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Models and Algorithms for Machine Scheduling with Setup Times
Published in Cornelius Leondes, Computer-Aided Design, Engineering, and Manufacturing, 2019
Tardiness measures the degree to which jobs are late. As suggested by its name, the weighted number of late jobs objectiveNW aims to maximize the (weighted) number of jobs completed before their due date. A costfj=Uj is assigned to each job according to: Uj=1ifTj>00otherwise
Simulated Annealing
Published in Nazmul Siddique, Hojjat Adeli, Nature-Inspired Computing, 2017
In manufacturing process, each job has a fixed processing route, which traverses all the machines in a predetermined order. The duration of each operation is fixed and known. Usually, a preset due date di and a preset weight wi are given for each job. Due dates are the preferred latest finishing time of each job, and the completion of the job after this specific time will result in losses. Minimizing tardiness is becoming more important in manufacturing sector due to completion time related losses and performance, which has further impact on market reputation. TWT as an objective in JSSP is not very common partly because this objective function is difficult and complex. Weights reflect the importance level of the orders from different customers, larger values suggesting higher strategic importance. The TWT is described as mixed-integer linear disjunctive programming model defined as TWT=∑i=1nwiTi
Introduction
Published in Joseph Y.-T. Leung, Handbook of SCHEDULING, 2004
Minimization of the makespan (completion time Cmax=maxCj where Cj is equal to σ(j)+pj(nbproc(j))Minimization of the average completion time ∑Ci[18,19] and its variant weighted completion time ∑ωiCi. Such a weight may allow us to distinguish some tasks from each other (priority for the smallest ones, etc.).Minimization of the mean stretch (defined as the sum of the difference between release times and completion times). In an online context it represents the average response time between the submission and the completion.Minimization of the maximum stretch (i.e., the longest waiting time for a user).Minimization of the tardiness. Each task is associated with an expected due date and the schedule must minimize either the number of late tasks, the sum of the tardiness or the maximum tardiness.Other criteria may include rejection of tasks or normalized versions (with respect to the workload) of the previous ones.
Practical factors in order picking planning: state-of-the-art classification and review
Published in International Journal of Production Research, 2023
Sarah Vanheusden, Teun van Gils, Katrien Ramaekers, Trijntje Cornelissens, An Caris
Customer orders are constrained by due times to be shipped on time. As accuracy in delivery times is an essential performance indicator for warehouses (Wruck, Vis, and Boter 2017), respecting due time constraints while planning picking operations is a critical issue (Çeven and Gue 2015). Most studies aim at minimising total tardiness of all customer orders (i.e. the positive difference between the order due time and the batch completion time to which the order is assigned) (Chen et al. 2015; André, Schubert, and Wäscher 2017) or ignore due times of orders (De Koster, Van der Poort, and Wolters 1999; Henn and Wäscher 2012). These solution algorithms often provide a solution in which one or more customer orders will be picked after the picking due time, resulting in orders that miss the shipping deadline (Henn and Schmid 2013). In practice, such solutions may not be accepted by most warehouses, as this reduces the customer service level. Rather than accepting tardiness, the resource capacity will be increased (e.g. by shifting workers from other departments) to prevent orders being picked after due time. Note that respecting due times in planning models does not guarantee that all order are being shipped on time. Tardiness may occur due to unforeseen circumstances, such as technical defects or unavailable inventory (Van Gils et al. 2019a).
Scheduling of autonomous mobile robots with conflict-free routes utilising contextual-bandit-based local search
Published in International Journal of Production Research, 2022
Sungbum Jun, Chul Hun Choi, Seokcheon Lee
All the required information for logistics problems with AMRs consists of three datasets: map, AMRs’ status, and transportation requests. The map data include work centres with loading/unloading stations, recharging stations, and obstacles. Also, at the beginning of formulating a new operational plan, we assume that the current status for each AMR, such as location and remaining battery level, is updated. Additionally, a set of transportation requests with two paired nodes (pickup and delivery) with due dates is given. Based on these datasets, optimisation problems can be disintegrated into the three sub-problems as shown in Figure 1. The objective function is to minimise the total tardiness, which is defined as the sum of all tardiness values of the transportation requests. Tardiness occurs when the completion time of a request is greater than its due date and, in this case, its tardiness is defined as the time difference between the completion time and the due date. The following sections elucidate the assumptions and characteristics for each sub-problem in this study.
Hybrid two stage flowshop scheduling with secondary resources based on time buckets
Published in International Journal of Production Research, 2022
Alex J. Ruiz-Torres, Giuseppe Paletta, Belarmino Adenso-Díaz
The schedule (a solution to the problem) consists of two components: (i) the allocation of the workers to workstations on a time bucket basis and (ii) the sequence of jobs in each workstation. Let be the ordered set of jobs (a sequence) in workstation . The schedule results in completion time for each job in stage 2 where is the completion time (at stage 2) of job and its tardiness is . Let represent the average tardiness. Accordingly, the results of this schedule are contemplated as: . The goal and intent of the scheduling process is to minimise the average tardiness.