Organizational well-being is increasingly shaped by the evolving landscape of digital workflows, driven by a surge in innovative software applications. Among these, online automation platforms have become central to improving operational health by enabling organizations to automate business processes through flexible, task-centric workflows that minimize human intervention. Despite widespread adoption, effectively structuring these digital workflows within automation environments remains a key challenge to maintaining productivity and organizational resilience. Inspired by the success of recommendation systems in domains like e-commerce, we propose an intelligent digital workflow recommendation framework aimed at enhancing decision-making and ensuring better process alignment. Our method captures the sequential usage patterns of applications across real-world digital workflows, utilizing data from a no-code automation platform. It combines the power of singular value decomposition with machine learning-based clustering to form a robust and adaptive recommendation engine. Through extensive experiments involving various workflow recommendation stages, we benchmark our model against traditional approaches, including the Markov chain and random recommendation strategies. The results consistently demonstrate the superior accuracy and adaptability of our model across all test scenarios. Beyond empirical performance, we examine the theoretical and practical implications of our approach. By supporting better workflow design and optimization, it contributes to the broader goal of organizational well-being–enhancing operational clarity, reducing cognitive load, and fostering agile adaptation in dynamic environments. As organizations increasingly depend on AI and automation for sustainable growth and efficiency, our methodology underscores the transformative role of recommender systems in shaping intelligent, data-driven digital workflows. Integrating sequential pattern analysis with AI-powered insights, our approach becomes a strategic asset in the journey toward digital well-being and resilience.

This study examines two consequences when a producer adds a new digital channel. The first is the channel’s interest effects between the newly added digital and the existing channel. The second is the rivalry effects between a producer and retailer. We analytically develop four models for four different channel strategies to optimize the price of channels. The present research informs the producer that if customers are very heterogeneous, then the producer may propose a multichannel strategy. If customers become homogenous, then the producer will acquire an omni-channel strategy. The producer provides a brick-and-mortar approach if the target customers are neither diverse nor comparable. We discuss the channel interest for market leadership. The producer employs the digital channel when the impact of rivalry becomes severe. The retailer might limit its market leadership when this independently constructed rivalry in the retail market helps to mitigate the optimization problem of channel pricing.

Frank Hilton Jackson extended the classical concept of derivative and introduced the qderivative, popularly known as Jackson’s derivative. To solve large-scale unconstrained optimization problems, we propose a q-spectral Polak-Ribiére-Polyak (PRP) conjugate gradient method. The method can be viewed as a generalization of the spectral PRP method, replacing the classical gradient with the q-gradient vector that utilises the first-order partial q-derivatives derived from Jackson’s derivative. Additionally, as the value of q approaches one, the proposed approach simplifies to the classical form. Numerical experiments are conducted and compared with existing methods to demonstrate the advantages of the proposed approach. Moreover, as an application, we solve the motion control problem.

Any country’s healthcare system is vital for its progress, quality of life, and long-term viability. During the pandemic, many developed countries encountered challenges of differing degrees in the administration of their healthcare systems. The overloading of healthcare services is common, leading to prolonged waiting times for medical services. Thus, the wastage of hospital resources must be taken seriously. In this paper, we examine the problem of no-shows and cancellations in outpatient clinics. By examining the literature and drawing from practical industry experience, we uncover the operational procedures of these clinics. We then suggest a robust optimization strategy for overbooking, incorporating both a conventional overbooking model and a resilient system approach. The proposed model seeks to address the substantial uncertainties in parameters encountered during the pandemic. Taking into account risk aversion, we develop an optimal overbooking policy that considers the associated costs. The primary contribution lies in introducing an alternative approach to manage the uncertainty of no-shows and cancellations through the utilization of an overbooking technique.

This book provides a better clue to apply quantum derivative instead of classical derivative in the modified optimization methods, compared with the competing books which employ a number of standard derivative optimization techniques to address large-scale, unconstrained optimization issues. Essential proofs and applications of the various techniques are given in simple manner without sacrificing accuracy. New concepts are illustrated with the help of examples. This book presents the theory and application of given optimization techniques in generalized and comprehensive manner. Methods such as steepest descent, conjugate gradient and BFGS are generalized and comparative analyses will show the efficiency of the techniques.

Quantum computing is an emerging field that has had a significant impact on optimization. Among the diverse quantum algorithms, quantum gradient descent has become a prominent technique for solving unconstrained optimization (UO) problems. In this paper, we propose a quantum spectral Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) approach. The technique is considered as a generalization of the spectral PRP method which employs a q-gradient that approximates the classical gradient with quadratically better dependence on the quantum variable q. Additionally, the proposed method reduces to the classical variant as the quantum variable q approaches closer to 1. The quantum search direction always satisfies the sufficient descent condition and does not depend on any line search (LS). This approach is globally convergent with the standard Wolfe conditions without any convexity assumption. Numerical experiments are conducted and compared with the existing approach to demonstrate the improvement of the proposed strategy.

The Physical Internet (PI) provides a solution for coping with the continuous rise in urban logistical demands by exploring same-level and cross-level paths. This research suggests a PI-based urban logistical distribution model based on PI distribution that minimizes transportation costs. It also intends to maintain the integrity of the logistical transportation process. This proposed model enhances the flexibility of goods operation and reduces the global cost of logistics’ distribution using an interconnected and open PI logistics distribution mode. This model also explores the functional aspects of the operational problems of city logistical systems and relates to optimization problems. These functionalities are realized by the hierarchical functional structure and are characterized by different cost specifications. The proposed framework provides better integration and cooperation between city logistics warehouses and higher utilization level of logistical infrastructure. The experimental results show that the distribution cost of the PI logistics model is significantly better than that of a traditional logistics model. The elastic and cost advantages grow relatively as the infrastructure for distribution scales up and interruptions from emergencies occur.

We propose a network optimization model for smart energy market management in the context of an uncertain environment. The network optimization considers the stochastic programming approach to capture the randomness of the unknown demands. We utilize the particle swarm optimization technique in the proposed model to solve the proposed optimization problem. The present research is based on the inclusion of stochastic demands and uncertain energy prices. Optimizing produced energy is crucial for efficient usage and meeting the targets. The proposed model also focuses on addressing sustainability concerns by minimizing energy consumption in the scheduling process. An improved particle swarm optimization technique is implemented for energy-efficient production. Parameters such as number of particles, iterations, and energy usage specification are customized. A fitness function is taken that considers both completion time and energy consumption. The optimal of energy consumption is also visualized. The decision makers employ risk aversion in the objective function of the optimization problem to measure the risk deviation of the expected energy management.

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.

The mobile emergency system is a new emergency mode that provides a solution to deal with increasingly frequent sudden disasters by reasonably allocating mobile emergency facilities and optimizing the allocation of mobile emergency materials. We consider mobile emergency cost and mobile emergency time as two objective functions. This paper establishes a multi-objective mobile emergency material allocation model, and transforms the multi-objective. We choose the emergency material transportation path for coding, and apply the hybrid leapfrog algorithm for material allocation to obtain the optimal solution. Finally, the feasibility of the model is verified by taking Zhengzhou urban area under the “21.7” severe rainstorm and flood disaster in Henan Province. The result analyses show that the model can correspond to each stage of mobile emergency material allocation based on the value of cost preference, and put forward suggestions on the location of mobile emergency facilities and the amount of material allocation.

A good port terminal is not only a major economic multiplier for the nation’s prosperity by being a gateway for trading, but is also an attractor for other commercial infrastructure development such as banks, logistics agencies, and manufacturing and trading investments. A measurement of the efficiency of a terminal is the duration-of-stay of visiting vessels. A quick and efficient loading/unloading process can increase productivity and thus reduce the waiting time for a vessel. In this study, we address the space allocation for stacking export containers. If the storage layout and the loading plan work well together, the productivity of the terminal can be increased and the duration-of-stay needed for each visiting vessel is reduced. In this paper, we propose a hybrid storage policy combining class-dedicated and sharing strategies, and construct a stochastic programming model using the concept of recourse.

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.

Because of their flexibility, controllability and convenience, Automated Guided Vehicles (AGV) have gradually gained popularity in intelligent manufacturing because to their adaptability, controllability, and simplicity. We examine the relationship between AGV scheduling tasks, charging thresholds, and power consumption, in order to address the issue of how AGV charging affects the scheduling of flexible manufacturing units with multiple AGVs. Aiming to promote AGVs load balance and reduce AGV charging times while meeting customer demands, we establish a scheduling model with the objective of minimizing the maximum completion time based on process sequence limitations, processing time restrictions, and workpiece transportation constraints. In accordance with the model’s characteristics, we code the machine, workpiece, and AGV independently, solve the model using a genetic algorithm, adjust the crossover mutation operator, and incorporate an elite retention strategy to the population initialization process to improve genetic diversity. Calculation examples are used to examine the marginal utility of the number of AGVs and electricity and validate the efficiency and viability of the scheduling model. The results show that the AVGs are effectively scheduled to complete transportation tasks and reduce the charging wait time. The multi-AGV flexible manufacturing cell scheduling can also help decision makers to seek AGVs load balance by simulation, reduce the charging times, and decrease the final completion time of manufacturing unit. In addition, AGV utilization can be maximized when the fleet size of AGV is 20%-40% of the number of workpieces.

The quality and experience of healthcare systems affect the economy and prosperity of cities all over the world. Governments of several countries are struggling to improve the efficiency of their healthcare systems and decrease healthcare spending costs. In this paper, we discuss one of the most critical and busy processes among healthcare topics: ambulatory care center (ACC) appointment scheduling systems. We investigate the appointment-scheduling issue using a robust optimization framework to minimize operational costs while ensuring the improvement of healthcare service quality. Our findings and insights provide healthcare practitioners with tools to improve operational efficiency and service quality.

We present an algorithm for solving unconstrained optimization problems based on the q-gradient vector. The main idea used in the algorithm construction is the approximation of the classical gradient by a q-gradient vector. For a convex objective function, the quasi-Fejér convergence of the algorithm is proved. The proposed method does not require the boundedness assumption on any level set. Further, numerical experiments are reported to show the performance of the proposed method.

A limited memory q-BFGS (Broyden–Fletcher–Goldfarb–Shanno) method is presented for solving unconstrained optimization problems. It is derived from a modified BFGS-type update using q-derivative (quantum derivative). The use of Jackson’s derivative is an effective mechanism for escaping from local minima. The q-gradient method is complemented to generate the parameter q for computing the step length in such a way that the search process gradually shifts from global in the beginning to almost local search in the end. Further, the global convergence is established under Armijo-Wolfe conditions even if the objective function is not convex. The numerical experiments show that proposed method is potentially efficient.

In this paper, we propose a modified q-Dai–Yuan (q-DY) conjugate gradient algorithm based on q-gradient for solving unconstrained optimization problems. The q-gradient is calculated based on q-derivative that requires a dilation parameter q for controlling the balance between the local and global search. The strong global convergence of the algorithm is proved under standard Wolfe conditions, and numerical results show the efficiency of the proposed algorithm.

A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

This paper deals with the existence of nonnegative solutions for a class of boundary value problems of fractional q-differential equation Dqσc[k](t)=w(t,k(t),cDqζ[k](t)) with three-point conditions for t∈ (0 , 1) on a time scale Tt0={t:t=t0qn}∪{0}, where n∈ N, t∈ R, and 0 < q< 1 , based on the Leray–Schauder nonlinear alternative and Guo–Krasnoselskii theorem. Moreover, we discuss the existence of nonnegative solutions. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

Variants of the Newton method are very popular for solving unconstrained optimization problems. The study on global convergence of the BFGS method has also made good progress. The q-gradient reduces to its classical version when q approaches 1. In this paper, we propose a quantum-Broyden–Fletcher–Goldfarb–Shanno algorithm where the Hessian is constructed using the q-gradient and descent direction is found at each iteration. The algorithm presented in this paper is implemented by applying the independent parameter q in the Armijo–Wolfe conditions to compute the step length which guarantees that the objective function value decreases. The global convergence is established without the convexity assumption on the objective function. Further, the proposed method is verified by the numerical test problems and the results are depicted through the performance profiles.

In this paper, we consider the Markowitz mean-variance model to minimize the risk on two assets and develop the program in R software to improve the performance of the model for two real stocks data with various combinations of the portfolios. We have taken two real stocks data upto 4514 each from yahoo database finance using our R program to show how fast our calculations are.

In this paper, we present a method of so-called q-Newton’s type descent direction for solving unconstrained multiobjective optimization problems. The algorithm presented in this paper is implemented by applying an independent parameter q (quantum) in an Armijo-like rule to compute the step length which guarantees that the value of the objective function decreases at every iteration. The search processes gradually shift from global in the beginning to local as the algorithm converges due to q-gradient. The algorithm is experimented on 41 benchmark/test functions which are unimodal and multi-modal with 1, 2, 3, 4, 5, 10 and 50 different dimensions. The performance of the proposed method is confirmed by comparing with three existing schemes.

A parameter-free optimization technique is applied in Quasi-Newton's method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at every iteration. The step-length is computed by an Armijo-like rule which is responsible to escape the point from local minimum to global minimum at every iteration due to q-derivative. Further, the rate of convergence is proved as a superlinear in a local neighborhood of a minimum point based on q-derivative. Finally, the numerical experiments show better performance.

The q-gradient is the generalization of the gradient based on the q-derivative. The q-version of the steepest descent method for unconstrained multiobjective optimization problems is constructed and recovered to the classical one as q equals 1. In this method, the search process moves step by step from global at the beginning to particularly neighborhood at last. This method does not depend upon a starting point. The proposed algorithm for finding critical points is verified in the numerical examples.

This book discusses unconstrained optimization with R-a free, open-source computing environment, which works on several platforms, including Windows, Linux, and macOS. The book highlights methods such as the steepest descent method, Newton method, conjugate direction method, conjugate gradient methods, quasi-Newton methods, rank one correction formula, DFP method, BFGS method and their algorithms, convergence analysis, and proofs. Each method is accompanied by worked examples and R scripts. To help readers apply these methods in real-world situations, the book features a set of exercises at the end of each chapter. Primarily intended for graduate students of applied mathematics, operations research and statistics, it is also useful for students of mathematics, engineering, management, economics, and agriculture.

This book is based on the lecture notes of the author delivered to the students at the Institute of Science, Banaras Hindu University, India. It covers simplex, revised simplex, two-phase method, duality, dual simplex, complementary slackness, transportation and assignment problems with good number of examples, clear proofs, MATLAB codes and homework problems. The book will be useful for both students and practitioners.