The notion of 'resource' plays an important role in the overall efficiency and performance of most cross-docks. The processing time can often be described in terms of the resources allocated to different trucks. Conversely, for a given processing time, different combinations of resources can be prescribed. We study the problem of truck scheduling and dock assignment in the presence of resource constraints. In the absence of a closed-form (or well-defined) linear formulation describing the processing times as a function of resources, expert' knowledge has been mobilised to enable modelling of the problem as an integer linear model. Two cases are taken into account: In the first one, the expert believes in his/her estimation of the processing time for every truck and only proposes a different combination of resources for his/her estimation, while in the second one the expert proposes a limited number of resource deployment scenarios for serving trucks, each of which has a different combination of resources and different processing times. We propose a novel compact integer programming formulation for the problem, which is particularly designed with an embedded structure that can be exploited in dual decomposition techniques with a remarkably computationally efficient column generation approach in this case. The case in which a scenario with invariant processing time is considered and modelled as a special case of the proposed model. Since a direct application of commercial solvers such as CPLEX to solve instances of this problem is not realistic, we propose a branch-and-price framework and, moreover, several classes of valid inequalities. Our extensive computational experiments confirm that the proposed exact solution framework is very efficient and viable in solving real-size instances of the practice and in a reasonable amount of time.

翻译：“资源”概念在多数越库中心的整体效率与性能中扮演着重要角色。加工时间通常可描述为分配给不同卡车的资源函数。反之，对于给定的加工时间，可规定不同的资源组合。我们研究存在资源约束条件下的卡车调度与码头分配问题。由于缺乏描述加工时间作为资源函数的闭式（或良定义）线性表达式，我们借助专家知识将问题建模为整数线性模型。我们考虑两种情形：第一种情形中，专家相信其对每辆卡车加工时间的估计，仅针对其估计值提出不同的资源组合；第二种情形中，专家提出有限数量的服务于卡车的资源部署场景，每个场景具有不同的资源组合和加工时间。我们提出一种新颖的紧凑整数规划模型，其内嵌结构可被有效利用于对偶分解技术中，并配合计算高效的列生成方法。将加工时间不变场景视为所提模型的特例进行建模。由于直接应用CPLEX等商业求解器求解该问题实例不现实，我们提出分支定价框架以及多类有效不等式。大量计算实验表明，所提精确求解框架在合理时间内求解实际规模实例时高效可行。