PhD Defense of Faycal Touzout

Friday 08 October 2021

M. Faycal TOUZOUT defends his PhD Friday October 8th 2021, entitled: "Inventory routing problem: Managing demand and travelling time uncertainties".


Vendor management inventory (VMI) changes the traditional division of decisions within the supply chain: the supplier controls the inventory of its clients by deciding when and how much to replenish their inventories. Built on trust, the VMI system is a win-win situation: the supplier is able to reduce its transportation cost by consolidating the dierent deliveries, whereas the client does not need dedicated resources to schedule its supplies.

The VMI supplier must thus manage both its deliveries to incur the least transportation cost, and the clients' inventory to satisfy their expected service level. The resulting problem is called the inventory routing problem (IRP). It integrates two operational problems of the supply chain: inventory management and routing. In the IRP network, a supplier is responsible for managing the inventory and the distribution of a set of clients, to satisfy their demands on a given time horizon. The objective of the decision maker is to decide, for each period of the time horizon, whether a client should be replenished, with which quantity and following which route, optimising both the inventory and transportation costs.

A common challenge faced by all supply chain operations is the management of uncertainty; this also applies to the IRP. Indeed, the multiplicity of actors and parameters of the IRP makes the range of uncertainty wide, as they can be related to both inventory management and routing components. The clients' demand may change unexpectedly; a driver may be confronted to an unexpected trac jam, or when arriving at a client's location, the delivery parking slot might be unavailable. By drastically increasing the travelling and service time, or modifying the demand, the decision-maker's plans may become unfeasible.

The most common way to take uncertainties into consideration in the literature is a priori approaches. The a priori approaches manage uncertainties in a proactive way by making robust replenishment plans, that will be feasible even when faced with a wide range of events. The main drawback of such approaches is the conservatism of their solutions, which makes them expensive, especially when the range of variability of the uncertain parameters is wide.

However, tackling uncertainties can be done in dierent fashions. A posteriori approaches handle uncertainties once they are revealed through either repair strategies or a full re-optimisation. The drawback of repairing the initial solution is the diculty to develop strategies that yield feasible solutions without a huge degradation of the solution's cost. Re-optimisation on the other hand can obtain cost-ecient solutions, although such a solution may be completely dierent from the initial one. This deviation between the two solutions may create organisational issues that lead to additional costs that are very dicult to quantify. Thus it is necessary to propose optimisation metrics that ensure the stability of the initial solution.

Another way of managing uncertainties is to study their sources. Indeed, depending on the data, one can notice that all uncertainties are not unpredictable and that some may depend on deterministic parameters. Therefore, it is possible to lift such uncertainties in a a priori but deterministic fashion. The objective of this dissertation is to tackle the IRP's uncertainties by focusing on two of its sources: the clients' demand and the travelling time.

The clients' demand uncertainty is handled through a re-optimisation approach with stability metrics. Stability metrics from the literature of sub-problems of the IRP such as routing and inventory management or similar sequencing problems such as scheduling are re-adapted for the IRP. These metrics are formulated and their correlation and impact on the cost investigated.

For the travelling time, it is managed in an a priori but deterministic fashion by considering it as time dependent. In this context, four mathematical formulations for the time dependent IRP (TD-IRP) inspired from the rich literature of time dependent routing problems are proposed. The four formulations are compared on a new generated benchmark based on benchmarks of the IRP and TD-TSP literature. The relevance of considering time dependent travelling times is investigated and a matheuristic proposed in order to solve large-sized instances.