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In modern manufacturing and service industries, urgent orders and service tasks are common, and the speed of handling such urgent tasks is an important indicator of production and service efficiency. In this study, we consider scheduling jobs on two parallel machines with the random arrival of an emergency job. The objective is to minimise the makespan, subject to a given maximum waiting time of the emergency job. We first show that the worst-case ratio of the existing algorithm LPT $ _l $ l -SPT $ _{m-l} $ m − l is at least 3/2 when m = 2. We then analyse some properties of the optimal schedule and derive lower bounds on the optimal makespan. Finally, we present an improved approximation algorithm with a tight worst-case ratio of 4/3. We also provide numerical results showing that our proposed algorithm outperforms algorithm LPT $ _l $ l -SPT $ _{m-l} $ m − l . [ABSTRACT FROM AUTHOR]

Drones are increasingly used for last-mile delivery due to their speed and cost-effectiveness. This study focuses on a novel locker-drone delivery system, where trucks transport parcels from the warehouse to lockers, and drones complete the final delivery. This system is ideal for community and intra-facility logistics. The research optimises the network design by determining the location of lockers, the number of drones at each locker, and the assignment of demands to lockers, minimising operating costs. Both single-parcel and multi-parcel capacity drones are examined. We build an optimisation model for each system, considering drone service capacity as a critical constraint. We design an algorithm combining average sample approximation and a genetic algorithm to address demand uncertainty. The algorithm's efficiency is validated through comparative analysis with Gurobi. Numerical experiments, using real and generated data, optimise the network design. Results show that the multi-capacity drone system requires fewer lockers and drones than the singlecapacity system. Although the single-capacity system yields lower drone delivery costs, it incurs higher truck delivery costs. Additionally, a comprehensive cost analysis compares the cost-efficiency of the locker-drone system with a conventional drone delivery system, revealing the cost-saving advantage of the locker-drone system. [ABSTRACT FROM AUTHOR]

Confidence bands are used to estimate the likely range of the true parameter, whereas prediction bands provide an idea of the possible values of the parameter after applying a regression model. This study proposes an equation to construct confidence and prediction bands applicable to any linear or nonlinear chemometric regression model; that is, statistical methods used in analytical chemistry to establish relationships between two or more variables. The proposed equation is developed and presented as a useful tool to represent the uncertainty in estimates based on a set of data in chemical measurements. Once the set of data is adjusted as a regression model (linear, polynomial, or multivariable), the proposed equation can be used to construct confidence and prediction bands based on the adjustment equation. The proposed equation operates if the adjustment equation is continuous and derivable. The plot bands on any regression model provide a solid understanding of uncertainty assessment and have the advantage of total control and independence of algorithms and numeral approximations. [ABSTRACT FROM AUTHOR]

In this paper we give a quantitative analysis of an explicit iteration method due to C.E. Chidume for the approximation of a zero of an m-accretive operator A : X → 2 X in Banach spaces which does not involve the computation of the resolvent of A. [ABSTRACT FROM AUTHOR]

We consider a single machine rescheduling problem where a set of original jobs have been scheduled to minimize the total weighted completion time. However, before formal processing begins, a new set of jobs arrives and creates a disruption. The decision maker can reject a subset of the new jobs by paying certain rejection penalties, and reschedule the original and the remaining new jobs without excessively disrupting the original schedule, which is measured by the maximum completion time deviation for any original jobs between the original and adjusted schedules. The objective is to minimize the sum of total weighted completion time of the original jobs and the accepted new jobs in the adjusted schedule, the weighted maximum completion time deviation and the total rejection cost. We first provide a dynamic programming-based exact algorithm running in pseudo-polynomial time, and then propose a fully polynomial time approximation scheme. Given the NP-hardness for the studied problem, our result is the best possible from the approximation algorithm perspective. In addition, we conduct extensive computational experiments to evaluate the performance of our proposed methods, and provide some managerial insights on their applicability under different situations. [ABSTRACT FROM AUTHOR]

This article proposes Bayesian nonparametric inference for panel Markov-switching GARCH models. The model incorporates series-specific hidden Markov chain processes that drive the GARCH parameters. To cope with the high-dimensionality of the parameter space, the article assumes soft parameter pooling through a hierarchical prior distribution and introduces cross sectional clustering through a Bayesian nonparametric prior distribution. An MCMC posterior approximation algorithm is developed and its efficiency is studied in simulations under alternative settings. An empirical application to financial returns data in the United States is offered with a portfolio performance exercise based on forecasts. A comparison shows that the Bayesian nonparametric panel Markov-switching GARCH model provides good forecasting performances and economic gains in optimal asset allocation. [ABSTRACT FROM AUTHOR]