Study on Re-entrant Flowshop Scheduling Problem(1st report)

A re-entrant shop describes a manufacturing environment in which a machine can process a job more than once. A re-entrant shop can be classified into a re-entrant job-shop (RJS) and a re-entrant flow-shop (RFS). This article presents the development of the mixed binary integer programming (BIP) technique for the RJS and the RFS scheduling problems. Eight mixed BIP models are proposed for solving re-entrant shop scheduling problems to minimize makespan. The models RJS-1, RJS-2, RJS-3, and RJS-4 are for the RJS problems, while the other four models (RFS-1, RFS-2, RFS-3, and RFS-4) are for the RFS problems. Computational results show that the RJS-4 model is the best of the RJS models, and the RFS-3 model is the best of the RFS models.

This paper presents a makespan minimization of -jobs -machines re-entrant flow shop scheduling problem (RFSP) under fuzzy uncertainties using Genetic Algorithm. The RFSP objective is formulated as a mathematical programme constrained by number of jobs and resources availability with traditional scheduling policies of First Come First Serve (FCFS) and the First Buffer First Serve (FBFS). Jobs processing times were specified by fuzzy numbers and modelled using triangular membership function representations. The modified centroid defuzzification technique was used at different alpha-cuts to obtain fuzzy processing times (FPT) of jobs to explore the importance of uncertainty. The traditional GA schemes and operators were used together with roulette wheel algorithm without elitism in the selection process based on job fuzzy completion times. A test problem of five jobs with specified Job Processing and Transit Times between service centres, Job Start Times and Job Due times was posed. Results obtained using the deterministic and fuzzy processing times were compared for the two different scheduling policies, FCFS and FBFS. The deterministic optimal makespan for FBFS schedule was 61.2% in excess of the FCFS policy schedule.  The results also show that schedules with fuzzy uncertainty processing times provides shorter makespans than those for deterministic processing times and those under FCFS performing better than those under FBFS policy for early jobs while on the long run the FBFS policy performs better. The results underscore the need to take account of comprehensive fuzzy uncertainties in job processing times as a trade-off between time and costs influenced by production makespan. http://dx.doi.org/10.4314/njt.v36i3.21

Pareto optimization for the two-agent scheduling problems with linear non-increasing deterioration based on Internet of Things

We consider scheduling problems for unit jobs with release times, where the number or size of the gaps in the schedule is taken into consideration, either in the objective function or as a constraint. Except for several papers on minimum-energy scheduling, there is no work in the scheduling literature that uses performance metrics depending on the gap structure of a schedule. One of our objectives is to initiate the study of such scheduling problems. We focus on the model with unit-length jobs. First we examine scheduling problems with deadlines, where we consider two variants of minimum-gap scheduling: maximizing throughput with a budget for the number of gaps and minimizing the number of gaps with a throughput requirement. We then turn to other objective functions. For example, in some scenarios gaps in a schedule may be actually desirable, leading to the problem of maximizing the number of gaps. A related problem involves minimizing the maximum gap size. The second part of the paper examines the model without deadlines, where we focus on the tradeoff between the number of gaps and the total or maximum flow time. For all these problems we provide polynomial time algorithms, with running times ranging from O(nlog n) for some problems to O(n^7) for other. The solutions involve a spectrum of algorithmic techniques, including different dynamic programming formulations, speed-up techniques based on searching Monge arrays, searching X+Y matrices, or implicit binary search. Throughout the paper, we also draw a connection between gap scheduling problems and their continuous analogues, namely hitting set problems for intervals of real numbers. As it turns out, for some problems the continuous variants provide insights leading to efficient algorithms for the corresponding discrete versions, while for other problems completely new techniques are needed to solve the discrete version.

A Pareto-optimal solution is developed in this paper for a scheduling problem on a single machine with periodic maintenance and non-preemptive jobs. Most of the scheduling problems address only one objective function, while in the real world, such problems are always associated with more than one objective. In this paper, both multi-objective functions and multi-maintenance periods are considered for a machine scheduling problem. To avoid complexities, multiple objective functions are consolidated and transformed into a single objective function after they are weighted and assigned proper weighting factors. In addition, periodic maintenance schedules are also considered in the model. The objective of the model addressed is to minimize the weighted function of the total job flow time, the maximum tardiness, and the machine idle time in a single machine problem with periodic maintenance and non-preemptive jobs. An algorithm is developed to solve this multiple criterion problem and to construct the Pareto-set. The parametric analysis of the trade-offs of all solutions with all possible weighted combination of the criteria is performed. A neighborhood search heuristic is also developed. Results are provided to explore the best schedule among all the Pareto-optimality sets and to compare the result of the modified Pareto-optimality algorithm with the result of the neighborhood search heuristic.

The flexible open shop scheduling problem is the combination of two classical open shop and a parallel machine scheduling problems. Due to the computational complexity of solving the open shop scheduling problem, so far, limited research has considered the assumption of flexibility in this problem. In this study, a bi-objective flexible open shop scheduling with independent setup time is considered. The considered objective functions are to minimize the maximum completion time of jobs and total tardiness. Using the first objective function, an attempt is made to balance the amount of workloads on the machines so that the completion time of the last job is minimized, while using the second one, from the customers' point of view, an attempt is made to reduce the amount of tardiness in delivery of jobs to the customers. Here, firstly, a mixed-integer nonlinear programming model is proposed. Then, to deal with the multi-objective problem, the weighted Lp-metric method is used. Since, this problem is a non-deterministic polynomial-time hard problem (NP-hard), a scatter search algorithm is developed to obtain near-optimal solutions in a reasonable time. In this regard, for the first time, a novel solution representation method is also presented. To ensure the efficiency of the proposed algorithm, the results were compared with NSGA-II using several instances. After analyzing the results using four evaluation metrics, it is observed that the scatter search algorithm performs better than the NSGA-II.

This paper proposes a new experimental identification method for the mass matrix and the stiffness matrix of vibration systems. In this method, the elements of the matrices are used as design variables, and the weighting sum of the absolute values of two differences is used as an objective function. One is the difference of the measured responses and the calculated responses by the designed matrices, another is the difference in measured natural frequencies and the calculated natural frequencies of the designed matrices. So long as the elements of the matrices are determined by the constraint conditions firstly used by authors, the identified matrices by the new method are of positive-definite. Finally, the validity of the method is verified by two examples of identification of the matrices of vibration systems.

Timetabling Problem (TP) relates to quality of education and the utilization of teaching resources with the further reform in teaching and growing expansion of recruitment scale in colleges and universities. Firstly, TP was detailedly analyzed, includes: timetabling objective, main influencing factors, constraint conditions and solving target. And then, an optimized mathematical model of TP was established, and the framework structure to solve TP was founded. Subsequently, according to characteristics of TP, GA was introduced, varieties of improved schemes were designed, which include: decimal encoding scheme, initial population design scheme, fitness function design scheme, adaptive crossover probability and adaptive mutation probability design scheme. Simulation results show that the proposed GA can satisfy multiple constraint conditions and resolve TP more effectively.

This paper proposes a self-adaptive hybrid population-based incremental learning algorithm (SHPBIL) for the m-machine reentrant permutation flow-shop scheduling problem (MRPFSSP) with makespan criterion. At the initial phase of SHPBIL, the information entropy (IE) of the initial population and an Interchange-based search are utilized to guarantee a good distribution of the initial population in the solution space, and a training strategy is designed to help the probability matrix to accumulate information from the initial population. In SHPBIL's global exploration, the IE of the probability matrix at each generation is used to evaluate the evolutionary degree, and then the learning rate is adaptively adjusted according to the current value of IE, which is helpful in guiding the search to more promising regions. Moreover, a mutation mechanism for the probability model is developed to drive the search to quite different regions. In addition, to enhance the local exploitation ability of SHPBIL, a local search based on critical path is presented to execute the search in some narrow and promising search regions. Simulation experiments and comparisons demonstrate the effectiveness of the proposed SHPBIL.

Order acceptance and scheduling (OAS) problems are realistic for enterprises. They have to select the appropriate orders according to their capacity limitations and profit consideration, and then complete these orders by their due dates or no later than their deadlines. OAS problems have attracted significant attention in supply chain management. However, there is an issue that has not been studied well. To our best knowledge, no prior research examines the carbon emission cost and the time-of-use electricity cost in the OAS problems. The carbon emission during the on-peak hours is lower than the one in mid-peak and off-peak hours. However, the electricity cost during the on-peak hours is higher than the one during mid-peak and off-peak hours when time-of-use electricity (TOU) tariff is used. There is a trade-off between sustainable scheduling and the electricity cost. To calculate the objective value, a carbon tax and carbon dioxide emission factor are included when we evaluate the carbon emission cost. The objective function is to maximize the total revenue of the accepted orders and then subtract the carbon emission cost and the electricity cost under different time intervals on a single machine with sequence-dependent setup times and release date. This research proposes a mixed-integer linear programming model (MILP) and a relaxation method of MILP model to solve this problem. It is of importance because the OAS problems are practical in industry. This paper could attract the attention of academic researchers as well as the practitioners.

Operating room (OR) planning and scheduling is a highly complex combinatorial optimization problem that involves patient assignment, OR allocation, and surgical sequencing within a constrained planning horizon. This study addresses the OR scheduling problem by incorporating downstream bed availability in both hospital wards and intensive care units (ICUs), aiming to improve operational efficiency and patient outcomes. A mixed-integer programming (MIP) model is developed to minimize the total completion time across all operating rooms during the planning period. Given the NP-hard nature of the problem, a novel Genetic Engineering Algorithm (GEA) is proposed as an advanced extension of the traditional Genetic Algorithm (GA). The GEA incorporates three innovative search strategies inspired by genetic engineering principles, refining the crossover and mutation operators to improve solution quality and convergence speed. To evaluate the effectiveness of the proposed algorithm, GEA and its variants are tested on 18 benchmark instances of varying problem sizes for the proposed OR planning and scheduling problem. A real-world case study from a hospital in Pakistan illustrates the practical applicability of the proposed approach using different real-world criteria. The results demonstrate that GEA consistently outperforms state-of-the-art metaheuristic algorithms. Its robustness and accuracy are further validated using 10 standard mathematical benchmark functions. The results confirm the GEA’s effectiveness and efficiency in addressing complex OR planning and scheduling problems and underscore its potential for advancing metaheuristic algorithm design in combinatorial optimization.

Hybrid method integrating agent-based modeling and heuristic tree search for scheduling of complex batch processes

<p style='text-indent:20px;'>In today's competitive world, scheduling problems are one of the most important and vital issues. In this study, a bi-objective unrelated parallel machine scheduling problem with worker allocation, sequence dependent setup times, precedence constraints, and machine eligibility is presented. The objective functions are to minimize the costs of tardiness and hiring workers. In order to formulate the proposed problem, a mixed-integer quadratic programming model is presented. A strategy called repair is also proposed to implement the precedence constraints. Because the problem is NP-hard, two metaheuristic algorithms, a multi-objective tabu search (MOTS) and a multi-objective simulated annealing (MOSA), are presented to tackle the problem. Furthermore, a hybrid metaheuristic algorithm is also developed. Finally, computational experiments are carried out to evaluate different test problems, and analysis of variance is done to compare the performance of the proposed algorithms. The results show that MOTS is doing better in terms of objective values and mean ideal distance (MID) metric, while the proposed hybrid algorithm outperforms in most cases, considering other employed comparison metrics.</p>

This paper considers the characteristics of hybrid flow shop with energy saving. First of all, established the model of hybrid flow shop with energy saving problem. Then Lagrangian relaxation was proposed to solve the energy scheduling problem in hybrid flow shop. Lagrangian relaxation algorithm introduced precedence constraints into the objective function, and the original problem was decomposed into a series of parallel machine sub-problems. A dynamic programming algorithm was then designed to solve these sub-problems. The method of updating of multiples was sub-gradient algorithm. Lastly, a two stage heuristic approach was constructed to convert the infeasible solution into a feasible solution. Testing results demonstrated that the proposed method can generate near optimal schedules in an acceptable computational time.

This paper considers the characteristics of a hybrid flow shop with JIT technical constraints. Lagrangian relaxation is presented to solve the Earliness/Tardiness problem in the hybrid flow-shop. By introducing precedence constraints into the objective function, the original problem is decomposed into a series of parallel machine sub-problems and a dynamic programming algorithm is designed to solve these sub-problems. Heuristic approach is further applied to convert the infeasible solution into a feasible solution. Testing results demonstrated that the proposed method can generate near optimal schedules in an acceptable computational time.