Motivated by distribution problems arising in the supply chain of Haleon, we investigate a discrete optimization problem that we call the "container delivery scheduling problem". The problem models a supplier dispatching ordered products with shipping containers from manufacturing sites to distribution centers, where orders are collected by the buyers at agreed due times. The supplier may expedite or delay item deliveries to reduce transshipment costs at the price of increasing inventory costs, as measured by the number of containers and distribution center storage/backlog costs, respectively. The goal is to compute a delivery schedule attaining good trade-offs between the two. This container delivery scheduling problem is a temporal variant of classic bin packing problems, where the item sizes are not fixed, but depend on the item due times and delivery times. An approach for solving the problem should specify a batching policy for container consolidation and a scheduling policy for deciding when each container should be delivered. Based on the available item due times, we develop algorithms with sequential and nested batching policies as well as on-time and delay-tolerant scheduling policies. We elaborate on the problem's hardness and substantiate the proposed algorithms with positive and negative approximation bounds, including the derivation of an algorithm achieving an asymptotically tight 2-approximation ratio.

翻译：受Haleon供应链中出现的分销问题驱动，我们研究了一个称为"集装箱配送调度问题"的离散优化问题。该问题建模了供应商将订购产品通过集装箱从制造工厂配送至分销中心的过程，买方在约定的到期时间从分销中心收集订单。供应商可加快或延迟产品配送以减少转运成本，但代价是增加库存成本——前者通过集装箱数量衡量，后者通过分销中心存储/积压成本衡量。目标是计算一个能在两者之间取得良好折衷的配送调度方案。该集装箱配送调度问题是经典装箱问题的时间变体，其中物品尺寸并非固定，而是取决于物品到期时间和配送时间。求解该问题的方法需规定集装箱合并的分批策略以及决定每个集装箱配送时间的调度策略。基于可用的物品到期时间，我们开发了采用顺序分批策略与嵌套分批策略的算法，以及采用准时调度策略与延迟容忍调度策略的算法。我们阐述了问题的难解性，并通过正负近似界验证了所提算法的有效性，包括推导出一个达到渐近紧致2-近似比的算法。