
Sina Keyhanian ◽  
Mojtaba Aryaee ◽  
Esmat Sangari
Keyword(s):  
Differential Evolution ◽  
Large Scale ◽  
High Sensitivity ◽  
Third Party ◽  
Mixed Integer ◽  
Heuristic Solution ◽  
Optimal Amount ◽  
Solution Approach ◽  
De Algorithm ◽  
Non Linear

In this article, an integrated sales and leasing company is considered. This company remanufactures leased products at the end of operating lease contracts to make them as good as new ones and sell them to the customers. In order to satisfy customers' demand, required products are provided from a third-party when the company meets inventory shortage. Non-linear competitive demand functions are used which are sensitive to manufacturer suggested retail price (MSRP) and inflation rate. A mixed integer non-linear mathematical model (MINLP) is developed to determine optimal price of selling products, optimal amount of monthly payments in leasing contracts, and optimal inventory control planning, i.e. the optimal amount of manufacturing and remanufacturing products and optimal inventory levels. The main objective is to maximize net profit of the company. Small, medium and large-scale sizes of the model are solved to show the applicability of the model. To solve the large-scale problem, differential evolution (DE) algorithm is applied as a meta-heuristic solution approach. Numerical results show high sensitivity of model to demands. Also, optimal trend behaviors of some main variables of the problem seem similar to the competitive behavior of demands.

A two-stage skilled manpower planning model with demand uncertainty

2018 ◽  
Vol 11 (4) ◽  
pp. 526-551 ◽  
Author(s):  
Mohsen Sadeghi-Dastaki ◽  
Abbas Afrazeh
Keyword(s):  
Large Scale ◽  
Demand Uncertainty ◽  
Benders Decomposition ◽  
Latin Hypercube Sampling ◽  
Sample Average Approximation ◽  
Manpower Planning ◽  
Mixed Integer ◽  
Planning Model ◽  
Two Stage ◽  
Content Type

Purpose Human resources are one of the most important and effective elements for companies. In other words, employees are a competitive advantage. This issue is more vital in the supply chains and production systems, because of high need for manpower in the different specification. Therefore, manpower planning is an important, essential and complex task. The purpose of this paper is to present a manpower planning model for production departments. The authors consider workforce with individual and hierarchical skills with skill substitution in the planning. Assuming workforce demand as a factor of uncertainty, a two-stage stochastic model is proposed. Design/methodology/approach To solve the proposed mixed-integer model in the real-world cases and large-scale problems, a Benders’ decomposition algorithm is introduced. Some test instances are solved, with scenarios generated by Monte Carlo method. For some test instances, to find the number of suitable scenarios, the authors use the sample average approximation method and to generate scenarios, the authors use Latin hypercube sampling method. Findings The results show a reasonable performance in terms of both quality and solution time. Finally, the paper concludes with some analysis of the results and suggestions for further research. Originality/value Researchers have attracted to other uncertainty factors such as costs and products demand in the literature, and have little attention to workforce demand as an uncertainty factor. Furthermore, most of the time, researchers assume that there is no difference between the education level and skill, while they are not necessarily equivalent. Hence, this paper enters these elements into decision making.

scholarly journals A Benders’ Decomposition Approach for Renewable Generation Investment in Distribution Systems

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1225 ◽  
Author(s):  
Sergio Montoya-Bueno ◽  
Jose Muñoz-Hernandez ◽  
Javier Contreras ◽  
Luis Baringo
Keyword(s):  
Distribution Systems ◽  
Benders Decomposition ◽  
Renewable Energy Sources ◽  
Mixed Integer ◽  
Planning Period ◽  
Decomposition Approach ◽  
Generation Planning ◽  
Operation Costs ◽  
Proposed Model ◽  
The Cost

A model suitable to obtain where and when renewable energy sources (RES) should be allocated as part of generation planning in distribution systems is formulated. The proposed model starts from an existing two-stage stochastic mixed-integer linear programming (MILP) problem including investment and scenario-dependent operation decisions. The aim is to minimize photovoltaic and wind investment costs, operation costs, as well as total substation costs including the cost of the energy bought from substations and energy losses. A new Benders’ decomposition framework is used to decouple the problem between investment and operation decisions, where the latter can be further decomposed into a set of smaller problems per scenario and planning period. The model is applied to a 34-bus system and a comparison with a MILP model is presented to show the advantages of the model proposed.

scholarly journals Routing Optimisation of Urban Medical Waste Recycling Network considering Differentiated Collection Strategy and Time Windows

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jiajing Gao ◽  
Haolin Li ◽  
Jingwen Wu ◽  
Junyan Lyu ◽  
Zheyi Tan ◽  
...  
Keyword(s):  
Large Scale ◽  
Programming Model ◽  
Time Windows ◽  
Computation Time ◽  
Waste Recycling ◽  
Medical Waste ◽  
Third Party ◽  
Mixed Integer ◽  
Routing Problem ◽  
Solution Approach

The increasing gap between medical waste production and disposal stresses the urgency of further development of urban medical waste recycling. This paper investigates an integrated optimisation problem in urban medical waste recycling network. It combines the vehicle routing problem of medical facilities with different requirements and the collection problem of clinics’ medical waste to the affiliated hospital. To solve this problem, a compact mixed-integer linear programming model is proposed, which takes account of the differentiated collection strategy and time windows. Since the medical waste recycling operates according to a two-day pattern, the periodic collection plan is also embedded in the model. Moreover, we develop a particle swarm optimisation (PSO) solution approach for problem-solving. Numerical experiments are also conducted to access the solution efficiency of the proposed algorithm, which can obtain a good solution in solving large-scale problem instances within a reasonable computation time. Based on the results, some managerial implications can be recommended for the third-party recycling company.

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