This research article proposes a single machine scheduling problem subject to Distinct due dates in fuzzy environment. The proposed problem is considered in fuzzy environment with an attempt to sequence of the 𝑛 − jobs. The total penalty cost is considered as the composition of all the total earliness and tardiness cost. The aim of this research work is to minimize the total penalty cost. A method to minimize the total penalty cost due to earliness or lateness of job in fuzzy environment is proposed. A numerical example is illustrated to support the proposed method in this study.

Technological advancements have fueled heightened competition in manufacturing, compelling companies to adopt strategies prioritizing swift, timely, and high-quality customer service. This necessitates seamless integration of supportive systems such as resources, equipment, facilities, and workforce, underscoring the criticality of scheduling in aligning activities and resources for on-time task completion. Scheduling, inseparable from sequencing, is pivotal in optimizing manufacturing and service industries' operations. However, challenges arise when tasks converge with limited facility capacities, necessitating effective resource allocation. By leveraging mathematical techniques and heuristic methods, scheduling optimizes resource utilization, minimizes production costs, and enhances service quality. Despite its significance, existing models often overlook critical aspects like identical job consideration and sequence-dependent setup times, limiting real-world applicability. This research addresses these gaps by proposing robust mathematical models for intricate scheduling requirements. The proposed approach seeks to optimize manufacturing operations by effectively handling complex scheduling needs, thereby minimizing production costs and enhancing operational efficiency. This research endeavours to advance scheduling optimization strategies through real-world implementation and evaluation and contribute to the manufacturing industry's sustainable growth.

This paper considers the problem of scheduling n jobs in the generalized tardiness flow shop problem with m machines. Seven algorithms are developed for finding a schedule with minimum total tardiness of jobs in the generalized flow shop problem. Two simple rules, the shortest processing time (SPT), and the earliest due date (EDD) sequencing rules, are modified and employed as the core of sequencing determination for developing these seven algorithms. We then evaluated the effectiveness of the modified rules through an extensive computational experiment.

scheduling consists of assignment resources in order to perform a set of tasks in a given time horizon, that optimizes the usage of available resources. Most of researches in open shop district (area) have stationary and certain status, means the situation that all data are certain and won't change in time horizon. Whereas real world scheduling problems are rarely stationary and certain. Reactive programming is a researching district that considers and peruses each changes and uncertain assumptions in real world scheduling problems, so in this paper, first we express a mixed integer programming model to produce initial scheduling for open shop problem, in continue we will generalize the presented model to its equivalent reactive programming with due date's changing. Finally we will express an algorithm due to necessity for revise the primal scheduling. This algorithm and whole models have been implemented and ran in AIMMS software environment and the computational results have been reported.

This paper addresses the Tardy/Lost penalty minimization with common due dates on a single machine. According to this performance measure, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Initially, we present a 2-approximation algorithm and examine its worst case ratio bound. Then, a pseudo-polynomial dynamic programming algorithm is developed. We show how to transform the dynamic programming algorithm to an FPTAS using the technique of "structuring the execution of an algorithm" and examine the time complexity of our FPTAS.

A field experiment was carried out to study the yield and physiological responses of rapeseed (Brassica napus L.) to boron application and high temperature stress due to late planting, in Ramin Agriculture and Natural Resources University of Khuzestan at 2013-2014. The experimental design was a split plots design in RCBD with four replications. Planting dates (18 November, 3 December, 17 December and 30 December) were placed in main plots and boron application treatments (control, 10 kg B.ha-1 incorporated with soil, boron spraying at 8 leaf stage and budding stages) were placed in sub plots. Planting date had significant effect on relative water content (RWC), cell membrane stability, peroxidase enzyme activity, leaf area index (LAI), canopy’s temperature, grain yield and dry matter. In addition, boron application had significant effect on LAI, peroxidase enzyme activity and yield. Late planting caused to decrease the grain yield and dry matter related to increased canopy’s temperature at flowering stages. Delayed planting from 18 November to 30 December, result in decreased grain yield about 60.5 percent. Boron application incorporated with soil caused to increased grain yield about 23 percent in comparison to control. High temperature stress due to late planting caused to decreased RWC, cell membrane stability and LAI in flowering stage. Generally, highest grain yield (4579.7 kg.ha-1) was obtained from planting at 18 November and 10 kg boron.ha-1 incorporated with soil, and lowest grain yield was obtained from planting at 30 December and without boron application.

Extensive research has been devoted to resource constrained project scheduling problem. However, little attention has been paid to problems where a certain time penalty must be incurred if activity preemption is allowed. In this paper, we consider the project scheduling problem of minimizing the total cost subject to resource constraints, earliness-tardiness penalties and preemption penalties, where each time an activity is started after being preempted, a constant setup penalty is incurred. We propose a solution method based on a pure integer formulation for the problem. Finally, some test problems are solved with LINGO version 8 and computational results are reported.

In this paper, a novel mathematical model for a preemption multi-mode multi-objective resource-constrained project scheduling problem with Distinct due dates and positive and negative cash flows is presented. Although optimization of bi-objective problems with due dates is an essential feature of real projects, little effort has been made in studying the P-MMRCPSP while due dates are included in the activities. This paper tries to bridge this gap by studying tardiness MMRCPSP, in which the objective is to minimize total weighted tardiness and to maximize the net present value (NPV). In order to solve the given problem, we introduced a Non-dominated Ranking Genetic Algorithm (NRGA) and Non-Dominated Sort Genetic Algorithm (NSGA-II). Since the effectiveness of most meta-heuristic algorithms significantly depends on choosing the proper parameters. A Taguchi experimental design method was applied to set and estimate the proper values of GAs parameters for improving their performances. To prove the efficiency of our proposed meta-heuristic algorithms, a number of test problems taken from the project scheduling problem library (PSPLIB) were solved. The computational results show that the proposed NSGA-II outperforms the NRGA.

due to having spring and autumn genotypes and adaptation to weather conditions, rapeseed is considered as a point hope to provide edible oil of country. Two separate experiments were set up as split-plot in a RCBD design with three replications in two fall and winter seasons during two years (2014-2015 and 2015-2016) at the research field of Seed and Plant Improvement Institute to investigate the effect of sowing season and date on the quantitative and qualitative yields of rapeseed genotypes in Karaj, Iran. In this study, the main plots were sowing dates (7, 17, and 27 October in fall sowing and 9 and 19 February, and 1 March in winter sowings) and sub-plots consisted of genotypes (RGS003, Dalgan, Zabol10, Hyola401, and Hyola4815). Rapeseed genotypes grain and oil yields were 4330 and 1840 kg ha-1 in fall sowing, respectively, while these traits were decreased 43.3 and 46.6% respectively, when rapeseed genotypes were planted in winter season. The highest grain and oil yields (5033 and 2202 kg ha-1) belonged to 7 October sowing date in fall sowing, while 9 February had the highest grain and oil yields (2996 and 1248 kg ha-1) in winter sowing. In general, the Dalgan genotype is recommended for cultivation due to suitable agronomic traits such as number of silique per plant, number of grain per silique, silique length, 1000-grain weight, as well as high grain and oil yields in cold temperate regions with arid and semi-arid climates such as Karaj, Iran.