Bi-objective Scheduling Problem Research Articles

A stochastic bi-objective cybersecurity analyst scheduling problem with preferential days off and upskilling decisions

With higher shifting rates towards digitalization, companies are more prone to the rising number of cyberattacks. Despite the insufficient supply of experts needed to safeguard the Information and Communications (ICT) system, their retention, training, and skill enhancement have become an additional challenge. The scheduling of experts is one among many areas in cybersecurity defense strategies which has attracted some recent concern. This work features a solution to a more generalized bi-objective scheduling problem using epsilon constraint and NSGA-II using a mixed integer linear program (MILP). Here, the model characterizes the enhancement of the employees’ analyzing ability while simultaneously focusing on overtime preferences. Although, a single objective approach is seen in a few articles yet bi-objective formulation in expert scheduling is never attempted. Results witness the optimal schedule in a tabulated structure with four overlapping shifts and eight-time windows implicitly representing rows and columns.

The Hot Strip Mill Scheduling Problem With Uncertainty: Robust Optimization Models and Solution Approaches.

In this article, we focus on a biobjective hot strip mill (HSM) scheduling problem arising in the steel industry. Besides the conventional objective regarding penalty costs, we have also considered minimizing the total starting times of rolling operations in order to reduce the energy consumption for slab reheating. The problem is complicated by the inevitable uncertainty in rolling processing times, which means deterministic scheduling models will be ineffective. To obtain robust production schedules with satisfactory performance under all possible conditions, we apply the robust optimization (RO) approach to model and solve the scheduling problem. First, an RO model and an equivalent mixed-integer linear programming model are constructed to describe the HSM scheduling problem with uncertainty. Then, we devise an improved Benders' decomposition algorithm to solve the RO model and obtain exactly optimal solutions. Next, for coping with large-sized instances, a multiobjective particle swarm optimization algorithm with an embedded local search strategy is proposed to handle the biobjective scheduling problem and find the set of Pareto-optimal solutions. Finally, we conduct extensive computational tests to verify the proposed algorithms. Results show that the exact algorithm is effective for relatively small instances and the metaheuristic algorithm can achieve satisfactory solution quality for both small- and large-sized instances of the problem.

An improved Pareto local search for solving bi-objective scheduling problems in hot rolling mills

Hot rolling scheduling is a complex decision-making optimization problem in the production management of the iron and steel industry. Comprehensively considering temporal and technical constraints of hot rolling production, we formulate a prize-collecting capacitated vehicle routing problem with time windows (PC-CVRPTW) involving special constraints and multiple objectives. Furthermore, this paper develops a Pareto local search (PLS)-based solving algorithm via leveraging problem-specific properties and implements three improvement mechanisms: (1) solution initialization with a greedy strategy; (2) promising solution selection with optimistic hypervolume contribution; (3) hybrid neighborhood exploration integrated variable neighborhood search with constraint programming. To validate the proposed method, computational experiments are conducted on a set of randomly synthetic and realistic industrial instances. The results compared with other variants of PLS and state-of-art algorithms demonstrate that the improved PLS algorithm is effective and can provide promising solutions for bi-objective hot rolling scheduling problems.

Scheduling in a flexible flow shop with unrelated parallel machines and machine-dependent process stages: Trade-off between Makespan and production costs

This paper aims to tackle bi-objective scheduling problem in a flexible flow shop containing unrelated parallel machines in the first stage. Due to the different technology levels of the parallel machines, their process speeds and production costs vary to each other. Therefore, minimizing the maximum completion time (Makespan) and the total production cost are considered as two objective functions. In addition, setup times are considered sequence-dependent and this system considers machine-dependent process steps and the process steps of an order depend on the assigned machine in the first stage. First, the problem is described and formulated as a bi-objective mathematical model. Since the problem is known to be strongly NP-hard, an approximate solution method is introduced based on the Non-dominated Sorting Genetic Algorithm (NSGA-II) to provide proper solutions for decision makers. The performance of the proposed solution method is investigated in comparison to another powerful multi-objective algorithm (SPEA 2) by solving different test problems. The computational results using various metrics such as Error Ratio (ER) and Generational Distance (GD) show the effectiveness of the proposed method in terms of optimality. The other indices such as Spacing (S), Diversification (D), and Mean Ideal Distance (MID) emphasize the superiority of the proposed algorithm compared to the rival algorithm in solving medium and large instances. In addition, supplementary analysis provided proper trade-off between two objectives for managers to select the best solution based on their preferences.

A novel hybrid-load AGV for JIT-based sustainable material handling scheduling with time window in mixed-model assembly line

ABSTRACT Since global warming and the needs for sustainable production models, this paper focuses on a Just-in-Time (JIT)-based sustainable material handling scheduling problem (JSMHSP) with time window and capacity constraints for mixed-model assembly lines in the automobile industry. A novel Hybrid-load Automated Guided Vehicle (H-AGV) is proposed to fulfil material handling tasks between supermarkets and assembly lines. The motivation is to minimise the total line-side inventory and the total energy consumption, which corresponds to JIT and environmental objectives. Due to the NP-hard nature of the proposed scheduling problem, a Deep Q network and Non-dominated sorting-based Hyper-Heuristic (DN-HH) algorithm is presented to solve the bi-objective scheduling problem, which benefits from the synergy of the Deep Q Network (DQN) and Hyper-Heuristic (HH). In the DQN, the states and rewards are designed according to the characteristics of the scheduling problem. To improve the performance of DQN, the experience pool (EP) and the target network are presented to improve the convergence speed. Computational results reveal that the proposed DN-HH algorithm outperforms the other two compared algorithms in both solution quality and convergence speed and the performance of the H-AGV is better than that of the other two types of AGVs.

A mathematical model and NSGA-II algorithm for bi-objective grid scheduling problem with quality of service satisfaction

Computational grids consist of the innovative technologies of the new era, which seek to accelerate performance through distributing tasks on computing resources. A grid system makes it feasible to run great computing operations through the connected processors. In this article, a bi-objective problem of grid scheduling based on quality of service concept is discussed. The first objective is to increase the profit earned from customers and the second, to increase the utilisation of computational resources. A mathematical programming model is proposed for the problem and a meta-heuristic NSGA-II algorithm is designed and customised for the problem. In the numerical analysis, by drawing Pareto diagrams and analysing the sensitivity thereof, the efficiency of the proposed methods and the effect of different parameters of the problem on both the methods are assessed. According to the results, the proposed NSGA-II algorithm is highly efficient in terms of solution quality and run time.

A mathematical model and NSGA-II algorithm for bi-objective grid scheduling problem with quality of service satisfaction

A mathematical model and NSGA-II algorithm for bi-objective grid scheduling problem with quality of service satisfaction

Design and analysis of bi-objective flexible job shop scheduling problem: A case study in construction equipment manufacturing industry

Bu calismada esnek atolye tipi uretim cizelgeleme probleminin kapasite kisitlari altinda programlanmasi icin karmasik tamsayi dogrusal optimizasyon modelinin tasarlanmasi ve gelistirilmesi kesin cozum algoritmasi kullanilarak saglanmistir. Modelleme yaklasimi, gercek vakalar uzerinden veri analizini saglamak, uretim hatlarindaki uretim suresini en aza indirmek, toplam uretim maliyetlerini azaltmak ve matematiksel programlama probleminin onemli ozelliklerini detayli olarak ortaya koymak icin tasarlanmistir. Bu calismanin temel amaci, iki amacli cizelgeleme problemleri icin ϵ-kisit yontemini kullanarak daha hizli ve verimli cozum setleri elde etmektir. Gercek hayat verileri kullanilarak elde edilen Pareto cozum setleri karar vericiler ile paylasilmistir. Iki amacli cizelgeleme problemi icin gelistirilen karmasik tamsayi dogrusal optimizasyon modelinin cozum asamasinda GAMS programlama dili kullanilmistir ve sirketin uretim maliyetlerinde %16.6’lik bir iyilestirme gerceklestirilmistir.

Toward an Efficient Resolution for a Single-machine Bi-objective Scheduling Problem with Rejection

Abstract We consider a single-machine bi-objective scheduling problem with rejection. In this problem, it is possible to reject some jobs. Four algorithms are provided to solve this scheduling problem. The two objectives are the total weighted completion time and the total rejection cost. The aim is to determine the set of efficient solutions. Four heuristics are described; they are implicit enumeration algorithms forming a branching tree, each one having two versions according to the root of the tree corresponding either to acceptance or rejection of all the jobs. The algorithms are first illustrated by a didactic example. Then they are compared on a large set of instances of various dimension and their respective performances are analysed.

Bi-objective optimization for Scheduling and Multi-skilled Worker Assignments in the Hybrid Flow Shop

This paper investigate a bi-objective scheduling and worker assignment problem in a hybrid flow shop. The difficulty of this problem lies in four aspects: (i) the workers differ with each other in both the quantity and proficiency of their acquired skilles; (ii) each processing stage is comprised of parallel unrelated machines; (iii) sequence dependent setup time should be considered and respected; (iv) both the makespan and the total flow time should be minimized simultaneously. To solve this bi-objective optimization problem, we first formulate it into a mixed integer linear programming model, then the commonly used exact solution method ϵ-constraint method is adopted to solve the model. A small instance is randomly generated and tested, the testing result demonstrates the effectiveness of the proposed model.

Bi-objective scheduling on two dedicated processors

In this work, we study a bi-objective scheduling problem on two dedicated processors. The aim is to minimise the makespan and the total tardiness. This NPhard problem in the strong sense requires the use of well-adapted methods. Our contribution includes lower bounds for each studied criterion and a genetic algorithm adapted for the multi-criteria context. The lower bounds allows us to evaluate the quality of feasible solutions and the genetic algorithm incorporates the optimisation part. We implemented our approach by considering the aggregative, NSGA-II and the Pareto scenarios on a large set of instances. The obtained results show the effectiveness of the proposed algorithms. [Received: 27 August 2018; Revised: 25 January 2019; Accepted: 12 March 2019]

Bi-objective scheduling on two dedicated processors

In this work, we study a bi-objective scheduling problem on two dedicated processors. The aim is to minimise the makespan and the total tardiness. This NPhard problem in the strong sense requires the use of well-adapted methods. Our contribution includes lower bounds for each studied criterion and a genetic algorithm adapted for the multi-criteria context. The lower bounds allows us to evaluate the quality of feasible solutions and the genetic algorithm incorporates the optimisation part. We implemented our approach by considering the aggregative, NSGA-II and the Pareto scenarios on a large set of instances. The obtained results show the effectiveness of the proposed algorithms. [Received: 27 August 2018; Revised: 25 January 2019; Accepted: 12 March 2019]

Bi-objective multi-resource scheduling problem for emergency relief operations

Resource scheduling for emergency relief operations is complex as it has many constraints. However, an effective allocation and sequencing of resources are crucial for the minimization of the completion times in emergency relief operations. Despite the importance of such decisions, only a few mathematical models of emergency relief operations have been studied. This article presents a bi-objective mixed integer programming (MIP) that helps to minimize both the total weighted time of completion of the demand points and the makespan of the total emergency relief operation. A two-phase method is developed to solve the bi-objective MIP problem. Additionally, a case study of hospital network in the Melbourne metropolitan area is used to evaluate the model. The results indicate that the model can successfully support the decisions required in the optimal resource scheduling of emergency relief operations.

A scatter simulated annealing algorithm for the bi-objective scheduling problem for the wet station of semiconductor manufacturing

Abstract This paper studies a single-machine scheduling problem where flexible maintenance is required in the planning horizon. The problem observed is in the clean operation of semiconductor manufacturing, where jobs are associated with release times, processing times, due dates, penalty weight of tardy jobs and the amount of dirt left on the machine during processing. The machine, named the wet station, should be stopped for cleaning or maintenance before a maximum amount of dirt has accumulated; the cleaning time is fixed and is known in advance. However, the starting point of each maintenance activity is a decision variable. Preemptive operation is not allowed. The bi-objective of minimizing total weighted tardiness and total completion time is considered in this paper. An intuitive threshold method and a dynamic programming approach are proposed for scheduling jobs and PMs under a given job sequence. A mixed-integer programming formulation is developed to obtain all efficient solutions for the small-size problems. In addition, this paper also develops a scatter simulated annealing (SSA) algorithm in which a scatter-search mechanism leads SSA to explore more potential solutions. Computational experiments are conducted to examine the efficiency of the SSA algorithm. For the small-size problems, SSA could obtain all non-dominated solutions except for a tiny fraction of the instances. For the large-size problems, SSA performs considerably well compared with SMOSA and NSGA-II, demonstrating its potential to efficiently solve bi-objective single problems with flexible maintenance activities.

Trade-off between process scheduling and production cost in cyclic flexible robotic cells

In this study, a bi-objective scheduling problem of a flexible robotic cell is considered aiming to a trade-off between cell’s processes scheduling and the production cost. At the cell, machines are identical and parallel and in line. There is an input buffer for the raw materials and an output buffer for the products. A robot is in charge of loading and unloading of the items from the input buffer to machines and from machines to the out put buffer. The system is cyclic means repeats the same processes in every cycle. It is assumed that each machine processes one part in each cycle. A bi-objective mathematical model is presented to solve the problem, and as an alternative, an NSGAII is developed for large-sized problems. Several numerical examples are solved for examining the proposed mathematical model and NSGAII method.

A hybrid data envelopment analysis_decision tree approach to evaluate the bi-criteria flow shop with blocking problem

The purpose of this paper is to evaluate the overall performance of a bi-objective scheduling problem using a method based on a combination of data envelopment analysis and decision tree. The hybrid approach is applied to the blocking flow shop scheduling problem with both makespan and total tardiness objectives. For this end, we propose two families of three-phase heuristics. In phase one, several constructive heuristics are used to generate initial solutions and in phase two, two improving heuristics are used to generate non-dominated solutions. One of the improving heuristics is based on the makespan criteria and the other one is based on the total tardiness criteria. The non-dominated solutions are then compared using the free disposal hull (FDH) formulation of data envelopment analysis (DEA). The overall performance of the composed heuristics is measured using a decision tree approach.

A hybrid data envelopment analysis_decision tree approach to evaluate the bi-criteria flow shop with blocking problem

The purpose of this paper is to evaluate the overall performance of a bi-objective scheduling problem using a method based on a combination of data envelopment analysis and decision tree. The hybrid approach is applied to the blocking flow shop scheduling problem with both makespan and total tardiness objectives. For this end, we propose two families of three-phase heuristics. In phase one, several constructive heuristics are used to generate initial solutions and in phase two, two improving heuristics are used to generate non-dominated solutions. One of the improving heuristics is based on the makespan criteria and the other one is based on the total tardiness criteria. The non-dominated solutions are then compared using the free disposal hull (FDH) formulation of data envelopment analysis (DEA). The overall performance of the composed heuristics is measured using a decision tree approach.

Bi-objective scheduling on uniform parallel machines considering electricity cost

ABSTRACTThis article investigates a bi-objective scheduling problem on uniform parallel machines considering electricity cost under time-dependent or time-of-use electricity tariffs, where electricity price changes with the hours within a day. The aim is to minimize simultaneously the total electricity cost and the number of machines actually used. A bi-objective mixed-integer linear programming model is first formulated for the problem. An insertion algorithm is then proposed for the single-objective scheduling problem of minimizing the total electricity cost for a given number of machines. To obtain the whole Pareto front of the problem, an iterative search framework is developed based on the proposed insertion algorithm. Computational results on real-life and randomly generated instances demonstrate that the proposed approach is quite efficient and can find high-quality Pareto fronts for large-size problems with up to 5000 jobs.

A bi-objective identical parallel machine scheduling problem with controllable processing times: a just-in-time approach

In this research, a bi-objective scheduling problem with controllable processing times on identical parallel machines is investigated. The direction of this paper is mainly motivated by the adoption of the just-in-time (JIT) philosophy on identical parallel machines in terms of bi-objective approach, where the job processing times are controllable. The aim of this study is to simultaneously minimize (1) total cost of tardiness, earliness as well as compression and expansion costs of job processing times and (2) maximum completion time or makespan. Also, the best possible set amount of compression/expansion of processing times on each machine is acquired via the proposed “bi-objective parallel net benefit compression-net benefit expansion” (BPNBC-NBE) heuristic. Besides that, a sequence of jobs on each machine, with capability of processing all jobs, is determined. In this area, no inserted idle time is allowed after starting machine processing. For solving such bi-objective problem, two multi-objective meta-heuristic algorithms, i.e., non-dominated sorting genetic algorithm II (NSGAII) and non-dominated ranking genetic algorithm (NRGA) are applied. Also, three measurement factors are then employed to evaluate the algorithms’ performance. Experimental results reveal that NRGA has better convergence near the true Pareto-optimal front as compared to NSGAII, while NSGAII finds a better spread in the entire Pareto-optimal region.

Fault-tolerant scheduling on parallel systems with non-memoryless failure distributions

As large parallel systems increase in size and complexity, failures are inevitable and exhibit complex space and time dynamics. Most often, in real systems, failure rates are increasing or decreasing over time. Considering non-memoryless failure distributions, we study a bi-objective scheduling problem of optimizing application makespan and reliability. In particular, we determine whether one can optimize both makespan and reliability simultaneously, or whether one metric must be degraded in order to improve the other. We also devise scheduling algorithms for achieving (approximately) optimal makespan or reliability. When failure rates decrease, we prove that makespan and reliability are opposing metrics. In contrast, when failure rates increase, we prove that one can optimize both makespan and reliability simultaneously. Moreover, we show that the largest processing time (LPT) list scheduling algorithm achieves good performance when processors are of uniform speed. The implications of our findings are the accelerated completion and improved reliability of parallel jobs executed across large distributed systems. Finally, we conduct simulations to investigate the impact of failures on the performance, which is done using an actual application of biological sequence comparison.