In this paper, we study event-based mixed-integer programming (MIP) formulations for the resource-constrained project scheduling problem (RCPSP) that represent an alternative to the more common time-indexed model (DDT) (Pritsker et al. in Manag Sci 16(1):93-108, 1969; Christofides et al. in Eur J Oper Res 29(3):262-273, 1987) for the case when the scheduling horizon is large. In contrast to time-indexed models, the size of event-based models does not depend on the time horizon. For two event-based models OOE and SEE introduced by Koné et al. (Comput Oper Res 38(1):3-13, 2011), we first present new valid inequalities that strengthen the original formulation. Furthermore, we state a new event-based model, the Interval Event-Based Model (IEE), and deduce natural linear transformations between all three models. Those transformations yield the strict domination order I E E S E E O O E for their respective linear programming relaxations, meaning that the new IEE model has the strongest linear relaxation among all known event-based models. In addition, we show that DDT can be retrieved from IEE by subsequent expansion and projection of the underlying solution space. This yields a unified polyhedral view on a complete branch of MIP models for the RCPSP. Finally, we also compare the computational performance between all models on common test instances of the PSPLIB (Kolisch and Sprecher in Eur J Oper Res 96(1):205-216, 1997).

We study the Min-Weighted Sum Bin Packing problem, a variant of the classical Bin Packing problem in which items have a weight, and each item induces a cost equal to its weight multiplied by the index of the bin in which it is packed. This is in fact equivalent to a batch scheduling problem that arises in many fields of applications such as appointment scheduling or warehouse logistics. We give improved lower and upper bounds on the approximation ratio of two simple algorithms for this problem. In particular, we show that the knapsack-batching algorithm, which iteratively solves knapsack problems over the set of remaining items to pack the maximal weight in the current bin, has an approximation ratio of at most 17/10.

(1) Background: One-day surgery has been widely adopted for many elective laparoscopic procedures in pediatric patients. Recently, the same protocol has been investigated for some emergency procedures, such as laparoscopic appendectomy. This study aimed to evaluate the safety and effectiveness of discharge from hospital within 24 h in pediatric patients who received laparoscopic appendectomy for uncomplicated acute appendicitis. (2) Methods: From 1 March 2021 to 1 May 2022, a total of 180 pediatric patients who were discharged from hospital within 24 h after laparoscopic appendectomy for uncomplicated appendicitis were included in this prospective single-center study. The primary outcome of this study was the safety of discharge from hospital within 24 h after laparoscopic appendectomy for uncomplicated appendicitis, as well as the parental satisfaction with this protocol. Secondary outcomes included the rate of readmission or unplanned return to the operating room, the complication rate and a cost-effectiveness analysis. For each patient, demographic data, preoperative evaluation (physical examination, laboratory data, imaging), duration of surgery, intraoperative and postoperative complications, length of hospital stay and pain levels, as well as parental satisfaction with this protocol, were recorded. (3) Results: The median age was 11 years (interquartile range (IQR) 10, 14). The majority of the patients (63.8%) were males. The median length of hospital stay after surgery was 15 h (IQR 12, 19). The highest level of satisfaction, at discharge, was recorded in most of the respondents (n = 155, 86.1%), while the remaining 25 (13.9%) expressed moderate levels of satisfaction. The median pain levels according to a visual analogue scale for all postoperative days were low (range 0–4). In four patients (2.2%), unplanned readmission before the seventh postoperative day because of postoperative intraabdominal abscess was recorded. All patients with abscess formation were treated conservatively. The majority of the parents (n = 175; 97.2%) expressed the highest level of satisfaction during the outpatient follow-up examination on the seventh postoperative day. (4) Conclusions: Same-day discharge after laparoscopic appendectomy for simple appendicitis in pediatric patients was safe and feasible. Parental satisfaction with this protocol was very high. With the right protocol and parent education, pediatric patients who underwent laparoscopic appendectomy because of non-complicated acute appendicitis may be successfully treated in this way.

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