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W e study a single-stage, continuous-time inventory model where unit-sized demands arrive according to a renewal process and show that an (s, S) policy is optimal under minimal assumptions on the ordering/procurement and holding/backorder cost functions. To our knowledge, the derivation of almost all existing (s, S)-optimality results for stochastic inventory models assume that the ordering cost is composed of a fixed setup cost and a proportional variable cost; in contrast, our formulation allows virtually any reasonable ordering-cost structure. Thus, our paper demonstrates that (s, S)-optimality actually holds in an important, primitive stochastic setting for all other practically interesting ordering cost structures such as well-known quantity discount schemes (e.g., all-units, incremental and truckload), multiple setup costs, supplier-imposed size constraints (e.g., batch-ordering and minimum-order-quantity), arbitrary increasing and concave cost, as well as any variants of these. It is noteworthy that our proof only relies on elementary arguments.

PurposeProviding care that is patient-centered is an important objective in the modern healthcare industry. Despite this objective, hospital inpatient case managers and the services they provide are evaluated routinely without including patients' perspectives. Therefore, the purpose of this study is to fill this research gap by using patient expectations and perceptions to assess the overall quality of and patient satisfaction with hospital case management services.Design/methodology/approachThis paper investigates five dimensions of case management services – reliability, responsiveness, assurance, empathy and tangibles – and how they affect overall quality and patient satisfaction. Study surveys are based on the SERVQUAL instrument. Survey data from a cross-sectional sample of 67 inpatients are analyzed using principal component analysis, confirmatory factor analysis, GAP analysis and a predictive model.FindingsThe preliminary part of the study identifies “tangibles” and “nontangibles” – reliability, responsiveness, assurance and empathy – as the main components. Among these two components, only nontangibles have a positive and significant effect on both quality and patient satisfaction according to patient perspectives. GAP analysis indicates that gaps between patient expectations and perceptions of reliability and assurance are significant. Finally, the proposed predictive model reveals that gaps in assurance have a significant impact on both overall quality and satisfaction, while gaps in empathy have a significant impact on satisfaction, but not overall quality.Originality/valueStudies on service quality at the case manager level are limited. This study is the first in this domain to evaluate quality and satisfaction from the patient perspective.

Emerging technologies such as drone delivery services enable retailers to cost‐effectively offer unprecedented delivery speed and adaptable delivery lead times using dedicated aerial vehicles for individual orders. A natural and important question arises: What is the impact of a drone delivery system (DDS) on a retailer’s extant logistics parameters, for example, the number of customer‐facing delivery centers (last‐mile warehouses) it uses and delivery lead times it offers? On the one hand, the ability to reach customers faster than through traditional means argues for more centralization of delivery services. On the other hand, more decentralization can allow the retailer to offer hitherto unheard‐of delivery lead times and thereby spur demand. We show that, as drone technology matures and becomes more cost‐effective, delivery networks will become increasingly decentralized while delivering products at faster speeds. While perfect delivery customization—under which each demand location is offered a customized delivery guarantee—is theoretically feasible under a DDS, it may not be practical to implement such a finely differentiated delivery strategy. Instead, we show that retailers can recover a significant portion of the profit under this ideal scenario by offering limited delivery‐time customization, that is, partitioning the market into a few delivery “zones” and offering the best feasible delivery guarantee for each zone. In physically congested metropolitan markets, where retailers may be forced to operate with only a few delivery centers, it may be optimal to operate a DDS by offering delivery guarantees that are inferior to the best possible in order to throttle unprofitable demand. In such markets, the effectiveness of limited delivery‐time customization increases as the extent of physical congestion increases.

Fixed costs of ordering items or setting up a production process arise in many real-life scenarios. In their presence, the most widely used ordering policy in the stochastic inventory literature is the (s, S) policy. Optimality of (s, S) policies and (s, S)-type policies have been examined for various inventory models, including those with the inventory level being reviewed in every period or continuously, finite and infinite horizons, discounted-cost and average-cost criteria, backlogging and lost-sales practices, standard and generalized demands and/or costs, deterministic and stochastic lead times, single-product and multi-product settings, and coordinated pricing-inventory decisions. We comprehensively survey the vast literature accumulated over seven decades in two papers. This paper is devoted to discrete-time models, and the companion paper, also published in this journal issue, reviews continuous-time models. We go over model specifications, proof techniques, specific results, and limitations of the articles published in the literature. We conclude each paper by providing corresponding suggestions for extensions and directions for future research. K E Y W O R D Sdiscounted-and average-cost criteria, discrete-time inventory models, K-convexity, Markovian demand, optimality of (s, S)-type policies CONTENTS