To perform diagnosis and treatment, health systems, hospitals, and other patient care facilities require a wide range of supplies, from masks and gloves to catheters and implants. The “healthcare supply chain/healthcare operation management” refers to the stakeholders, systems, and processes required to move products from the manufacturer to the patient’s bedside. The ultimate goal of the healthcare supply chain is to ensure that the right products, in the right quantities, are available in the right places at the right time to support patient care. Hospitals and the concept of a healthcare delivery system are practically synonymous. Surgical services, emergency and disaster services, and inpatient care are the three main types of services they offer. Outpatient clinics and facilities are also available at some hospitals, where patients can receive specialty consultations and surgical services. There will always be a need for inpatient care, regardless of how care models develop. The focus of this monograph was on recent OM work that models the dynamic, interrelated effects of demand-supply matching in the ED, OR, and inpatient units. Decisions about staffing and scheduling in these areas are frequently made independently by healthcare managers and clinicians. Then, as demand changes in real-time, clinicians and managers retaliate as best as they can to reallocate staffing to the areas that require it most at a particular moment in time in order to relieve patient flow bottlenecks. We, as OM researchers, must create models that help healthcare administrators enhance OR scheduling policies, ED demand forecasting, and medium- and short-term staffing plans that consider the interdependence of how demand develops.

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In the context of frequent public emergencies, emergency logistics distribution is particularly critical, and because of the unique advantages of unmanned aerial vehicles (UAVs), the model of coordinated delivery of vehicles and UAVs is gradually becoming an essential form of emergency logistics distribution. However, the omission of start-up costs prevents the cost of UAV battery replacement and the sorting, assembly and verification of packages from being factored into the total cost. Furthermore, most existing models focus on route optimization and delivery cost, which cannot fully reflect the customer’s desire for service satisfaction under emergency conditions. It is necessary to convert the unsatisfactory degree of time window into a penalty cost rather than a model constraint. Additionally, there is a lack of analysis on the mutual waiting cost between vehicles and UAVs when one of them is performing delivery tasks. Considering the effects of the time window, customer demand, maximum load capacity, and duration of distribution benefits, we propose a collaborative delivery path optimization model for vehicles and UAVs to minimize the total distribution cost. A genetic algorithm is used to obtain the model solution under the constraints of distribution subloops, distribution order, and take-off and landing nodes. To assess the efficacy of the vehicle and UAV collaborative delivery path optimization model, this paper employs a county-level district in Xi’an city as a pilot area for an emergency delivery. Compared with the vehicle-alone delivery model, the UAV-alone delivery model and vehicle-UAV collaborative delivery model, this model can significantly reduce the utilization of distribution vehicles while also significantly lowering the start-up cost, waiting cost and penalty cost. Thus, the model can effectively improve delivery timeliness and customer satisfaction. The total cost of this model is 39.2% less than that of the vehicle-alone delivery model and 16.5% less than that of the UAV-alone delivery model. Although its delivery cost is slightly higher than the vehicle-UAV collaborative delivery model, the reduction in the start-up cost and penalty cost decrease the overall cost of distribution by 11.8%. This suggests that to cut costs of all sizes and conserve half of the resources used by vehicles, employing the vehicle-UAV collaborative delivery model for emergency distribution is preferable. Moreover, the model integrating the start-up cost, penalty cost, waiting cost, etc., can more effectively express the requirements of timeliness for UAV delivery under emergency conditions.

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The distribution of emergency perishable materials after a disaster, such as an earthquake, is an essential part of emergency resource dispatching. However, the traditional single-period distribution model can hardly solve this problem because of incomplete demand information for emergency perishable materials in affected sites. Therefore, for such problems we firstly construct a multi-period vehicle path distribution optimization model with the dual objectives of minimizing the cost penalty of distribution delay and the total corruption during delivery, and minimizing the total amount of demand that is not met, by applying the interval boundary and most likely value weighting method to make uncertain demand clear. Then, we formulate the differential evolutionary whale optimization algorithm (DE-WOA) combing the differential evolutionary algorithm with the whale algorithm to solve the constructed model, which is an up-and-coming algorithm for solving this type of problem. Finally, to validate the feasibility and practicality of the proposed model and the novel algorithm, a comparison between the proposed model and the standard whale optimization algorithm is performed on a numerical instance. The result indicates the proposed model converges faster and the overall optimization effect is improved by 23%, which further verifies that the improved whale optimization algorithm has better performance.

The connection between generalized convexity and symmetry has been studied by many authors in recent years. Due to this strong connection, generalized convexity and symmetry have arisen as a new topic in the subject of inequalities. In this paper, we introduce the concept of interval-valued preinvex functions on the coordinates in a rectangle from the plane and prove Hermite–Hadamard type inclusions for interval-valued preinvex functions on coordinates. Further, we establish Hermite–Hadamard type inclusions for the product of two interval-valued coordinated preinvex functions. These results are motivated by the symmetric results obtained in the recent article by Kara et al. in 2021 on weighted Hermite–Hadamard type inclusions for products of coordinated convex interval-valued functions. Our established results generalize and extend some recent results obtained in the existing literature. Moreover, we provide suitable examples in the support of our theoretical results.

We introduce a new class of interval-valued preinvex functions termed as harmonically h-preinvex interval-valued functions. We establish new inclusion of Hermite–Hadamard for harmonically h-preinvex interval-valued function via interval-valued Riemann–Liouville fractional integrals. Further, we prove fractional Hermite–Hadamard-type inclusions for the product of two harmonically h-preinvex interval-valued functions. In this way, these findings include several well-known results and newly obtained results of the existing literature as special cases. Moreover, applications of the main results are demonstrated by presenting some examples.

This paper presents a modification of the q-BFGS method for nonlinear unconstrained optimization problems. For this modification, we use a simple symmetric positive definite matrix and propose a new q-quasi-Newton equation, which is close to the ordinary q-quasi-Newton equation in the limiting case. This method uses only first order q-derivatives to build an approximate q-Hessian over a number of iterations. The q-Armijo-Wolfe line search condition is used to calculate step length, which guarantees that the objective function value is decreasing. This modified q-BFGS method preserves the global convergence properties of the q-BFGS method, without the convexity assumption on the objective function. Numerical results on some test problems are presented, which show that an improvement has been achieved. Moreover, we depict the numerical results through the performance profiles.