Algorithms for dynamic scheduling in manufacturing, towards digital factories Improving Deadline Feasibility and Responsiveness via Temporal Networks

TL;DR

This work addresses robust deadline satisfaction in flexible job-shop scheduling under stochastic task durations by integrating offline constraint programming (CP) with online temporal-network execution through Simple Temporal Networks with Uncertainty (STNUs). The approach first produces a deadline-aware CP baseline and then translates it to an STNU, verifying dynamic controllability (DC) to guarantee feasible re-timing for all bounded duration realizations; an online policy via RTE* provides reactive adjustment without re-optimisation. A closed-form slack bound Δ^* ensures hard deadlines are met in the offline plan and DC in the STNU layer, with soft-deadline incentives (weights $w_e$, $w_t$) balancing makespan against robustness. Empirical evaluation on the Kacem 1–4 benchmarks demonstrates elimination of deadline violations observed in state-of-the-art meta-heuristics, with only 3–5% makespan overhead and sub-second CP/DC runtimes for medium-sized instances. The findings support a practical pathway toward self-correcting, digital factories by combining routing-capable CP with provably robust online scheduling via temporal networks. $D_j$ represents per-job deadlines and $\Delta^*$ is the critical slack that guarantees both CP feasibility and STNU DC under uncertainty $\alpha$.

Abstract

Modern manufacturing systems must meet hard delivery deadlines while coping with stochastic task durations caused by process noise, equipment variability, and human intervention. Traditional deterministic schedules break down when reality deviates from nominal plans, triggering costly last-minute repairs. This thesis combines offline constraint-programming (CP) optimisation with online temporal-network execution to create schedules that remain feasible under worst-case uncertainty. First, we build a CP model of the flexible job-shop with per-job deadline tasks and insert an optimal buffer $Δ^*$ to obtain a fully pro-active baseline. We then translate the resulting plan into a Simple Temporal Network with Uncertainty (STNU) and verify dynamic controllability, which guarantees that a real-time dispatcher can retime activities for every bounded duration realisation without violating resource or deadline constraints. Extensive Monte-Carlo simulations on the open Kacem~1--4 benchmark suite show that our hybrid approach eliminates 100\% of deadline violations observed in state-of-the-art meta-heuristic schedules, while adding only 3--5\% makespan overhead. Scalability experiments confirm that CP solve-times and STNU checks remain sub-second on medium-size instances. The work demonstrates how temporal-network reasoning can bridge the gap between proactive buffering and dynamic robustness, moving industry a step closer to truly digital, self-correcting factories.

Figures (10)

• Figure 1: STNU controllability versus slack $\Delta$ for seven uncertainty factors $\alpha$. Dynamic controllability jumps from 0 % to 100% exactly at the predicted slack
• Figure 2: Per-job tardiness probability. A stronger early-reward ($w_e{=}10$) mainly rescues the worst-case jobs, leaving punctual ones unchanged.
• Figure 3: Empirical makespan–earliness Pareto front ($w_e,w_t$). The elbow at $w_e{=}5,w_t{=}20$ gives the best makespan/robustness balance under $\alpha=0.6$, $\Delta_{\text{soft}}=45$.
• Figure 4: Online makespan standard deviation over 500 runs: $w_e{=}1$ halves volatility versus $w_e{=}0$. A tiny early-reward ($w_e=1$) halves makespan volatility
• Figure 5: Average makespan versus $w_e$ for three $w_t$ slices. “Green basin" shows weight pairs with low tardy risk and approx. 5 % makespan hit. Makespan varies by approx. 2 % across the entire weight grid