Supplementary Webpage

The table below provides results for all 40 instances. Instance names give the customer count followed by the replicate number: for example, 10_1 is the first 10-customer instance. ALNS means adaptive large neighborhood search and denotes the proposed matheuristic; subscripts G and H identify Gurobi and ALNS, respectively.

Objectives. L is probability-weighted total customer lateness over the 20 stored service-duration scenarios, measured in the instance time units; C is facility-opening plus routing cost, measured in the instance cost units. L_G and C_G are recomputed from Gurobi’s returned routes. Best L_H and Best C_H are the two components of the same best ALNS solution among 30 runs with different random seeds, selected by minimizing L first and then C. Zero lateness means no late customer in any of the 20 scenarios.

Optimality gaps. Gap L (%) and Gap C (%) are Gurobi’s relative incumbent-to-bound optimality gaps for the lateness-minimization and cost-minimization phases, respectively; % means percent. These gaps refer to the raw phase objectives, not the route-recomputed objectives or an ALNS-to-Gurobi cost difference. “—” denotes an unavailable cost-phase gap because the cost-minimization phase was not attempted.

Timing. t_G is Gurobi’s recorded solve-procedure elapsed time, including phase transitions but excluding initial model construction and queueing. Mean t_H is the average elapsed time of one ALNS run across all 30 seeds. 30-run effort is the sum of those 30 run times, not a single-run time; ALNS times exclude batch setup and inter-job waiting. All reported computing times are in seconds, distinct from the instance time units used for L.

Status. OPT means both Gurobi phases were optimal within the configured relative gap tolerance of 0.01% and numerical tolerances. ML1 means a memory limit ended the lateness phase before optimality was certified; the cost phase was not attempted. ML2 means zero lateness was certified, but a memory limit ended the cost phase before optimality was certified. Neither ML1 nor ML2 certifies minimum cost.

Links. The instance name opens its input file. Schedule opens the selected ALNS solution’s graphical route schedule using nominal service durations. Solution opens that same solution in JSON (JavaScript Object Notation), a machine-readable format.