It is critical to accurately identify patients with severe acute pancreatitis (SAP) in a timely manner. This study aimed to develop a new simplified AP scoring system based on data from Chinese population. We retrospectively analyzed a consecutive series of 585 patients diagnosed with SAP at the Changhai hospital between 2009 and 2017. The new Chinese simple scoring system (CSSS) was derived using logistic regression analysis and was validated in comparison to 4 existing systems using receiver operating characteristic curves. Six variables were selected for incorporation into CSSS, including serum creatinine, blood glucose, lactate dehydrogenase, heart rate, C-reactive protein, and extent of pancreatic necrosis. The new CSSS yields a maximum total score of 9 points. The cut-offs for predicting mortality and severity (discriminating moderately SAP from SAP) were set as 6 points and 4 points respectively. Compared with 4 existing scoring systems, the area under the receiver operating characteristic of CSSS for prediction of mortality was 0.838, similar to acute physiology and chronic health evaluation II (0.844) and higher than Ranson's score (0.702, P < .001), bedside index of severity in acute pancreatitis (0.615), and modified computed tomography severity index (MCTSI) (0.736). For predicting SAP severity, CSSS was the most accurate (0.834), followed by acute physiology and chronic health evaluation II (0.800), Ranson's score (0.702), MCTSI (0.660), and bedside index of severity in acute pancreatitis (0.570). Further, the accuracy of predicting pancreatic infection with CSSS was the highest (0.634), similar to that of MCTSI (0.641). A new prognostic scoring system for SAP was derived and validated in a Chinese sample. This scoring system is a simple and accurate method for prediction of mortality.

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We consider the problem of managing production in a production-inventory system where a firm is subject to an allowance (a limit) on either the amount of input it can use or the amount of output it can produce over a specified compliance period (in addition to being subject to a constraint on the production capacity). Examples of such settings are numerous and include those where limits are placed on the use of scarce natural resources as input or on the amount of waste or harmful pollution generated by production as output. We study the structure of the optimal production policy for such systems and show that it is determined by dynamic thresholds that depend only on the sum of the on-hand inventory level and the remaining allowance. We provide an effective approximate solution approach that can compute these thresholds efficiently while retaining their essential properties. We examine the differences between how an allowance constraint and a constraint on production capacity affect production decisions and show that they exhibit opposite effects over time. We also examine, in the context of an extended version of the problem where both the allowance amount and the production capacity are endogenous, optimal investments in allowance and production capacity and the impact of both on firm profit. We also consider the optimal demand fulfillment policy in settings where the firm can decide whether to back-order or to reject demand that cannot be satisfied from on-hand inventory. The online appendix is available at https://doi.org/10.1287/msom.2016.0603 .

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 .

W e consider service systems with a finite number of customer arrivals, where customer interarrival times and service times are both stochastic and heterogeneous. Applications of such systems are numerous and include systems where arrivals are driven by events or service completions in serial processes as well as systems where servers are subject to learning or fatigue. Using an embedded Markov chain approach, we characterize the waiting time distribution for each customer, from which we obtain various performance measures of interest, including the expected waiting time of a specific customer, the expected waiting time of an arbitrary customer, and the expected completion time of all customers. We carry out extensive numerical experiments to examine the effect of heterogeneity in interarrival and service times. In particular, we examine cases where interarrival and service times increase with each subsequent arrival or service completion, decrease, increase and then decrease, or decrease and then increase. We derive several managerial insights and discuss implications for settings where such features can be induced. We validate the numerical results using a fluid approximation that yields closed-form expressions.