An extended and integrated approach to the mobile repairman problem

[Pieter Vansteenwegen]

For professor Cattrysse:

The service sector is a rapidly growing sector, also in Belgium. Although many optimization opportunities exist, research aimed at supporting decision making in this sector is still limited. The research project proposed here focuses on a specific problem in this sector, i.e. the "mobile repairman problem". The typical problem setting here can be described as follows: a technician/repairman is sent out to around 5 to 10 customers per day, to carry out a maintenance intervention (repair, inspection, etc.) on equipment which is not mobile, such as ATM's, elevators, large household appliances, photocopiers, gear boxes, etc.
Specific for the mobile repairman problem is the combination of three traditional problems from the field of operations research: routing/scheduling (which technician is visiting which customers and in which sequence?), maintenance optimization (how can we better prevent, predict and manage maintenance?) and inventory control (which and how many spare parts are to be carried in the van of the technician?)
The routing/scheduling modeling should be able to cope with uncertainties in traveling time (traffic jams and incidents) and time windows. The fact that different technicians can have different skills should be taken into account, as well as the fact that some jobs have priority (e.g. for customers with a service level agreement stipulating that an installation problem should be solved within 4 hours). A further complicating matter is the fact that the technician should dispose of the right stock of spares in his van to finish the jobs planned.
The resources/inventory problem in the mobile repairman problem is twofold. On the one hand there is the optimization of the global stock of spares parts and on the other hand there is the optimization of the stock of spares in the technician's van. The latter, the so-called repair-kit problem, is complex here due to the uncertainty in demand and the problem dimensions. The first problem is a traditional inventory control problem however also decisions concerning the stock location ((de)centralization, “city stock”), pooling, make-to-order vs make-to-stock and multi-echelon aspects should be incorporated. Additionally, the planning of a workforce that has appropriate skills should be considered.
Another problem dimension is the optimization of the maintenance strategy for the installations. Based on trade-off between costs (total intervention cost, spare parts management, damage costs) and technical risks a decision on the desired mix of corrective, preventive and predictive maintenance (including intelligent condition monitoring and prognostics) should be made. This requires a complex stochastic modeling approach.
Although for each of these separate problems many models and optimization approaches have been reported in literature, research efforts to combine these problems are very limited. However, major benefits can be expected from an integrated approach; similar integrated approaches have already been validated in supply chain optimization.
It is clear that considerable interaction between the three above mentioned problem areas exist. A good predictability of the maintenance and failure behavior of installations can e.g. reduce the uncertainty in routing and inventory control. The repair-kit will depend on the maintenance strategy, the inventory control and the routing planning. We expect that integrated models will lead to a better customer service as well as to a reduction in costs for the service provider.
The research aims at developing integrated models and solution approaches incorporating the interaction between the different subproblems, i.e. routing, inventory and maintenance. The models will be formalized mathematically using MIP (mixed integer programming). Seen the complexity, the stochastic character and the size of the problems, it is expected that black-box optimization techniques such as linear and mixed-integer programming will not be sufficient to solve these problems. The solution approaches that will be developed will be mainly heuristic (e.g. metaheuristics such as e.g. genetic algorithms and guided local search methods). These will be validated using simulation and MIP relaxation. The models will also be validated using real-life cases; some industrial companies have already expressed their interest in this project (Miele, Wincor Nixdorf, Hansen Services, Schindler and Belgacom).

This research will have a considerable theoretical contribution (publications) to decision making for mobile repairman problems and has a large practical relevance for the service sector.

Note that studying the mobile repairmen problem will also provide useful insights for related (i.e. in which two of the three subproblems of the mobile repairman problem are present) problems like emergency road service, road maintenance, security patrolling, medical home care including remote patients monitoring, stock management for vending machines distributed over different locations, …