This problem is inspired by a large multinational automotive company, which imposes cadences when manufacturing their cars, so the ones with more demanding features aren't scheduled in close proximity to each other. Hereafter, cars will be denoted as jobs. The goal of this project is to sequence the maximum number of consecutive jobs, while respecting their cadences.

Each cadence is described by one of the following policies.

• Policy 1: given a subset of jobs S, at most C(S) jobs in S can be scheduled contiguously in the sequence;
• Policy 2: given a subset of jobs T, all jobs in T put in the sequence must have at least A(T) jobs outside of T in between them.

There are four sets of instances: A, B, C and D. Set A was obtained by real demands of the company. The remaining sets had the addition of one extra cadence and have different limits on the number of jobs with the same cadence pattern. Set B has at most 8 jobs with the same cadences, if there are enough cadence patterns to do so. This limit is 4 and 2 for sets C and D, respectively. Hence there is an increasing difficulty from set A to set D.

Different strategies were tested to solve this problem:

• Feasibility checking using binary and iterative searches with trivial, combinatorial and heuristic bounds;
• Optimization model based on jobs (F1);
• Optimization model based on families of jobs to reduce symmetries (F2).

The detailed results can be found in the folder "results".

• Lara di Cavalcanti Pontes
• Carlos Vinícius Costa Neves (https://github.com/cvneves)