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Flow shop scheduling problems with sequence-dependent setup times and minimising the number of tardy jobs as the criterion (F m |prmu, S ijk |∑U j) are considered in this research. A mixed-integer linear programming model is developed for the research problem. Since the proposed research problem has been proven to be NP-hard, several meta-heuristic algorithms based on tabu search (TS) and the imperialist competitive algorithm (ICA) are proposed to heuristically solve the problem. In order to find the best meta-heuristic algorithm, random test problems, ranging in size from small, medium, to large, are generated and solved by the meta-heuristic algorithms. Then, a detailed statistical... 

This paper investigates permutation flow shop scheduling problems with sequencedependent setup times with minimizing the number of tardy jobs as criterion (F m|prmu, S ijk|σU j). Since the proposed research problem has been proven to be NP-hard, three different meta heuristic algorithms based on tabu search (TS) has been proposed to solve the problem. These three algorithms are different based on their tabu list characteristics. In order to evaluate the performance of the proposed TS algorithms, test problems in different ranges are generated to find the best algorithm. The comparison shows that the TS algorithm which its tabu list keeps track of the slots that the jobs are assigned has a... 

This research considers a flexible flowshop sequence-dependent group scheduling problem with minimization of total completion time. A mixed integer linear mathematical model for the research problem is developed. Since the research problem is shown to be strongly NP-hard, a metaheuristic algorithm based on memetic algorithm (MA) is proposed. A lower bounding method based on the Branch and Price algorithm is also proposed to evaluate the quality of the MA. In order to evaluate the performance of the proposed algorithms, random test problems, ranging in size from small, medium, to large are generated and solved by the MA and the lower bounding method. The results show that the average... 

In this research, we approach the flowshop sequence-dependent group scheduling problem with minimisation of total weighted earliness and tardiness as the objective for the first time. A mixed integer linear programming model is developed to solve the problem optimally. Since the proposed research problem is proven to be NP-hard, a hybrid meta-heuristic algorithm based on the particle swarm optimisation (PSO) algorithm, enhanced with neighbourhood search is developed to heuristically solve the problem. Since the objective is a non-regular, a timing algorithm is developed to find the best schedule for each sequence provided by the metaheuristic algorithm. A lower bounding method is also... 

Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have received less attention in the literature. In this paper, we present the definition, properties, characteristics and PH representations of ADPH distributions and their subclasses with finite state space. Based on the definitions of geometric and shifted geometric distributions, we propose a distinct... 

Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show its flexibility in producing a wide range of variances as well as its adequacy in fitting fat-tailed distributions. These properties render MSNB... 

Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show its flexibility in producing a wide range of variances as well as its adequacy in fitting fat-tailed distributions. These properties render MSNB... 

The vast nationwide COVID-19 vaccination programs are implemented in many countries worldwide. Mass vaccination is causing a rapid increase in infectious and non-infectious vaccine wastes, potentially posing a severe threat if there is no well-organized management plan. This paper develops a mixed-integer mathematical programming model to design a COVID-19 vaccine waste reverse supply chain (CVWRSC) for the first time. The presented problem is based on minimizing the system's total cost and carbon emission. The uncertainty in the tendency rate of vaccination is considered, and a robust optimization approach is used to deal with it, where an interactive fuzzy approach converts the model into... 

In this paper, we consider a dual-sourcing model with constant demand and stochastic lead times. Two suppliers may be different in terms of purchasing prices and lead-time parameters. The ordering takes place when the inventory level depletes to a reorder level, and the order is split among two suppliers. Unlike previous works in the order splitting literature, the supply lead time between vendor and buyer as well as unit purchasing prices is considered to be order quantity dependent. The proposed model finds out the optimal reorder point, order quantity and splitting proportion, using a solution procedure. Numerical results show that neglecting the relationship between ordering batch size... 

Adsorption of human serum proteins (Albumin and total protein) onto high purity synthesis nano-hydroxyapatite (HA), Ca 10(PO 4) 6(OH) 2, has been studied in a wide temperature range by UV-visible spectrophotometer. Adsorption isotherm is basically important to describe how solutes interact with adsorbent, andiscriticalinoptimizing the use of adsorbent. Inthe present study, the experimental results werefitted tothe Langmuir, Freundlich, Temkin and Dubinin-Radushkevich (DR) models to obtain the characteristic parameters of each model and square of the correlation coefficients (R 2). According to the results, the DR isotherm model had the best agreement with the experimental data. The effect of...