FRS-DSTA-Technical-Report-final v2
Technical note (FRS Technical Notes Series No.03, Mar 2023) by Dr Alberto Costa and Dr Jonas Joerin (with DSTA contributors) presenting a mixed robust–stochastic approach to a logistic planning problem: equipment redistribution and shipping to scheduled training events under uncertainty in start times and local equipment availability. The problem is formulated as an MILP with here-and-now (x) and recourse (y) decisions; authors implement two sampled approaches—ACM (sample average) and WCM (worst-case over n samples)—train on n samples and evaluate on N > n samples. Key experiment: N=1000, n=25 (training); WCM at n=24 selected as final robust solution with high feasibility (~95.4%) and objective ≈195. Solving ACM/WCM with n=25 took ≈12 hours each. Comparison vs just-in-time (per-scenario optimal) shows robust here-and-now solutions trade slight optimality loss (~1–2% avg) for much higher feasibility vs deterministic here-and-now (which is highly infeasible ~99.3%). Recommendations: prefer robust optimization for low-tolerance infeasibility contexts; compute both ACM and WCM if resources allow.
Questions this document answers
Testing N = 1000 and training n = 25 (with selected robust solution found at n = 24).
WCM solution at n = 24; feasibility ≈ 95.4%; objective function value ≈ 195.
Approximately 12 hours per problem (ACM and WCM).
Deterministic: 99.3%; Robust (n=18): 45.6%; Robust (n=24): 4.6%.
Deterministic avg deviation: 8.85%; Robust (n=24) avg deviation: 1.42%.