scholarly journals Solution procedures for block selection and sequencing in flat-bedded potash underground mines

OR Spectrum ◽  
2021 ◽  
Author(s):  
Cinna Seifi ◽  
Marco Schulze ◽  
Jürgen Zimmermann
Keyword(s):  
Crop Yields ◽  
Decisive Role ◽  
Planning Horizon ◽  
Underground Mines ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Constructive Heuristic ◽  
Processing Plants ◽  
Problem Instances ◽  
Feasible Solutions

AbstractPhosphates, and especially potash, play an essential role in the increase in crop yields. Potash is mined in Germany in underground mines using a conventional drill-and-blast technique. The most commercially valuable mineral contained in potash is the potassium chloride that is separated from the potash in aboveground processing plants. The processing plants perform economically best if the amount of potassium contained in the output is equal to a specific value, the so-called optimal operating point. Therefore, quality-oriented extraction plays a decisive role in reducing processing costs. In this paper, we mathematically formulate a block selection and sequencing problem with a quality-oriented objective function that aims at an even extraction of potash regarding the potassium content. We, thereby, have to observe some precedence relations, maximum and minimum limits of the output, and a quality tolerance range within a given planning horizon. We model the problem as a mixed-integer nonlinear program which is then linearized. We show that our problem is $${\mathcal {NP}}$$ NP -hard in the strong sense with the result that a MILP-solver cannot find feasible solutions for the most challenging problem instances at hand. Accordingly, we develop a problem-specific constructive heuristic that finds feasible solutions for each of our test instances. A comprehensive experimental performance analysis shows that a sophisticated combination of the proposed heuristic with the mathematical program improves the feasible solutions achieved by the heuristic, on average, by $$92.5\%$$ 92.5 % .

Hybrid Evolutionary Optimization of Two-Stage Stochastic Integer Programming Problems: An Empirical Investigation

2009 ◽  
Vol 17 (4) ◽  
pp. 511-526 ◽  
Author(s):  
Thomas Tometzki ◽  
Sebastian Engell
Keyword(s):  
Evolutionary Algorithm ◽  
Empirical Investigation ◽  
Scale Up ◽  
Exact Algorithm ◽  
Integer Program ◽  
Mixed Integer ◽  
Two Stage ◽  
Integer Programming Problems ◽  
Problem Instances ◽  
Feasible Solutions

In this contribution, we consider decision problems on a moving horizon with significant uncertainties in parameters. The information and decision structure on moving horizons enables recourse actions which correct the here-and-now decisions whenever the horizon is moved a step forward. This situation is reflected by a mixed-integer recourse model with a finite number of uncertainty scenarios in the form of a two-stage stochastic integer program. A stage decomposition-based hybrid evolutionary algorithm for two-stage stochastic integer programs is proposed that employs an evolutionary algorithm to determine the here-and-now decisions and a standard mathematical programming method to optimize the recourse decisions. An empirical investigation of the scale-up behavior of the algorithms with respect to the number of scenarios exhibits that the new hybrid algorithm generates good feasible solutions more quickly than a state of the art exact algorithm for problem instances with a high number of scenarios.

Optimization Methods for Lot-Sizing Problem in an Automated Foundry

2013 ◽  
Vol 58 (3) ◽  
pp. 863-866 ◽  
Author(s):  
J. Duda ◽  
A. Stawowy
Keyword(s):  
Production Planning ◽  
Lot Sizing ◽  
Planning Horizon ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Planning Problem ◽  
Lot Size ◽  
Mip Model ◽  
Production Planning Problem ◽  
Problem Instances

Abstract In the paper we studied a production planning problem in a mid-size foundry that provides tailor-made cast products in small lots for a large number of clients. Assuming that a production bottleneck is the furnace, a mixed-integer programming (MIP) model is proposed to determine the lot size of the items and the required alloys to be produced during each period of the finite planning horizon that is subdivided into smaller periods. As using an advanced commercial MIP solvers may be impractical for more complex and large problem instances, we proposed and compared a few computational intelligence heuristics i.e. tabu search, genetic algorithm and differential evolution. The examination showed that heuristic approaches can provide a good compromise between speed and quality of solutions and can be used in real-world production planning.

scholarly journals Designing a Supply Chain Network under the Risk of Disruptions

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Armin Jabbarzadeh ◽  
Seyed Gholamreza Jalali Naini ◽  
Hamid Davoudpour ◽  
Nader Azad
Keyword(s):  
Supply Chain ◽  
Supply Chain Design ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Supply Chain Network ◽  
Large Problem ◽  
Solution Methods ◽  
Total Profit ◽  
Order Quantities ◽  
Problem Instances

This paper studies a supply chain design problem with the risk of disruptions at facilities. At any point of time, the facilities are subject to various types of disruptions caused by natural disasters, man-made defections, and equipment breakdowns. We formulate the problem as a mixed-integer nonlinear program which maximizes the total profit for the whole system. The model simultaneously determines the number and location of facilities, the subset of customers to serve, the assignment of customers to facilities, and the cycle-order quantities at facilities. In order to obtain near-optimal solutions with reasonable computational requirements for large problem instances, two solution methods based on Lagrangian relaxation and genetic algorithm are developed. The effectiveness of the proposed solution approaches is shown using numerical experiments. The computational results, in addition, demonstrate that the benefits of considering disruptions in the supply chain design model can be significant.

scholarly journals Optimal Policies for a Finite-Horizon Production Inventory Model

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Lakdere Benkherouf ◽  
Dalal Boushehri
Keyword(s):  
Simple Procedure ◽  
Optimal Schedule ◽  
Planning Horizon ◽  
Inventory Model ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Integer Variable ◽  
Optimal Production ◽  
Production Inventory ◽  
Varying Demand

This paper is concerned with the problem of finding the optimal production schedule for an inventory model with time-varying demand and deteriorating items over a finite planning horizon. This problem is formulated as a mixed-integer nonlinear program with one integer variable. The optimal schedule is shown to exist uniquely under some technical conditions. It is also shown that the objective function of the nonlinear obtained from fixing the integrality constraint is convex as a function of the integer variable. This in turn leads to a simple procedure for finding the optimal production plan.

scholarly journals Comparing greedy constructive heuristic subtour elimination methods for the traveling salesman problem

2020 ◽  
Vol 4 (2) ◽  
pp. 167-182
Author(s):  
Petar Jackovich ◽  
Bruce Cox ◽  
Raymond R. Hill
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Computational Results ◽  
Content Type ◽  
Constructive Heuristic ◽  
Subtour Elimination ◽  
Constructive Heuristics ◽  
Problem Instances ◽  
Feasible Solutions ◽  
The Traveling Salesman Problem

Purpose This paper aims to define the class of fragment constructive heuristics used to compute feasible solutions for the traveling salesman problem (TSP) into edge-greedy and vertex-greedy subclasses. As these subclasses of heuristics can create subtours, two known methodologies for subtour elimination on symmetric instances are reviewed and are expanded to cover asymmetric problem instances. This paper introduces a third novel subtour elimination methodology, the greedy tracker (GT), and compares it to both known methodologies. Design/methodology/approach Computational results for all three subtour elimination methodologies are generated across 17 symmetric instances ranging in size from 29 vertices to 5,934 vertices, as well as 9 asymmetric instances ranging in size from 17 to 443 vertices. Findings The results demonstrate the GT is the fastest method for preventing subtours for instances below 400 vertices. Additionally, a distinction between fragment constructive heuristics and the subtour elimination methodology used to ensure the feasibility of resulting solutions enables the introduction of a new vertex-greedy fragment heuristic called ordered greedy. Originality/value This research has two main contributions: first, it introduces a novel subtour elimination methodology. Second, the research introduces the concept of ordered lists which remaps the TSP into a new space with promising initial computational results.

Using a genetic algorithm to solve the troops-to-tasks problem in military operations planning

2017 ◽  
Vol 14 (4) ◽  
pp. 439-446 ◽  
Author(s):  
Maria Fleischer Fauske
Keyword(s):  
Genetic Algorithm ◽  
Time Frame ◽  
Optimization Techniques ◽  
Operational Planning ◽  
Mixed Integer ◽  
Data Sets ◽  
Military Operations ◽  
Mixed Integer Linear Program ◽  
Problem Instances ◽  
Feasible Solutions

The troops-to-tasks analysis in military operational planning is the process where the military staff investigates who should do what, where, and when in the operation. In this paper, we describe a genetic algorithm for solving troops-to-tasks problems, which are typically solved manually. The study was motivated by a request from Norwegian military staff, who acknowledged the potential for solving the troops-to-tasks analysis more effectively by using optimization techniques. Also, NATO’s operational planning tool, TOPFAS, lacks an optimization module for the troops-to-tasks analysis. The troops-to-tasks problem generalizes the well-known resource-constrained project scheduling problem, and thus it is very difficult to solve. As the troops-to-tasks problem is particularly complex, the main purpose of our study was to develop an algorithm capable of solving real-sized problem instances. We developed a genetic algorithm with new features, which were crucial to finding good solutions. We tested the algorithm on two different data sets representing high-intensity military operations. We compared the performance of the algorithm to that of a mixed integer linear program solved by CPLEX. In contrast to CPLEX, the algorithm found feasible solutions within an acceptable time frame for all instances.

scholarly journals Bi-objective design-for-control of water distribution networks with global bounds

2021 ◽  
Author(s):  
Aly-Joy Ulusoy ◽  
Filippo Pecci ◽  
Ivan Stoianov
Keyword(s):  
Water Distribution ◽  
Distribution Networks ◽  
Water Distribution Networks ◽  
Mixed Integer ◽  
Global Optimality ◽  
Linear Programs ◽  
Design For Control ◽  
Non Linear ◽  
Feasible Solutions

AbstractThis manuscript investigates the design-for-control (DfC) problem of minimizing pressure induced leakage and maximizing resilience in existing water distribution networks. The problem consists in simultaneously selecting locations for the installation of new valves and/or pipes, and optimizing valve control settings. This results in a challenging optimization problem belonging to the class of non-convex bi-objective mixed-integer non-linear programs (BOMINLP). In this manuscript, we propose and investigate a method to approximate the non-dominated set of the DfC problem with guarantees of global non-dominance. The BOMINLP is first scalarized using the method of $$\epsilon $$ ϵ -constraints. Feasible solutions with global optimality bounds are then computed for the resulting sequence of single-objective mixed-integer non-linear programs, using a tailored spatial branch-and-bound (sBB) method. In particular, we propose an equivalent reformulation of the non-linear resilience objective function to enable the computation of global optimality bounds. We show that our approach returns a set of potentially non-dominated solutions along with guarantees of their non-dominance in the form of a superset of the true non-dominated set of the BOMINLP. Finally, we evaluate the method on two case study networks and show that the tailored sBB method outperforms state-of-the-art global optimization solvers.

scholarly journals Investment Incentives in Competitive Electricity Markets

2018 ◽  
Vol 8 (10) ◽  
pp. 1978 ◽  
Author(s):  
Jaber Valinejad ◽  
Taghi Barforoshi ◽  
Mousa Marzband ◽  
Edris Pouresmaeil ◽  
Radu Godina ◽  
...  
Keyword(s):  
Electricity Markets ◽  
Electricity Market ◽  
Planning Horizon ◽  
Optimization Method ◽  
Design Criterion ◽  
Mixed Integer ◽  
Investment Incentives ◽  
Mixed Integer Linear Program ◽  
Interconnected Power System ◽  
The Impact

This paper presents the analysis of a novel framework of study and the impact of different market design criterion for the generation expansion planning (GEP) in competitive electricity market incentives, under variable uncertainties in a single year horizon. As investment incentives conventionally consist of firm contracts and capacity payments, in this study, the electricity generation investment problem is considered from a strategic generation company (GENCO) ′ s perspective, modelled as a bi-level optimization method. The first-level includes decision steps related to investment incentives to maximize the total profit in the planning horizon. The second-level includes optimization steps focusing on maximizing social welfare when the electricity market is regulated for the current horizon. In addition, variable uncertainties, on offering and investment, are modelled using set of different scenarios. The bi-level optimization problem is then converted to a single-level problem and then represented as a mixed integer linear program (MILP) after linearization. The efficiency of the proposed framework is assessed on the MAZANDARAN regional electric company (MREC) transmission network, integral to IRAN interconnected power system for both elastic and inelastic demands. Simulations show the significance of optimizing the firm contract and the capacity payment that encourages the generation investment for peak technology and improves long-term stability of electricity markets.

scholarly journals Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Ehsan Molaee ◽  
Ghasem Moslehi
Keyword(s):  
Branch And Bound ◽  
Single Machine ◽  
Planning Horizon ◽  
Single Machine Scheduling ◽  
Upper And Lower Bounds ◽  
Scheduling Problems ◽  
Bearing Witness ◽  
Number Of Tardy Jobs ◽  
Problem Instances ◽  
Tardy Jobs

Most scheduling problems are based on the assumption that machines work continuously during the planning horizon. This assumption is not true in many production environments because the machine may not be available during one or more periods such as during breakdowns or maintenance operations. In this paper, the problem of the single machine scheduling with one unavailability period and nonresumable jobs with the aim of minimizing the number of tardy jobs is studied. A number of theorems are proved and a heuristic procedure is developed to solve the problem. A branch-and-bound approach is also presented which includes upper and lower bounds and efficient dominance rules. Computational results for 2680 problem instances show that the branch-and-bound approach is capable of solving 98.7% of the instances optimally, bearing witness to the efficiency of the proposed procedure. Our results also indicate that the proposed approaches are more efficient when compared to other methods.

Optimization of the Receipt and Delivery Schedules for a Transfer Tank Farm of Products Pipeline Network

2017 ◽  
Author(s):  
Li Wang ◽  
Changchun Wu ◽  
Lili Zuo ◽  
Yanfei Huang ◽  
Haihong Chen
Keyword(s):  
Material Balance ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Oil Products ◽  
Mixed Integer ◽  
Pipeline Network ◽  
Schedule Optimization ◽  
Tank Farm ◽  
Dynamic Time ◽  
Products Pipeline

Transfer tank farms play an important role in an oil products pipeline network, which receive oil products from upstream pipelines and deliver them to downstream pipelines. The scheduling problem for oil products supply chain is very complicated because of numerous constraints to be considered. The published literatures on schedule optimization of oil products pipeline network usually focus on the batch plans of each pipeline, without consideration on the receipt and delivery schedule of transfer tank farm. In this paper, a mixed-integer linear programming (MILP) model is developed for the schedule optimization of transfer tank farm. The objective of the model is to minimize switching times of the tank operations of a tank farm during a planning horizon, while fulfilling the products transmission requirements of the upstream and downstream pipelines of the tank farm. The constraints of the model include material balance, the operational rules of tanks, the topological structure constraints of the tank farm, the settling period of the oil products stored in dedicated tank and so on. To satisfy the constraint of fulfilling the specific transmission requirements of pipelines, concepts of static and dynamic time slot are proposed. A continuous time representation is used to obtain accurate optimal schedules and decrease scale of the model by reducing the number of variables. The model is solved by CPLEX solver for a transfer tank farm of an oil products pipeline network in China. Some examples are tested under different scenarios and the results show that global optimal solution can be obtain at acceptable computational costs.

Sign in / Sign up

Export Citation Format

Share Document