scholarly journals A Parallelized Variable Fixing Process for Solving Multistage Stochastic Programs with Progressive Hedging

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Martin B. Bagaram ◽  
Sándor F. Tóth ◽  
Weikko S. Jaross ◽  
Andrés Weintraub
Keyword(s):  
Forest Management ◽  
Probability Space ◽  
Forest Growth ◽  
Scenario Tree ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Scheduling Problems ◽  
Harvest Scheduling ◽  
Progressive Hedging ◽  
Climate Uncertainty

Long time horizons, typical of forest management, make planning more difficult due to added exposure to climate uncertainty. Current methods for stochastic programming limit the incorporation of climate uncertainty in forest management planning. To account for climate uncertainty in forest harvest scheduling, we discretize the potential distribution of forest growth under different climate scenarios and solve the resulting stochastic mixed integer program. Increasing the number of scenarios allows for a better approximation of the entire probability space of future forest growth but at a computational expense. To address this shortcoming, we propose a new heuristic algorithm designed to work well with multistage stochastic harvest-scheduling problems. Starting from the root-node of the scenario tree that represents the discretized probability space, our progressive hedging algorithm sequentially fixes the values of decision variables associated with scenarios that share the same path up to a given node. Once all variables from a node are fixed, the problem can be decomposed into subproblems that can be solved independently. We tested the algorithm performance on six forests considering different numbers of scenarios. The results showed that our algorithm performed well when the number of scenarios was large.

scholarly journals A GRASP Approach for Solving Large-Scale Electric Bus Scheduling Problems

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6610
Author(s):  
Raka Jovanovic ◽  
Islam Safak Bayram ◽  
Sertac Bayhan ◽  
Stefan Voß
Keyword(s):  
Public Transport ◽  
High Speed ◽  
Large Scale ◽  
Integer Program ◽  
Mixed Integer ◽  
Transport Systems ◽  
Mixed Integer Program ◽  
Scheduling Problems ◽  
Electric Bus ◽  
Battery Capacity

Electrifying public bus transportation is a critical step in reaching net-zero goals. In this paper, the focus is on the problem of optimal scheduling of an electric bus (EB) fleet to cover a public transport timetable. The problem is modelled using a mixed integer program (MIP) in which the charging time of an EB is pertinent to the battery’s state-of-charge level. To be able to solve large problem instances corresponding to real-world applications of the model, a metaheuristic approach is investigated. To be more precise, a greedy randomized adaptive search procedure (GRASP) algorithm is developed and its performance is evaluated against optimal solutions acquired using the MIP. The GRASP algorithm is used for case studies on several public transport systems having various properties and sizes. The analysis focuses on the relation between EB ranges (battery capacity) and required charging rates (in kW) on the size of the fleet needed to cover a public transport timetable. The results of the conducted computational experiments indicate that an increase in infrastructure investment through high speed chargers can significantly decrease the size of the necessary fleets. The results also show that high speed chargers have a more significant impact than an increase in battery sizes of the EBs.

scholarly journals Partitioning and solving large-scale tactical harvest scheduling problems for industrial plantation forests

2020 ◽  
Vol 50 (8) ◽  
pp. 811-818
Author(s):  
Pedro Bellavenutte ◽  
Woodam Chung ◽  
Luis Diaz-Balteiro
Keyword(s):  
Large Scale ◽  
Optimization Procedure ◽  
Mixed Integer ◽  
Forest Planning ◽  
Planning Problem ◽  
Optimization Approach ◽  
Scheduling Problems ◽  
Harvest Scheduling ◽  
Plantation Forests ◽  
Industrial Plantation

Spatially explicit, tactical forest planning is a necessary but challenging task in the management of plantation forests. It involves harvest scheduling and planning for road access and log transportation over time and space. This combinatorial problem can be formulated into the fixed-charge transportation problem (FCTP), in which the sum of fixed and variable costs is minimized while meeting harvest volume requirements and allowing necessary road maintenance and log hauling activities. The problem can be solved using general optimization methods such as mixed-integer linear programming (MILP), but the computational efficiency of the MILP-based approach quickly drops as the size and complexity of the problem increases. We developed a new optimization procedure that partitions the large planning problem into smaller subproblems. We applied a hybrid optimization approach using both MILP and heuristic rules to efficiently solve the large FCTP that otherwise may not be solvable using traditional methods. We applied our approach to an industrial plantation forest in Brazil. Our applications demonstrate the performance of the new optimization procedure and the benefit of solving large forest planning problems that integrate harvest scheduling with road access and transportation.

Allowable cut effects without even flow constraints

1984 ◽  
Vol 14 (3) ◽  
pp. 317-320 ◽  
Author(s):  
Clark S. Binkley
Keyword(s):  
Forest Management ◽  
Economic Analysis ◽  
General Situation ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Harvest Scheduling ◽  
General Part ◽  
Flow Constraints

The allowable cut effect in harvest scheduling problems stems from the constraints which link harvests between periods. Historically, allowable cut effects have been associated with even flow constraints, but this is only one example of a more general situation. This paper describes two generic problems where allowable cut effects arise without any flow constraint. Allowable cut effects are a general part of the harvest scheduling problem. Valid economic analysis of forest management programs requires the inclusion of the positive or negative incomes associated with them.

scholarly journals Sustainable Scheduling of the Production in the Aluminum Furnace Hot Rolling Section with Uncertain Demand

2021 ◽  
Vol 13 (14) ◽  
pp. 7708
Author(s):  
Yiping Huang ◽  
Qin Yang ◽  
Jinfeng Liu ◽  
Xiao Li ◽  
Jie Zhang
Keyword(s):  
Hot Rolling ◽  
Production Scheduling ◽  
Demand Uncertainty ◽  
Flow Shop ◽  
Operation Time ◽  
Decision Time ◽  
Scenario Tree ◽  
Mixed Integer ◽  
Rolling Horizon ◽  
The Sustainable Development

In order to reduce the energy consumption of furnaces and save costs in the product delivery time, the focus of this paper is to discuss the uncertainty of demand in the rolling horizon and to globally optimize the sustainability of the production in the aluminum furnace hot rolling section in environmental and economic dimensions. First, the triples α/β/γ are used to describe the production scheduling in the aluminum furnace hot rolling section as the scheduling of flexible flow shop, satisfied to constraints of demand uncertainty, operation logic, operation time, capacity and demand, objectives of minimizing the residence time of the ingot in the furnace and minimizing the makespan. Second, on the basis of describing the uncertainty of demand in rolling horizon with the scenario tree, a multi-objective mixed integer linear programming (MILP) optimization model for sustainable production in the aluminum furnace hot rolling section is formulated. Finally, an aluminum alloy manufacturer is taken as an example to illustrate the proposed model. The computational results show that when the objective weight combination takes the value of α=0.7, β=0.3, the sustainability indicators of the environmental and economic dimensions can be optimized to the maximum extent possible at the same time. Increasingly, managerial suggestions associated with the trade-off between environmental and economic dimensions are presented. Scheduling in the rolling horizon can optimize the production process of the aluminum furnace hot rolling section globally, indicating that it is more conducive to the sustainable development of the environment and economic dimensions than scheduling in a single decision time period.

A stochastic mixed integer program to model spatial wildfire behavior and suppression placement decisions with uncertain weather

2016 ◽  
Vol 46 (2) ◽  
pp. 234-248 ◽  
Author(s):  
Erin J. Belval ◽  
Yu Wei ◽  
Michael Bevers
Keyword(s):  
Wildland Fire ◽  
Fire Behavior ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Weather Forecasts ◽  
Placement Decisions ◽  
Weather Events ◽  
Weather Changes ◽  
Nonanticipativity Constraints

Wildfire behavior is a complex and stochastic phenomenon that can present unique tactical management challenges. This paper investigates a multistage stochastic mixed integer program with full recourse to model spatially explicit fire behavior and to select suppression locations for a wildland fire. Simplified suppression decisions take the form of “suppression nodes”, which are placed on a raster landscape for multiple decision stages. Weather scenarios are used to represent a distribution of probable changes in fire behavior in response to random weather changes, modeled using probabilistic weather trees. Multistage suppression decisions and fire behavior respond to these weather events and to each other. Nonanticipativity constraints ensure that suppression decisions account for uncertainty in weather forecasts. Test cases for this model provide examples of fire behavior interacting with suppression to achieve a minimum expected area impacted by fire and suppression.

A Priority-Slot Based Continuous-Time Formulation for Crude-Oil Scheduling Problems with Oil Residency Time Constraint

2014 ◽  
Vol 998-999 ◽  
pp. 1532-1535
Author(s):  
Yu Ming Zhao
Keyword(s):  
Crude Oil ◽  
Time Constraint ◽  
Mixed Integer ◽  
Scheduling Problems ◽  
Operation Sequencing ◽  
The Past ◽  
Time Formulation ◽  
New Formulation ◽  
Single Sequence ◽  
Residency Time

The optimal scheduling of crude-oil operation in refineries has been studied by various groups during the past decade leading to different mixed integer linear programming or mixed nonlinear programming formulations. This paper presents a new formulation with oil residency time constraint based on single-operation sequencing (SOS). It is different from previous formulations as it considers oil residency time constraint and pipeline transfer and does not require to postulate the number of priority-slots in which operations take place. This model is also based on the representation of a crude-oil scheduling by a single sequence of transfer operations. A simple MILP procedure has been used to solve this model leading to an satisfactory optimal result.

A Note on a Conceptual Framework for Dynamic Location—Allocation Analysis

1976 ◽  
Vol 8 (4) ◽  
pp. 443-446
Author(s):  
W G Truscott
Keyword(s):  
Conceptual Framework ◽  
Integer Program ◽  
Original Version ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Location Allocation ◽  
Dynamic Location

This note examines a previously published model for dynamic location—allocation analysis. The usefulness of this model is enhanced by reformulating the problem as an operational zero-one, mixed-integer program while retaining the intent of the original version.

Design of hydrogen supply chains under demand uncertainty – a case study of passenger transport in Germany

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anton Ochoa Bique ◽  
Leonardo K. K. Maia ◽  
Ignacio E. Grossmann ◽  
Edwin Zondervan
Keyword(s):  
Stochastic Optimization ◽  
Demand Uncertainty ◽  
Programming Model ◽  
Cost Minimization ◽  
Water Electrolysis ◽  
Scenario Tree ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Strong Impact ◽  
Hydrogen Supply

Abstract A strategy for the design of a hydrogen supply chain (HSC) network in Germany incorporating the uncertainty in the hydrogen demand is proposed. Based on univariate sensitivity analysis, uncertainty in hydrogen demand has a very strong impact on the overall system costs. Therefore we consider a scenario tree for a stochastic mixed integer linear programming model that incorporates the uncertainty in the hydrogen demand. The model consists of two configurations, which are analyzed and compared to each other according to production types: water electrolysis versus steam methane reforming. Each configuration has a cost minimization target. The concept of value of stochastic solution (VSS) is used to evaluate the stochastic optimization results and compare them to their deterministic counterpart. The VSS of each configuration shows significant benefits of a stochastic optimization approach for the model presented in this study, corresponding up to 26% of infrastructure investments savings.

Modeling and scheduling hybrid open shops for makespan minimization

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kennedy Anderson Guimarães de Araújo ◽  
Tiberius Oliveira e Bonates ◽  
Bruno de Athayde Prata
Keyword(s):  
Programming Model ◽  
Computing Time ◽  
Iterated Local Search ◽  
Mixed Integer ◽  
Scheduling Problems ◽  
Priority Rules ◽  
Production Flow ◽  
Solution Quality ◽  
Content Type ◽  
Constructive Heuristics

Purpose This study aims to address the hybrid open shop problem (HOSP) with respect to the minimization of the overall finishing time or makespan. In the HOSP, we have to process n jobs in stages without preemption. Each job must be processed once in every stage, there is a set of mk identical machines in stage k and the production flow is immaterial. Design/methodology/approach Computational experiments carried out on a set of randomly generated instances showed that the minimal idleness heuristic (MIH) priority rule outperforms the longest processing time (LPT) rule proposed in the literature and the other proposed constructive methods on most instances. Findings The proposed mathematical model outperformed the existing model in the literature with respect to computing time, for small-sized instances, and solution quality within a time limit, for medium- and large-sized instances. The authors’ hybrid iterated local search (ILS) improved the solutions of the MIH rule, drastically outperforming the models on large-sized instances with respect to solution quality. Originality/value The authors formalize the HOSP, as well as argue its NP-hardness, and propose a mixed integer linear programming model to solve it. The authors propose several priority rules – constructive heuristics based on priority measures – for finding feasible solutions for the problem, consisting of adaptations of classical priority rules for scheduling problems. The authors also propose a hybrid ILS for improving the priority rules solutions.

Production Process Modeling for Demand Side Management

2017 ◽  
Vol 871 ◽  
pp. 77-86
Author(s):  
Stefanie Kabelitz ◽  
Sergii Kolomiichuk
Keyword(s):  
Energy Efficiency ◽  
Energy Consumption ◽  
Supply And Demand ◽  
Demand Side Management ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Business Practices ◽  
Demand Side ◽  
Manufacturing Companies ◽  
Consumption Data

The supply of electricity is growing increasingly dependent on the weather as the share of renewable energies increases. Different measures can nevertheless maintain grid reliability and quality. These include the use of storage technologies, upgrades of the grid and options for responsiveness to supply and demand. This paper focuses on demand side management and the use of flexibility in production processes. First, the framework of Germany’s energy policy is presented and direct and indirect incentives for businesses to seek as well as to provide flexibility capabilities are highlighted. Converting this framework into a mixed integer program leads to multi-objective optimization. The challenge inherent to this method is realistically mapping the different objectives that affect business practices directly and indirectly in a variety of laws. An example is introduced to demonstrate the complexity of the model and examine the energy flexibility. Second, manufacturing companies’ energy efficiency is assessed under the frequently occurring conditions of heavily aggregated energy consumption data and of information with insufficient depth of detail to perform certain analyses, formulate actions or optimize processes. The findings obtained from the energy assessment and energy consumption projections are used to model the production system’s energy efficiency and thus facilitate optimization. Methods of data mining and machine learning are employed to project energy consumption. Aggregated energy consumption data and different production and environmental parameters are used to assess indirectly measured consumers and link projections of energy consumption with the production schedule.

Sign in / Sign up

Export Citation Format

Share Document