“KaPeJu Titanium knees” case study

In this case study, an inventory management problem is introduced.Maheut, JPD.; García Sabater, JP. (2022). “KaPeJu Titanium knees” case study. http://hdl.handle.net/10251/18077

A solution method for a car fleet management problem with maintenance constraints

The problem retained for the ROADEF'99 international challenge was an inventory management problem for a car rental company. It consists in managing a given fleet of cars in order to satisfy requests from customers asking for some type of cars for a given time period. When requests exceed the stock of available cars, the company can either offer better cars than those requested, subcontract some requests to other providers, or buy new cars to enlarge the available stock. Moreover, the cars have to go through a maintenance process at a regular basis, and there is a limited number of workers that are available to perform these maintenances. The problem of satisfying all customer requests at minimum cost is known to be NP-hard. We propose a solution technique that combines two tabu search procedures with algorithms for the shortest path, the graph coloring and the maximum weighted independent set problems. Tests on benchmark instances used for the ROADEF'99 challenge give evidence that the proposed algorithm outperforms all other existing methods (thirteen competitors took part to this contest

On the Sample Size of Random Convex Programs with Structured Dependence on the Uncertainty (Extended Version)

The "scenario approach" provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled constraints (scenarios). The sample size critically depends on Helly's dimension, a quantity always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost and violation probability. We derive improved bounds of Helly's dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of scenarios required for these problems, leading both to improved objective value and reduced computational complexity. Our results are generally applicable to Randomized Model Predictive Control of chance constrained linear systems with additive uncertainty and affine disturbance feedback. The efficacy of the proposed bound is demonstrated on an inventory management example.Comment: Accepted for publication at Automatic

Solving a Supply Chain Optimization Problem Collaboratively

We propose a novel algorithmic framework to solve an integrated planning and scheduling problem in supply chain management. This problem involves the integration of an inventory management problem and the vehicle routing problem with time windows, both of which are known to be NP-hard. Under this framework, algorithms that solve the underlying sub-problems collaborate rigorously yet in a computationally efficient manner to arrive at a good solution. We will then present two algorithms to solve the inventory management problem: a complete mathematical model integrating integer programming with constraint programming, and an incomplete algorithm based on tabu search. We present experimental results based on extended Solomon benchmark vehicle routing problems