Minimizing the Total Weighted Waiting Times and Instability in a Rescheduling Problem with Dynamic Jobs Weight

Abstract

Thanks to smart technological tools, customers can at any moment create or modify their commands. This reality forced many production firms to become sensitive in rescheduling processes. In the literature, most of rescheduling problems consider classical efficiency measures. However, some existing works also consider stability as a measure for limiting the deviation from initial schedule. In this work, we aim to bridge the gap in existing works on rescheduling by investigating a new approach to measure simultaneously efficiency by the total weighted waiting times and stability by the total weighted completion time deviation. This combination of criteria is very significant in industrial and hospital environments. In this paper, a single machine rescheduling problem with jobs arriving over time is considered. A mixed integer linear programming (MILP) model is designed for this problem and an iterative predictive-reactive strategy for dealing with the online part. Numerical results show that, at each time the jobs are rescheduled, the low weight ones move forward. Consequently, a new concept consisting in increasing the jobs weight as function of time is established. The effect of this new conception is evaluated by the evolution of the maximum flowtime. Eventually, the computing time of the MILP resolution is studied to explore its limitations.

Rescheduling of a Single Machine Problem Thanks to Time Dependent Variable Weights

“…The MILP formulation consists of assigning orders to positions. It is provided by [22] for a single machine rescheduling problem, we then adapted it to match time -72-…”

“…such as the Makespan [11,12,13], tardiness [14,15], total flow time [16], and maximum lateness [17]. However, other authors have studied weighted criteria like the total weighted completion times [18,19], the total weighted tardiness [20], or the total weighted waiting time [21,22,23]. The integration of the weight into the performance measure consists of prioritizing the important orders.…”

Multi-Stove Scheduling for Sustainable On-Demand Food Delivery

“…Expressing all time interval with this small square solves the schedule problem with the release dates and deadlines. Tighazoui et al [6] proposed the idea of measuring efficiency by the total weighted waiting times and stability on a single machine rescheduling problem. The authors extend decision-making from the makespan to the weighted sum of waiting time.…”