In this paper, we study a multi-periodic production planning problem in agriculture. This problem belongs to the class of crop rotation planning problems, which have received increased attention in the literature in recent years. Crop cultivation and fallow periods must be scheduled on land plots over a given time horizon so as to minimize the total surface area of land used, while satisfying crop demands every period. This problem is proven strongly N P -hard. We propose a 0-1 linear programming compact formulation based on crop-sequence graphs. An extended formulation is then provided with a polynomial-time pricing problem, and a Branch-and-Priceand-Cut (BPC) algorithm is presented with adapted branching rules and cutting planes. The numerical experiments on instances varying the number of crops, periods and plots show the effectiveness of the BPC for the extended formulation compared to solving the compact formulation, even though these two formulations have the same linear relaxation bound.

This paper introduces an optimization model of a multi-terminal, multi-modal maritime container port, such as the ones in the European northern range. The decisions concern the scheduling of ships, trains and trucks on terminals, while limiting inter-terminal transport of containers and minimizing weighted turnaround time. Heuristics based on the decomposition of the resulting mixed-integer program are proposed and tested on realistic generated instances with up to four terminals. The efficiency of the restrict-and-fix heuristic allows to investigate the impact of a global management on port's performance: an average improvement of 5% was observed.