Effective Solution Approach Research Articles

An adaptive large neighborhood search approach for multiple traveling repairman problem with profits

The Multiple Traveling Repairman Problem with Profits (MTRPP) is a generalization of the Traveling Repairman Problem with Profits (TRPP) by considering multiple servers. In the MTRPP, each vertex is associated with a time-dependent profit. The objective of the MTRPP is to maximize the total profit collected by the servers. In this study, a mixed-integer linear programming model is developed for the MTRPP. To solve the problem, an adaptive large neighborhood search (ALNS) approach is proposed. The performance of the proposed ALNS is tested on a set of generated MTRPP instances as well as on the TRPP instances from the literature. The computational results reveal that the proposed ALNS is an effective and time-efficient solution approach for the MTRPP. Especially, it has been observed that the developed ALNS has improved the best-known solutions for 36 out of 40 large-size TRPP instances.

A biased‐randomized algorithm for redistribution of perishable food inventories in supermarket chains

AbstractIn supermarkets, perishable products need to be sold to consumers before a given deadline, after which their monetary value is significantly diminished or even completely lost. In the case of valuable products that should not be wasted, the following operational decision needs to be made as this deadline approaches: which is the best way to reallocate products from stores with surplus inventories to stores with unsatisfied demand? This question results in an optimization problem in which the goal is to minimize total transport cost plus opportunity cost associated with a reduction in market value of products being delivered after a given deadline. Our paper examines this inventory reallocation problem, which is modeled as an extension of the multi‐depot vehicle routing problem with soft deadlines, that is, delivery deadlines can be violated by incurring an opportunity or penalty cost. Being an NP‐hard optimization problem, a metaheuristic algorithm using biased‐randomization techniques is proposed as an effective solution approach. A series of computational experiments contribute to validate our algorithm and to illustrate the potential benefits that can be obtained by reallocating perishable and valuable products in various problem settings.

An effective solution approach for multi-objective fractional fixed charge problem with fuzzy parameters

A multi-objective fixed charge problem in existence of several fractional objective functions with triangular fuzzy parameters is considered in this study. The problem previously has been tackled only by Upmanyu and Saxena (2016) with a method containing wrong mathematical concepts (see the commentary of Kaur and Kumar (2017)). To overcome the shortcomings of the literature, an effective solution approach based on a typical goal programming approach is proposed to solve the problem for obtaining a Pareto-optimal solution. The proposed approach considers the shortcomings of the method of Upmanyu and Saxena (2016) and applies no ranking function of fuzzy numbers. In addition, the goal programming stage considers no preference from decision maker. The computational experiments provided by an example of the literature, prove the effectiveness of the proposed approach.

ACOPF for three‐phase four‐conductor distribution systems: semidefinite programming based relaxation with variable reduction and feasible solution recovery

Emerging distribution systems with a proliferation of distributed energy resources are facing with new challenges, such as voltage collapse and power flow congestion in unsymmetrical network configurations. As a fundamental tool that could help quantify these new challenges and further mitigate their impacts on the secure and economic operation of distribution systems, effective AC optimal power flow (ACOPF) models and solution approaches are in urgent need. This study focuses on ACOPF of three-phase four-conductor configured distribution systems, in which neutral conductors and ground resistances are modelled explicitly to reflect practical situation. In addition, by leveraging the Kirchhoff's current law (KCL) theorem and the effect of zero injections, voltage variables of neutrals and zero-injection phases can be effectively eliminated. The ACOPF problem is formulated as a convex semidefinite programming (SDP) relaxation model in complex domain. In recognising possible solution inexactness of SDP relaxation model, a Karush-Kuhn-Tucker condition based process is further proposed to effectively recover feasible solutions to the original ACOPF problem by calculating a set of computational-inexpensive non-linear equations. Numerical studies on a modified IEEE 123-bus system show the effectiveness of the proposed SDP relaxation model with variable reductions and the feasible solution recovery process for three-phase four-conductor configured distribution systems.

An Effective Solution Approach Based on Extension Principle for Fuzzy Minimal Cost Flow Problem

A well-known version of minimal cost flow problem with fuzzy arc costs is focused in this study. The fuzzy arc costs is applied as in most of real-world applications, the parameters have high degree of uncertainty. The goal of this problem is to determine the minimum fuzzy cost of sending and passing a specified flow value in to and from a network. A decomposition-based solution methodology is introduced to tackle this problem. The methodology applies Zadeh’s extension principle to decompose the problem to two upper bound and lower bound problems. These problems are capable of being solved for different α-cut values to construct the fuzzy cost flow value as the objective function value. The efficiency of the proposed solution methodology is studied over some well-known examples of the minimal cost flow problem. The obtained results and the procedure applied to obtain them prove the superiority of the proposed approach comparing to the previous approaches of the literature.

Simultaneous Penalization and Subsidization for Stabilizing Grand Cooperation

In this paper we propose a new instrument, a simultaneous penalization and subsidization, for stabilizing the grand coalition and enabling cooperation among all players of an unbalanced cooperative game. The basic idea is to charge a penalty z from players who leave the grand coalition, and at the same time provide a subsidy ω to players who stay in the grand coalition. To formalize this idea, we establish a penalty-subsidy function ω(z) based on a linear programming model, which allows a decision maker to quantify the trade-off between the levels of penalty and subsidy. By studying function ω(z), we identify certain properties of the trade-off. To implement the new instrument, we design two algorithms to construct function ω(z) and its approximation. Both algorithms rely on solving the value of ω(z) for any given z, for which we propose two effective solution approaches. We apply the new instrument to a class of machine scheduling games, showing its wide applicability. The e-companion is available at https://doi.org/10.1287/opre.2018.1723 .

An Effective Solution Approach to Fuzzy Programming with Application to Project Scheduling

In the present paper, a novel solution approach is proposed for a class of fuzzy programming models. In this direction, we prove that the lower and upper bounds of their fuzzy optimal objective values at a possibility level, $$\alpha \in [0,1]$$ , can be calculated solving a pair of crisp mathematical programming models. Thus, their membership functions are simulated enumerating the upper and lower bounds obtained from a series of $$\alpha$$ -level calculations. Motivated from real-world project scheduling applications, several numerical examples are considered to evaluate the accuracy, efficiency and applicability of our treatment. The results derived are compared with those of Chen and Tsai (Eur J Oper Res 212(2):386–397, 2011) to demonstrate that our method is easier to be utilized, with lower computational complexity, nonetheless without losing its effectiveness. Finally, the new approach does not suffer from the limitation to be applicable only to linear programming models that makes it suitable for a wider range of models and applications.

A two-phase solution algorithm for the Flexible Periodic Vehicle Routing Problem

The Flexible Periodic Vehicle Routing Problem is the problem of visiting a given set of customers considering a certain periodicity to attend their demands. It is a generalization of the Periodic Vehicle Routing Problem where the fixed schedule constraint is relaxed and the quantity to deliver to each customer at each visit is a decision variable. This flexibility leads to remarkable savings in total costs and this explains the interest in studying the problem and developing effective solution approaches. In this work, an iterative two-phase matheuristic is developed to solve medium and large instances of the problem. Computational tests are made on benchmark instances and on newly generated instances. The results of the matheuristic are compared to the best-known solutions, on small-size instances, and to lower bounds on larger instances. Computational results show that good quality solutions are obtained in a reasonable amount of time.

Development of an automatic solar-powered domestic water cooling system with multi-stage Peltier devices

Abstract One of the major problem that comes with summer season in the arid countries is rise in the temperature of water for both domestic and commercial building usage. At a persistent high temperature up to 55 °C for almost half of the year, people have to face challenging and sometimes unbearable hot water for drinking, bathing, and other general use. Cooling this water using conventional cyclic refrigeration is usually met with huge energy consumption that leads to upsurge in electricity tariff, and indirect rise in environmental pollution associated with all processes involved. By leveraging on the abundant solar energy during this period with a cooling technique based on thermoelectric device approach, an effective solution approach is proposed in this study. The proposed method is based on the philosophy of, “cooling the water by the heat of the sun”, annexes the environmental friendly solar energy source and cooling technique to provide comfortable water. Design and implementation strategy towards practical deployment of the proposed solution is presented. The real-time results and analysis with a developed laboratory scale prototype show the effectiveness of the system in providing solution to this perennial water problem, and in addition serves as platform for further study.

A new effective solution method for fully intuitionistic fuzzy transportation problem

A transportation problem in its balanced form where all parameters and variables are of triangular intuitionistic fuzzy values is considered in this study. In the literature of the field, the existing proposed approaches have many shortcomings, e.g., obtaining negative solutions for the variables and obtaining negative objective function value in existence of positive unit transportation costs. In this study, considering the existing shortcomings, a new and effective solution approach is proposed to overcome such shortcomings. The performed computational experiments prove the superiority of the proposed approach over those of the literature from the results’ quality.

Minimizing total weighted tardiness and overtime costs for single machine preemptive scheduling

This paper studies the scheduling of a finite set of jobs on a single resource that operates under both regular and overtime capacity modes. Jobs, which can be preempted, have associated release and due dates. Limited overtime capacity can be utilized to reduce tardiness. However, since overtime is costly, justification of the overtime use depends on the trade-off between the tardiness and the overtime costs. The overall objective is to minimize the total cost of tardiness and overtime. To achieve this objective, we develop a holistic method composed of three-stages. We first provide a heuristic based on an effective priority rule for the base case where no overtime capacity is considered. This heuristic is later employed in the first-stage to produce a compact non-delay schedule built based on the assumption that overtime capacity incurs no additional cost. In the second stage, the overtime usage is reduced by shifting workload and generating a full-delay schedule without altering the tardiness of jobs produced in the first stage. The third stage improves the total costs by altering the tardiness of jobs in return for savings in overtime utilization. Using computational tests, we compare the performance of our heuristics to the upper bounds generated by the exact mixed-integer programming formulation. The results show that the proposed method is efficient in obtaining solutions that are considerably better than the generated upper bounds in significantly short times and as such, it can be quite useful as an effective solution approach especially for large size problems.

Flexible power system operation accommodating uncertain wind power generation using transmission topology control: an improved linearised AC SCUC model

Stochastic security constrained unit commitment (SSCUC) based on a DC model could be problematic in AC networks because the DC model is potentially inaccurate. However, solving SSCUC problems using an AC model is still very challenging. Accordingly, an improved linearised AC optimal power flow (ILACOPF) model is provided in order to optimise the SSCUC problem. The proposed SSCUC model includes a linear representation of network losses and reactive power and bus voltage magnitudes. Moreover, in this study, transmission switching (TS), a powerful tool for grid side flexibility, is introduced and utilised to facilitate the mitigation of the uncertainty of wind power generation. Nevertheless, solving the SSCUC problem with TS in a full AC network is still one of the challenges in practical implementation, which is facilitated by the proposed ILACOPF model. Additionally, the aim of this study is to develop a more accurate power flow model to obtain a more realistic SSCUC solution using TS. The proposed ILAC-SSCUC model using TS is formulated as a mixed-integer linear programme, being solved by the proposed effective solution approach based on Benders’ decomposition. Numerical simulations on a 6-bus and IEEE 118-bus systems have been performed to evaluate the effectiveness of the method.

Real-Time Decision Support for Crew Assignment in Double-Ended Districts for U.S. Freight Railways

Crew costs are a significant portion of rail operating expenses, and so effective deployment of train crews is an important priority for freight railroads. This paper proposes an optimization model and develops an effective solution approach to assign crews to trains and decide when to deadhead crew members in double-ended crew districts in U.S. freight railways. To solve this model quickly, we develop several modeling and methodological enhancements including methods to reduce the problem size, strengthen the model, and generate good heuristic solutions. Computational testing and validation using 140 real-life problem instances demonstrate that our algorithm can find optimal and implementable solutions very quickly (typically within one minute), making it well-suited for practical use to provide real-time decision support to crew planners.

Robust Security-Constrained Unit Commitment and Dispatch With Recourse Cost Requirement

With increasing renewable energy resources, price- sensitive loads, and electric-vehicle charging stations in the power grid, uncertainties on both power generation and consumption sides become critical factors in the Security-Constrained Unit Commitment (SCUC) problem. Recently, worst scenario based robust optimization approaches are employed to consider uncertainties. This paper proposes a non-conservative robust SCUC model and an effective solution approach. The contributions of this paper are three-fold. First, the commitment and dispatch solution obtained in this paper can be directly used in day-ahead market as it overcomes two issues, conservativeness and absence of robust dispatch, which are the two largest obstacles to applying robust SCUC in real markets. Secondly, a new concept recourse cost requirement, similar to reserve requirement, is proposed to define the upper bound of re-dispatch cost when uncertainties are revealed. Thirdly, a novel decomposition approach is proposed to effectively address the well-known computational challenge in robust approaches. Simulation results on the IEEE 118-bus system validate the effectiveness of the proposed novel model and solution approach.

A simulation-optimisation approach for supply chain network design under supply and demand uncertainties

We investigate a three-echelon stochastic supply chain network design problem. The problem requires selecting suppliers, determining warehouses locations and sizing, as well as the material flows. The objective is to minimise the total expected cost. An important feature of the investigated problem is that both the supply and the demand are uncertain. We solve this problem using a simulation-optimisation approach that is based on a novel hedging strategy that aims at capturing the randomness of the uncertain parameters. To determine the optimal hedging parameters, the search process is guided by particle swarm optimisation procedure. We present the results of extensive computational experiments that were conducted on a large set of instances and that provide evidence that the proposed hedging strategy constitutes an effective viable solution approach.

Models for single-sector stochastic air traffic flow management under reduced airspace capacity

Air traffic efficiency is heavily influenced by unanticipated factors that result in capacity reduction. Of these factors, weather is the most significant cause of delays in airport and airspace operations. Considering weather-related uncertainty, air traffic flow management involves controlling air traffic through allocation of available airspace capacity to flights. The corresponding decision process results in a stochastic dynamic problem where aircraft on the ground and in the air are controlled based on the evolution of weather uncertainty. We focus on the single-sector version of the problem that is applicable to a majority of cases where a volume of airspace has reduced capacity due to convective weather. We model the decision process through stochastic integer programming formulations and computationally analyse it for tractability. We then demonstrate through actual flight schedule data that a simplistic but practically implementable approximation procedure is a generally effective solution approach for these models.

Effective Solution Approach for Integrated Optimization Models of Refinery Production and Utility System

A typical refinery consists of the production system and the utility system that are routinely optimized in a hierarchical procedure. To meet the demand for higher profit and energy utilization, it is imperative to integrate the two systems for refinery-wide simultaneous optimization, although the integrated model results in a mixed-integer nonlinear programming (MINLP) problem in which the bilinear terms for the correlation of the blending process and gas emission directly result in inconsistency between solution quality and time. The main aim of this work is to propose a solution strategy based on heuristics to decompose the integrated model of the two systems into a mixed-integer linear programming (MILP) model and a nonlinear programming (NLP) model which are then solved iteratively through variables transferring to further reduce the solution time. The solution of the traditional sequential method is incorporated to generate better initial estimates for the decomposed model to gain better solution quality and efficiency. The proposed solution approach is compared with the basic sequential method and the standard MINLP solvers. The results obtained in two scenarios of a case study from a real refinery demonstrate the effectiveness of the proposed decomposition strategy.

A decision model to allocate protective safety barriers and mitigate domino effects

In this paper, we present a model to support decision-makers about where to locate safety barriers and mitigate the consequences of an accident triggering domino effects.Based on the features of an industrial area that may be affected by domino accidents, and knowing the characteristics of the safety barriers that can be installed to stall the fire propagation between installations, the decision model can help practitioners in their decision-making. The model can be effectively used to decide how to allocate a limited budget in terms of safety barriers. The goal is to maximize the time-to-failure of a chemical installation ensuring a worst case scenario approach.The model is mathematically stated and a flexible and effective solution approach, based on metaheuristics, is developed and tested on an illustrative case study representing a tank storage area of a chemical company. We show that a myopic optimization approach, which does not take into account knock-on effects possibly triggered by an accident, can lead to a distribution of safety barriers that are not effective in mitigating the consequences of a domino accident. Moreover, the optimal allocation of safety barriers, when domino effects are considered, may depend on the so-called cardinality of the domino effects.

Grade control in multi-variable ore deposits as a quality management problem under uncertainty

Purpose – The purpose of this paper is to provide a decision-making tool on where to send mining parcels extracted in such a way as to minimize losses arising from mis-classification. The problem is complicated because actual values of mining parcels cannot be known and the decision is made on the basis of the estimation/simulations of the parcels generated from sparse data. Design/methodology/approach – The loss minimization associated with mis-classification is formulated as a non-linear optimization problem and solved by successive mixed integer programming. By assigning reasonable values to some variables making problem non-linear, the problem is converted to a mixed integer programming (MIP) and is solved by a standard MIP optimization engine. Findings – A case study was conducted to see the performance of the proposed approach on a deposit with gold and silver variables. The proposed approach was also compared with conventional grade control approaches. The results showed that the approach proposed could be used for solving grade quality control problem. Practical implications – Grade quality control problem is well-known problem and there is no effective solution approach. This paper proposes to solve the problem through standard operation research software. As such, mine planner and engineers have a means to deal with grade quality problem in mining operations. Originality/value – The paper formulates multi-variable grade quality control problem as an optimization problem on the contrary to previous one-shot approaches. This can increase profit and operation efficiency. The research also use target grades rather than cut-off grade posing problems in mining operations.

Managing Production-Inventory Systems with Scarce Resources

We consider the problem of managing production in a production-inventory system where a firm is subject to an allowance (a limit) on either the amount of input it can use or the amount of output it can produce over a specified compliance period (in addition to being subject to a constraint on the production capacity). Examples of such settings are numerous and include those where limits are placed on the use of scarce natural resources as input or on the amount of waste or harmful pollution generated by production as output. We study the structure of the optimal production policy for such systems and show that it is determined by dynamic thresholds that depend only on the sum of the on-hand inventory level and the remaining allowance. We provide an effective approximate solution approach that can compute these thresholds efficiently while retaining their essential properties. We examine the differences between how an allowance constraint and a constraint on production capacity affect production decisions and show that they exhibit opposite effects over time. We also examine, in the context of an extended version of the problem where both the allowance amount and the production capacity are endogenous, optimal investments in allowance and production capacity and the impact of both on firm profit. We also consider the optimal demand fulfillment policy in settings where the firm can decide whether to back-order or to reject demand that cannot be satisfied from on-hand inventory. The online appendix is available at https://doi.org/10.1287/msom.2016.0603 .