A Greedy Randomized Adaptive Search Procedure for Technicians and Interventions Scheduling for Telecommunications

The subject of the 5th challenge proposed by the French Society of Operations Research and Decision Analysis (ROADEF) consists in scheduling technicians and interventions for telecommunications (http://www.g-scop.inpg.fr/ChallengeROADEF2007/ or http://www.roadef.org/). We detail the algorithm we proposed for this challenge which is a Greedy Randomized Adaptative Search Procedure (GRASP). Computational results led us to the 1st position in the Junior category and to the 4th position in All category of the Challenge ROADEF 2007.

💡 Research Summary

The paper addresses the scheduling problem posed in the 2007 ROADEF challenge, which involves assigning a set of telecommunications maintenance interventions to teams of technicians under a rich set of constraints. Each intervention has a priority (four levels) and a duration, and the objective is to minimize a weighted sum of the latest completion times for each priority class (weights 28, 14, 4, and 1). Additional constraints include: a team cannot change during a day, two interventions assigned to the same team on the same day must not overlap, all precedence relations must be respected, daily working time is limited to Hmax, each intervention requires a specific skill level in a given domain, and a limited budget A may be spent on outsourcing interventions to an external contractor.

Recognizing the NP‑hard nature of the problem, the authors propose a Greedy Randomized Adaptive Search Procedure (GRASP) that consists of three main phases.

Phase 1 – Pre‑processing and outsourcing selection
For each intervention I the minimal number of technicians required (mintec(I)) is obtained by solving a small 0‑1 linear program (P1(I)). Multiplying mintec(I) by the intervention duration T(I) yields a weight wI. The set of interventions to be outsourced is then selected by solving a 0‑1 knapsack problem (KP) that maximizes the total wI while respecting the outsourcing budget A and the precedence constraints. Interventions with xI = 1 in the knapsack solution are outsourced, thereby reducing the size of the remaining problem.

Phase 2 – Determination of promising insertion orders
The authors assign an initial priority weight ωI(p) = {28, 14, 4, 1} according to the four priority levels. All 4! = 24 permutations of the priority classes are examined. For each permutation p a simple greedy insertion is performed: interventions are sorted by decreasing ωI(p) and inserted at the earliest feasible day and team (respecting skill, time, and precedence constraints). The two permutations that produce the best greedy solutions (p1 and p2) are retained for the next phase. This exhaustive permutation search guarantees that the algorithm starts from the most promising insertion heuristics.

Phase 3 – GRASP proper
For each of the two selected permutations the following loop is executed until a time limit is reached:

1. Greedy construction – The current criterion CI = ωI(p) is assigned to every remaining intervention. The intervention with the highest CI is selected and placed at the earliest possible day, on the team that requires the fewest additional technicians and yields the smallest start time.

2. Local search – If the greedy construction improves the incumbent solution, a two‑stage local search is applied:
   Critical‑path phase attempts to reduce the weighted completion times tλ by moving or swapping interventions that belong to higher‑priority classes.
   Packing phase seeks to compact the schedule without increasing any tλ, thereby improving resource utilization.

3. Update of criteria – After each complete construction, the criteria of the last inserted interventions of each priority class and all their predecessors are increased by the corresponding ωI(p). This adaptive update introduces randomness and prevents premature convergence.

The algorithm was tested on the benchmark instances supplied by France Telecom (datasets A and B). Table 1 in the paper reports the number of interventions, number of technicians, number of domains, number of skill levels, the best known objective value, the value obtained by the proposed method, and the relative gap. Across all 20 instances the average gap is below 0.1 %, and the method achieved first place in the Junior category and fourth overall in the ROADEF 2007 competition.

Key contributions of the work are:

• A novel pre‑processing step that models outsourcing decisions as a knapsack problem based on a lower bound of required technician‑time, effectively shrinking the problem size while respecting budget constraints.
• An exhaustive exploration of all priority permutations to identify the two most effective insertion orders, providing a systematic way to exploit problem structure.
• A GRASP framework that combines deterministic greedy construction, adaptive randomization through criterion updates, and a two‑stage local search tailored to the weighted‑completion‑time objective.

The paper demonstrates that, even for large‑scale, highly constrained industrial scheduling problems, a carefully designed meta‑heuristic can achieve near‑optimal performance with reasonable computational effort. Future research directions suggested include handling dynamic arrival of interventions, multi‑objective extensions (e.g., cost versus quality), and parallel implementations to further reduce runtime for real‑time decision support.