Zhenzhen Yan

Problem definition: A significant percentage of online consumers place consecutive orders within a short duration. To reduce the total order arrangement cost, an online retailer may consolidate consecutive orders from the same consumer. We investigate how long the retailer should hold the consumer’s orders before sending them to a third-party logistics provider (3PL) for processing. In this order-holding problem, we optimize the holding time to balance the total order arrangement cost and the potential delay in delivery. Methodology/results: We model the order-holding problem as a Markov decision process. We show that the optimal order-holding decisions follow a threshold-type policy that is straightforward to implement: Hold any pending orders if the holding time is within a threshold or send them to the 3PL otherwise. Whenever the consumer places a new order, the holding time is reset, and the threshold is updated based on a cumulative set of the past consecutive orders in the consumer’s shopping journey. Using a consumer’s sequential decision model, we personalize the threshold by finding its closed-form expression in the consumer’s order features. We determine the model’s coefficients and evaluate the threshold-type policy using the data of the 2020 MSOM Data Driven Research Challenge. Extensive numerical experiments suggest that the personalized threshold-type policy outperforms two commonly used benchmarks by having fewer order arrangements or shorter holding times. Furthermore, personalizing the order-holding decisions is significantly more valuable for “enterprise” customers. Managerial implications: Our research suggests a higher threshold for consumers who are more likely to place consecutive orders within a short duration. The consumers’ demographic information has a significant effect on the threshold. Specifically, the threshold is higher for “plus” consumers, female consumers, and consumers in the age group of 16–25 years. The threshold for tier 1 cities is lower than that for tier 2 to tier 4 cities but higher than that for tier 5 cities. History: This paper has been accepted as part of the 2020 MSOM Data Driven Challenge. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71931009, 72201237, and 72231009], the Research Grants Council of Hong Kong [Grants 15501920 and 15501221], the Singapore Ministry of Education Academic Research Fund [Tier 1, Grant RG17/21; Tier 2, Grant MOE2019-T2-1-045], the Association of South-East Asian Nations Business Research Initiative Grant [Grant G17C20421], and the Neptune Orient Lines [Fellowship NOL21RP04]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.1201 .

Problem definition: This paper studies an appointment system where a finite number of customers are scheduled to arrive in such a way that (1) the expected waiting time of each individual customer cannot exceed a given threshold; and (2) the appointment times are set as early as possible (without breaking the waiting time constraint). Methodology/results: First, we show that, under the service-level constraint, a prospective schedule can be obtained from a sequential scheduling approach. In particular, we can schedule the appointment time of the next customer based on the scheduled appointment times of the previous customers. Then, we use a transient queueing-analysis approach and apply the theory of majorization to analytically characterize the structure of the optimal appointment schedule. We prove that, to keep the expected waiting time of each customer below a certain threshold, the minimum inter-appointment time required increases with the arrival sequence. We further identify additional properties of the optimal schedule. For example, a later arrival has a higher chance of finding an empty system and is more likely to wait less than the duration of his expected service time. We show the convergence of the service-level-constrained system to the D/M/1 queueing system as the number of arrivals approaches infinity and propose a simple, yet practical, heuristic schedule that is asymptotically optimal. We also develop algorithms that can help system managers determine the number of customers that can be scheduled in a fixed time window. We compare the service-level-constrained appointment system with other widely studied systems (including the equal-space and cost-minimization systems). We show that the service-level-constrained system leads to a lower upper bound on each customer’s waiting time; ensures a fair waiting experience among customers; and performs quite well in terms of system overtime. Finally, we investigate various extended settings of our analysis, including customer no-shows; mixed Erlang service times; multiple servers; and probability-based service-level constraints. Managerial implications: Our results provide guidelines on how to design appointment schedules with individual service-level constraints. Such a design ensures fairness and incorporates the threshold-type waiting perception of customers. It is also free from cost estimation and can be easily applied in practice. In addition, under the service-level-constrained appointment system, customers with later appointment times can have better waiting experiences, in contrast to the situation under other commonly studied systems. Funding: Z. Yan was partly supported by a Nanyang Technological University startup grant; the Ministry of Education Academic Research Fund Tier 1 [Grant RG17/21] and Tier 2 [Grant MOE2019-T2-1-045]; and Neptune Orient Lines [Fellowship Grant NOL21RP04]. Supplemental Material: The online supplement is available at https://doi.org/10.1287/msom.2022.1159 .