We study request acceptance dynamics in same-day delivery systems by formulating the Dynamic Dispatch Waves Problem with Immediate Acceptance, which models integrated management and distribution for dynamically arriving customer requests. We consider an e-commerce platform that attempts to serve most customers with same-day delivery service. When a shopper attempts to place an order, a decision is made immediately to offer same-day delivery service (accept the request) or to deny service. Accepted requests are not available for immediate dispatch; they must be processed (picked and packed) before they are loaded for delivery. Vehicle routes are updated dynamically and serve each accepted delivery request no later than the end of the service day. In this work, we limit the study to the case of a single vehicle serving requests, potentially using multiple trips from the distribution center. The objective is to make request acceptance and distribution decisions that minimize the expected sum of vehicle travel costs and penalties for service denials. We develop a framework for dynamic decision policies over continuous time for such systems, where a feasible vehicle dispatch plan is redesigned and used to guide decisions over time. We design methods for determining an initial optimal a priori plan and for updating the plan using a heuristic roll-out procedure. Our methods are tested on a family of simulated instances against two common-sense benchmarks and an infeasible relaxed policy that allows the dispatcher to delay the acceptance or rejection of a request until the end of the service day. We demonstrate in our computational study that the cost-per-request of the best benchmark policy is on average 9.7% higher than our proposed dynamic policy and furthermore that the dynamic policy leads to only a 4.4% cost increase over the infeasible relaxed policy lower bound.

我们通过制定具有立即接受的动态调度波问题来研究当日交货系统中的请求接受动态，该问题为动态到达的客户请求建模了集成的管理和分发。我们考虑一个电子商务平台，该平台试图为大多数客户提供当日送货服务。当购物者试图下订单时，将立即决定提供当日送货服务（接受请求）或拒绝服务。接受的请求不可立即发送；必须先对它们进行处理（挑选和包装），然后再进行装载。车辆路线会动态更新，并在服务日结束之前为每个接受的交货请求服务。在这项工作中，我们将研究范围限制在单个车辆满足要求的情况下，可能会使用配送中心的多次行程。目的是做出请求接受和分配决策，以最大程度地减少预期的车辆旅行成本和拒绝服务罚款的总和。我们为此类系统的连续时间开发了动态决策策略框架，其中重新设计了可行的车辆调度计划，并用于指导随着时间的推移做出决策。我们设计用于确定初始最优值的方法先验计划，并使用试探性推出程序更新计划。我们的方法已在一系列两个常识性基准的模拟实例上进行了测试，并且采用了一种不可行的宽松政策，该政策允许调度员将接受或拒绝请求的时间推迟到服务日结束之前。我们在计算研究中证明，最佳基准策略的平均每次请求费用比我们提出的动态策略平均高出9.7％，此外，动态策略只会导致不可行的宽松策略下限仅增加4.4％的成本。