Online food delivery companies, nowadays, allow a customer to place an order for a combination of dishes from one or more restaurants. To meet a customer’s demand, the company then arranges for the pickups from different restaurants, perhaps located distantly, before delivering them to the customer. The company caters to a set of such customers, through a fleet of capacitated vehicles. In this paper, we propose an augmented two-index formulation to find least cost vehicle routes to satisfy the set of customer requests under the constraints of time windows of the pickup and delivery locations along with the capacity constraints of the fleet of vehicles. We use branch-and-cut algorithm to solve the benchmark problem instances. The proposed formulation and the problem specific valid inequalities lead to more efficient solution performance as against the existing formulations. The computational experiments indicate that the proposed approach can solve a majority of benchmark problem instances with 25, 35 and 50 nodes, many of which were reported unsolved using exact solution approaches in the extant literature.

如今，在线食品配送公司允许顾客从一家或多家餐厅下订单组合菜肴。为了满足客户的需求，该公司会安排从不同的餐厅（可能距离较远）取货，然后再将其交付给客户。该公司通过一支有能力的车队来满足一批此类客户的需求。在本文中，我们提出了一种增强的二指数公式，以在取货和送货地点的时间窗口以及车队的容量限制的约束下找到满足客户要求的最低成本车辆路线。我们使用分支剪切算法来解决基准问题实例。与现有的公式相比，所提出的公式和问题特定的有效不等式导致更有效的解决方案性能。计算实验表明，所提出的方法可以解决大多数具有 25、35 和 50 个节点的基准问题实例，其中许多问题在现有文献中使用精确求解方法无法解决。