A methodology for the cross-dock door platforms design under uncertainty
arxiv(2024)
摘要
The cross dock door design problem consists of deciding on the number and
capacity of inbound and outbound doors for receiving product pallets from
origin nodes and exiting them to destination nodes. The uncertainty, realized
in scenarios, lies in the occurrence of these nodes, the number and cost of the
pallets, and the disruption of the capacity of the doors. It is represented
using a stochastic two stage binary quadratic model. The first stage decisions
are related to the cross dock infrastructure design, and the second stage
decisions are related to the node to assignments of the doors. This is the
first time, as far as we know, that a stochastic two stage binary quadratic
model has been presented for minimizing the construction cost of the
infrastructure and its exploitation expected cost in the scenarios. Given the
difficulty of solving this combinatorial problem, a mathematically equivalent
mixed integer linear formulation is introduced. However, searching an optimal
solution is still impractical for commercial solvers. Thus, a scenario cluster
decomposition based matheuristic algorithm is introduced to obtain feasible
solutions with small optimality gap and reasonable computational effort. A
broad study to validate the proposal gives solutions with a much smaller gap
than the ones provided by a state of the art general solver. In fact, the
proposal provides solutions with a 1 to 5
does it with up to a 12
magnitude higher.
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