Timetabling of sorting slots in a logistic warehouse

We study a problem appearing at the end of a logistic stream in a warehouse and which concerns the timetabling of sorting slots necessary to accomodate the prepared orders before being dispatched. We consider a set of orders to be prepared on some preparation shops over a given time horizon. Each order is associated with the truck handling its transportation to its customer. A sorting slot is an accumulation area where processed orders await to be loaded on a truck. To a given truck, a known number of sorting slots is needed from the time the first order associated with the truck begins to be prepared, and this, until the known departure time of the truck. Since several orders associated with different trucks are processed simultaneously and since the number of sorting slots is limited, the timetabling of these resources is necessary to ensure that all orders can be processed over the considered time horizon without violating the resource constraint on sorting slots. In this talk, we describe the general industrial context of the problem and we formalize it. We state that some particular cases of the problem are polynomially solvable while the general problem is NP-complete. Then, we propose optimization methods to solve it.