Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

Abstract

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

An approximate dynamic programming approach for production‐delivery scheduling under non‐stationary demand

“…In the context of machine scheduling, Kanet and Sridharan (2000) showed that the schedules with inserted idle time are significant, especially in multimachine circumstances in which the earliness cost or dynamically arriving jobs come into play, and they also reveal that incorporating idle time is also beneficial for the machine scheduling problems with regular objectives, such as minimizing maximum lateness, flow time-related measures, and earliness/tardiness-related objective and maximum lateness. This observation is further validated in Ronconi and Powell (2010) that considered a single machine scheduling problem with artificial idle time to minimize total tardiness. In our IPDS model, since the orders are placed dynamically, and the objective is to minimize the waiting time, we consider inserting the idle times into production schedules.…”

“…It has been widely used in many scheduling problems, such as crane scheduling (Yuan & Tang, 2017), healthcare scheduling (Nasrollahzadeh et al, 2018), and transportation scheduling with dynamic requests (Ulmer et al, 2019). Nevertheless, ADP is rarely seen in the stochastic machine scheduling literature, where one representative work is Ronconi and Powell (2010) that deployed ADP to minimize total tardiness in a single machine scheduling problem with dynamic order arrivals and due dates. For parallel machine scheduling, besides the assignment of orders to machines, we also need to determine the order processing sequence on each machine, which greatly enlarges the action (decision) space because the complexity of determining a sequence grows factorially.…”

“…Based on these components, we can characterize post‐decision state . Consequently, we define following five basis functions based on derived features from , some of which are based on the insights in Ronconi and Powell (2010). The first basis function is .…”

Analysis of computer job control under uncertainty

“…In [17], the E/T problem is solved for the case when the machine fails and resumes operation in accordance with the given allocation. Minimization of the number of tardy jobs is considered in [18][19][20][21]. The most complete review of the available results can be found in [22].…”

Multi-objective optimization of stochastic failure-prone manufacturing system with consideration of energy consumption and job sequences

“…Also, he proposed a heuristic solution to determine the optimal sequence of jobs in general mode where processing times have arbitrary distribution. Ronconi and Powell (2010) solved stochastic single-machine problem with the purpose of minimization of total tardiness via proposing the approximate dynamic programming method. Mokhtari and Salmasnia (2015) employed the combination of Monte Carlo simulation and differential evolution metaheuristic algorithm in order to analyze a parallel processor system and minimize the expected value of completion time.…”