An intelligent water drop algorithm to identical parallel machine scheduling with controllable processing times: a just-in-time approach

In the optimization areas, there are different algorithms that have been applied such as swarm intelligence algorithms. The researchers have found different algorithms by simulating the behaviors of various swarms of insects and animals such as fishes, bees, and ants. The intelligent water drops algorithm is one of the recently developed algorithms in the swarm intelligence field; this algorithm mimicked the dynamic of river systems. The natural water drops used to develop Intelligent Water Drop (IWD) algorithm. Therefore, the mechanisms that happen in rivers have inspired the researchers mainly to create new algorithms. IWD is a population-based algorithm where each drop represents a solution and the sharing between the drops during the search lead to a better drops (or solutions). This paper presents recent developments of the IWD algorithms in terms of theory and application. This paper concludes many of research directions that are necessary for the future of IWD algorithm.

The use of B-spline curves has spreaded too many fields such as computer aided design (CAD), data visualization, surface modelling, signal processing and statistics. The flexible and powerful mathematical properties of B-spline are the cause of being one of the most preferred curve in literature. They can represent a large variety of shapes efficiently. The curve behind of the model can be obtained by doing approximation of control points, approximation of knot points or parameterization. It is obvious that the selection of knot points in B-spline curve approximation has an important and considerable effect on the behaviour of final approximation. In addition to this, an unreasonable knot vector may introduce unpredictable and unacceptable shape. Recently, in literature, there has been a considerable attention on the algorithms inspired from natural processes or events to solve optimization problems such as simulated annealing, ant colony optimization, particle swarm optimization, artificial bee colony optimization, and genetic algorithms. This paper implements and analyses a solution to approximate B-spline curves using Intelligent Water Drops (IWD) algorithm. This algorithm is a swarm based optimization algorithm inspired from the processes that happen in the natural river systems. The algorithm is based on the actions and reactions that take place between water drops in the river and the changes that happen in the environment. Some basic properties of natural water drops are adopted in the algorithm here to solve B-spline curve fitting problem. Optimal knots are selected through IWD algorithm. The proposed algorithm convergences optimal solutions and finds good and promising results.

This paper proposes an optimization model that simultaneously incorporates the selection of advertising investments plan and transportation scheduling for low carbon logistics routing optimization model to achieve profit maximization in the company's investment decision-making. The main contents consist of four steps: (1) to achieve profit maximization, construct the Investment decision model that is affected by investment volume and demands, (2) design the demand analysis model based on the dynamic theory, (3) build the low-carbon logistics routing optimization model with the minimum logistics distribution cost, (4) apply an intelligent water drops (IWD) algorithm to solve the proposed model. Simulation results show that the established model and algorithm are effective and reasonable, which could provide references on the investment decision-making.

Identical parallel machine scheduling problem for minimizing the makespan is a very important production scheduling problem which has been proven to be NP-hard. The problem further compounds with additional constraints. Genetic algorithms (GA) have shown great advantages in solving the combinatorial optimization problem in view of its characteristic that has high efficiency and that is fit for practical application. In this chapter we present a spreadsheet based GA approach for minimizing the makespan for scheduling of a set of tasks for identical parallel machines and worker assignment to machines. The results obtained from the proposed approach are compared with two sets of benchmark problems consisting of 100 problems each. It has been demonstrated that the performance of proposed approach is superior to the results that have been obtained earlier. The proposed approach produces optimal solution for almost 95% of the problems demonstrating the effectiveness of the proposed approach. An empirical analysis of GA parameters has also been carried out to see the effect on the performance of the proposed algorithm.

• Examines scheduling on m identical parallel machines with a common server. • Considers sequence-dependent setup times in parallel machine scheduling. • Introduces an arc-based MILP formulation for makespan minimization. • Presents a GRASP-enhanced Iterated Greedy algorithm with strong performance. • Reports 21 new best-known solutions across benchmark test instances. The identical parallel machine scheduling problem with a single server and sequence-dependent setup times is a challenging optimization problem with important applications in manufacturing and service industries. In such environments, several machines depend on a common server to perform setup operations before production can begin, which creates strong interdependencies and demands more effective scheduling strategies. This characteristic highlights the practical relevance of the problem. The interaction between machine availability and server operations often becomes a critical bottleneck. This study introduces two complementary approaches. The first is an exact method based on a novel arc-based mixed-integer linear programming (ABF) model, which extends the modeling capability of existing formulations by capturing server-related constraints more effectively. The second is an approximation method built on an Iterated Greedy (IG) algorithm. The IG procedure is improved by two evaluation mechanisms: one model-based evaluation derived from the proposed ABF model, and another employing a greedy randomized adaptive search procedure (GRASP)-based strategy that integrates greedy selection, randomization, and reconstruction to enhance solution quality. Computational experiments are conducted on existing benchmark instances. The results show that the proposed ABF model performs well on small and medium-sized instances compared to existing exact methods, while the IG variants, particularly the proposed GRASP-based version, deliver strong performance against state-of-the-art metaheuristics developed for this problem. In addition, 21 new best-known solutions are reported, further demonstrating the effectiveness of the proposed approaches.

Scheduling with controllable release dates and processing times: Total completion time minimization

Minimizing the total completion time on a parallel machine system with tool changes

A multi-objective intelligent water drop algorithm to minimise cost Of goods sold and time to market in logistics networks

Industrial Clusters (ICs) are companies that are active in the same commercial section in adjacent geographical area. Several articles have investigated the mathematical structure of ICs under different business rules and objectives. However, There is a dearth of research in mathematical relationship between Supply Chain Management and ICs. To bridge this gap, we propose a multi-echelon supply-distribution model that optimize collaborations of different echelons. The two considered objectives are minimizing the total incurred logistics costs, and maximizing the service level of customers. We solve this problem using the intelligent water drops (IWD) algorithm. We also compare IWD with reference-point based non-dominated sorting genetic algorithm (NSGA-III) and non-dominated ranking genetic algorithm (NRGA). Finally, we illustrate the validity of the proposed approach through experimental results.

Minimizing total tardiness and earliness on unrelated parallel machines with controllable processing times

Using a variable neighborhood search to solve a bi-objective identical parallel machine scheduling problem

Production scheduling and reliability of machinery are prominent issues in flexible manufacturing systems that are led to decreasing of production costs and increasing of system efficiency. In this paper, multiobjective optimization of stochastic failure‐prone job shop scheduling problem is sought wherein that job processing time seems to be controllable. It endeavours to determine the best sequence of jobs, optimal production rate, and optimum preventive maintenance period for simultaneous optimization of three criteria of sum of earliness and tardiness, system reliability, and energy consumption. First, a new mixed integer programming model is proposed to formulate the problem. Then, by combining of simulation and NSGA‐II algorithm, a new algorithm is put forward for solving the problem. A set of Pareto optimal solutions is achieved through this algorithm. The stochastic failure‐prone job shop with controllable processing times has not been investigated in the earlier research, and for the first time, a new hedging point policy is presented. The computational results reveal that the proposed metaheuristic algorithm converges into optimal or near‐optimal solution. To end, results and managerial insights for the problem are presented.

Efficient scheduling of a stochastic no-wait job shop with controllable processing times

Scheduling of jobs has been a challenging task in manufacturing and the most real life scheduling problems, which involves multi-objectives and multi-machine environments. This paper presents tabu search and simulated annealing approaches for scheduling jobs on identical parallel machines. The identical parallel machine scheduling problem has been considered to minimize the mean tardiness for the jobs. Initially, an initial solution has been obtained using EDD dispatching rule then, simulated annealing and tabu search have been applied to reach a near optimal solution. Computational experiments are performed on problems with up to 10 machines and 150 jobs. The computational results indicate that the two proposed approaches are capable of obtaining better solutions for the given scheduling problem. Moreover, the tabu search approach provides better solution then simulated annealing approach.

This paper addresses a real-life production scheduling problem with identical parallel machines, originating from a plant producing Acrylonitrile-Butadiene-Styrene (ABS) plate products. In the considered practical scheduling problem, ABS plate has some specific specifications and each specification has several different levels. Because there is at least one different level of specification between two ABS plate products, it is necessary to make a set-up adjustment on each machine whenever a switch occurs from processing one ABS plate product to another product. As tardiness leads to extra penalty costs and opportunity losses, the objective of minimising total tardiness has become one of the most important tasks for the schedule manager in the plant. The problem can be classified as an identical parallel machine scheduling problem to minimise the total tardiness. A dispatching rule is proposed for this problem and evaluated by comparing it with the current scheduling method and several existing approaches. Moreover, an iterated greedy-based metaheuristic is developed to further improve the initial solution. The experimental results show that the proposed metaheuristic can perform better than an existing tabu search algorithm, and obtain the optimal solution for small-sized problems and significantly improve the initial solutions for large-sized problems.