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Abstract In pursuit of reducing dependence on oil, the Kingdom of Saudi Arabia has made significant efforts to advance sustainability under the strategic framework known as Saudi Vision. This initiative encompasses a range of activities aimed at promoting sustainability within the energy sector. This paper aims to analyze the existing sustainable practices of companies, employees, and the broader community in the supply chain. The objective is to evaluate current progress toward the sustainability goals of the Kingdom and assess the competitiveness of firms in the energy sector based on the effectiveness of sustainability management in their supply chain. Based on data collected from Saudi energy companies, structural equation modeling (SEM) techniques are utilized to investigate sustainable supply chain management (SSCM) practices and their influence on CP in Saudi Arabian energy companies. This study examines the influence of several practices on competitiveness (CP), including environmental practices (EMPs), social practices for employees (SPEs), social practices for the community (SPCs), operational practices (OPs), and supply chain integration practices (SCIs). The study incorporates five distinct independent variables, namely, EMP, SPE, SPC, OP, and SCI, where the dependent variable under investigation is denoted as CP. The findings from the SEM analysis show that three variables—SPE, SPC, and OP—demonstrate statistical significance, while EMP and SCI do not. These findings enhance the continuing academic discussion about balancing economic growth and environmental preservation through sustainable practices in the energy sector.

E-scooters are gaining popularity for short-distance travel, but their recharging presents challenges. To reduce their downtime, we propose a Hybrid K-Means/Particle Swarm Optimisation (PSO) approach, optimizing charging routes using machine learning and meta-heuristics. The research in this paper attempts to determine if a combination of a meta-heuristic such as PSO and a machine learning algorithm for clustering such as K-Means, would be effective at solving the vehicle routing problem for e-scooters. We compared this method with other algorithms and found that Tabu Search excelled in over 95% of tests. While Hybrid K-Means/PSO led in only approximately 52% of scenarios, it was also the only one to provide an output that surpassed Tabu Search in one of the scenarios. The core difference in efficiency is due to traditional meta-heuristic methods providing routes that while optimal, may also travel from locations relatively far from each other, while Hybrid K-Means/PSO will provide routes between locations that are clustered and in local groups. This results in Hybrid K-Means/PSO being slightly less efficient but may be more practical for charging personnel as they can operate in designated areas close to each other rather than a more optimal route with nodes further apart. This research underscores the effectiveness of Tabu Search and the potential of our Hybrid K-Means/PSO approach for optimizing e-scooter charging routes.

Nowadays, with the advancement of technological innovations and wide implementation of modern mining equipment, research topics on mining equipment management are attracting more and more attention from both academic scholars and industrial practitioners. With this background, this paper comprehensively reviews recent publications in the field of mining equipment management. By analysing the characteristics of open-pit mine production and haulage equipment types, problem definitions, formulation models and solution approaches in the relevant literature, the reviewed papers are classified into three main categories, i.e., shovel–truck (ST); in-pit crushing–conveying (IPCC); and hybrid IPCC-ST systems. Research progress and characteristics in each categorized mining equipment system are discussed and evaluated, respectively. With a thorough assessment of recent research agendas, the significance of developing state-of-the-art mining equipment scheduling/timetabling methodologies is indicated, based on the application of classical continuous-time machine scheduling theory. Promising future research directions and hotspots are also provided for researchers and practitioners in the mining industry.

Abstract Beef production drives a significant proportion of Australia's agricultural economy, representing AUD11 billion in agricultural production value annually. The profitability of cattle farms across seasons varies greatly and is particularly influenced by weather and associated uncertainty through pasture growth. Furthermore, producers must be careful in managing stocking rates to avoid overgrazing which has a significant environmental and economic impact. Predictive modelling of pasture and cattle liveweight can help producers to better manage this difficult balancing act. In this paper, we integrate a model for pasture growth and cattle weight gain to formulate predictions of liveweight production volume and pasture biomass. Monte‐Carlo simulation was used to understand the impact of uncertainty in model inputs relating to weather. Through such an approach, a distribution of possible pasture outcomes and beef production is formed which can be inspected to determine, for example expected production volume and risk of overgrazing. The methodology is demonstrated and validated through application to case study data sourced from Australian beef producers. Results demonstrate that it is possible to obtain reasonable predictions of liveweight gain and highlight the importance of considering the associated uncertainty. The accuracy of the proposed models has been examined by calculating statistical parameters MSE, MAE and R2. This approach can provide insight into the distribution of possible production outcomes given the long‐term rainfall outlook. The use of such predictive models and simulations by producers will lead to better‐informed planning of stocking rates, with benefits to productivity and sustainable utilisation of pasture.

The Global Navigation Satellite System (GNSS) is unreliable in some situations. To mend the poor GNSS signal, an autonomous vehicle can self-localize by matching a ground image against a database of geotagged aerial images. However, this approach has challenges because of the dramatic differences in the viewpoint between aerial and ground views, harsh weather and lighting conditions, and the lack of orientation information in training and deployment environments. In this paper, it is shown that previous models in this area are complementary, not competitive, and that each model solves a different aspect of the problem. There was a need for a holistic approach. An ensemble model is proposed to aggregate the predictions of multiple independently trained state-of-the-art models. Previous state-of-the-art (SOTA) temporal-aware models used heavy-weight network to fuse the temporal information into the query process. The effect of making the query process temporal-aware is explored and exploited by an efficient meta block: naive history. But none of the existing benchmark datasets was suitable for extensive temporal awareness experiments, a new derivative dataset based on the BDD100K dataset is generated. The proposed ensemble model achieves a recall accuracy R@1 (Recall@1: the top most prediction) of 97.74% on the CVUSA dataset and 91.43% on the CVACT dataset (surpassing the current SOTA). The temporal awareness algorithm converges to R@1 of 100% by looking at a few steps back in the trip history.

Red light running at signalised intersections is a growing road safety issue worldwide, leading to the rapid development of advanced intelligent transportation technologies and countermeasures. However, existing studies have yet to summarise and present the effect of these technology-based innovations in improving safety. This paper represents a comprehensive review of red-light running behaviour prediction methodologies and technology-based countermeasures. Specifically, the major focus of this study is to provide a comprehensive review on two streams of literature targeting red-light running and stop-and-go behaviour at signalised intersection – (1) studies focusing on modelling and predicting the red-light running and stop-and-go related driver behaviour and (2) studies focusing on the effectiveness of different technology-based countermeasures which combat such unsafe behaviour. The study provides a systematic guide to assist researchers and stakeholders in understanding how to best identify red-light running and stop-and-go associated driving behaviour and subsequently implement countermeasures to combat such risky behaviour and improve the associated safety.

One of the most critical objectives in the healthcare system is maximising patient flows in the emergency care patient pathway. Patient emergency flow analysis indicates that the timetabling of a patient’s movement from one activity to another through the Emergency Department (ED) is critical for treating patients. The ED deals with the patient’s arrival, triage, physician assessment, imaging and laboratory studies, treatment planning, nursing procedures, and decisions to admit or discharge the patient. Any delayed activities in patient flow reduce the service level of healthcare. To address these challenges, this paper develops a stochastic ED Simulation-Optimisation approach by considering stochastic variables, such as patient interarrival times and treatment times, using statistical distributions. This type of distribution depends on two main elements: day shifts and patient categories. A hybrid evolutionary algorithm is integrated with the simulation to find a satisfactory solution for this stochastic optimisation problem in real time. Computational experiments show that the proposed approach can serve more patients in specific time windows or provide the same quality of the service with the use of fewer medical resources.

Trajectory movement labelling is an important pre-stage for predicting connected vehicle (CV) movement at intersections. Drivers’ movement prediction and warning at intersections ensure advanced transportation safety and researchers use machine learning-based data-driven approaches to implement these technologies. However, prediction of drivers’ movements at intersections requires labelling the train and test dataset accurately with different vehicle movements at intersections to evaluate the performance of the prediction model by comparing the actual and predicted intersection movements. Moreover, due to GPS detection error or missing co-operative awareness messages (CAM), the data resides with many abnormal trajectories which are unable to be matched with regular straight or any turning movements. Especially for big data with million trajectories, it is tedious to label the movements manually. To solve this problem, we have created an automated trajectory movement classification technique using a dual approach of map matching technique and deep transfer learning modelling. Data of connected vehicle trajectory information is taken from the Ipswich Connected Vehicle Pilot (ICVP) Project, which is one of the largest connected vehicle pilots within a naturalistic driving environment in Australia. Map matching approach is performed as initial labelling by analysing the origin and destination of the vehicle CAM messages at intersections and then was converted as image datasets of 19202 samples. The map matching error and abnormal trajectories are identified by visual inspection. With properly labelled 9496 training images, 10 transfer learning models are built and tested through the remaining 9706 testing images. The maximum testing accuracy (99.73%) is achieved from the Densenet169 model, and the result shows satisfactory accuracy for individual classes: straight (99.85%), turn left (99.59), turn right (99.25), u-turn (100%), abnormal (98.63%). This model becomes a routine tool that is used daily to automatically classify thousands of trajectory movements of the C-ITS data in the ICVP project.

In this study, we propose a general method for tackling the Pickup and Drop-off Problem (PDP) using Hybrid Pointer Networks (HPNs) and Deep Reinforcement Learning (DRL). Our aim is to reduce the overall tour length traveled by an agent while remaining within the truck's capacity restrictions and adhering to the node-to-node relationship. In such instances, the agent does not allow any drop-off points to be serviced if the truck is empty; conversely, if the vehicle is full, the agent does not allow any products to be picked up from pickup points. In our approach, this challenge is solved using machine learning-based models. Using HPNs as our primary model allows us to gain insight and tackle more complicated node interactions, which simplified our objective to obtaining state-of-art outcomes. Our experimental results demonstrate the effectiveness of the proposed neural network, as we achieve the state-of-art results for this problem as compared with the existing models. We deal with two types of demand patterns in a single type commodity problem. In the first pattern, all demands are assumed to sum up to zero (i.e., we have an equal number of backup and drop-off items). In the second pattern, we have an unequal number of backup and drop-off items, which is close to practical application, such as bike sharing system rebalancing. Our data, models, and code are publicly available at Solving Pickup and Dropoff Problem Using Hybrid Pointer Networks with Deep Reinforcement Learning.

Maximising the patient flows throughout the emergency care patient pathway is one of the most important objectives in the healthcare system. The emergency department (ED) is the critical point of this pathway in most hospitals, as the potential delays reduce the number of patients seen in the recommended time. One of the key delays in the ED is the waiting time of a patient prior to treatment, which can be reduced by optimising the patient treatment schedules with priorities. In this paper, a novel blocking patient flow (BPF) algorithm is developed and tested using the real data from a hospital in Brisbane, Australia. Initially, a simulation model of real-life ED operations is developed by characterising patient interarrival and treatment times according to different disease categories. Subsequently, a BPF heuristic algorithm is designed and benchmarked via computational experiments using two dominance rules: first come first served (FCFS) and shortest processing time (SPT). The computational results show that the proposed approach leads to a reduction of the total waiting time by more than 8 % in comparison to the current hospital practice, which implies that more patients will be served in a specified time window.

Dimensionality reduction in the machine learning field mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the last decade, researchers proposed many new non-linear techniques for dimensionality reduction based on the assumption that data laying on or near a complex low-dimensional manifold is embedded in the high-dimensional space. On the other side, new techniques for dimensionality reduction aim to identify and extracting the manifold from the high-dimensional space. Isomap is one of widely-used low-dimensional embedding methods, where geodesic distances on a weighted graph are incorporated with the classical scaling (metric multidimensional scaling). The Isomap chooses the k-nearest neighbors based on the distance only which causes bridges and topological instability. In this paper, we propose a new algorithm to find the nearest neighbors to optimize the number of short-circuit errors and thus improve the topological stability. We assume that any point on the manifold and its nearest neighbors form a vector subspace and the orthogonal to that subspace is orthogonal to all vectors spans the vector subspace. Therefore, in the proposed algorithm, the point on the manifold and its nearest neighbors (i.e. the selected number of nearest neighbors based on the required subspace’s dimension) are used to find the bases of the subspace and the orthogonal to that subspace which belongs to the orthogonal complementary subspace. Then, candidate neighbors points will be added to the nearest neighbors based on the distance and the angle between each candidate point and the orthogonal to the subspace. The new algorithm is tested using low dimensional (3D) synthesized datasets and high dimensional real datasets. The superior performance of the new algorithm in choosing the nearest neighbors is confirmed through visually inspecting its capability find to the correct $2D$ representation of the synthesized datasets at different $k$ . Moreover, In the case of the high dimensional real datasets, the new algorithm yields a lower residual variance than the standard Isomap. Finally, we investigated using the new algorithm to find the nearest neighbors for the Locally Linear Embedding (LLE) algorithm. We tested the LLE variant using synthesized datasets and high dimensional real datasets and the results were promising

Due to emerging requirements and pressures related to environmental protection, manufacturing enterprises have expressed growing concern for adopting various energy-saving strategies. However, environmental criteria were usually not considered in traditional production scheduling problems. To overcome this deficiency, energy-saving scheduling has drawn more and more attention from academic scholars and industrial practitioners. In this paper, an energy-saving flexible job shop scheduling problem (EFJSP) is introduced in accordance with the criterion of optimizing power consumption and processing costs simultaneously. Since the classical FJSP is strongly NP-hard, an Improved Sparrow Search Algorithm (ISSA) is developed for efficiently solving the EFJSP. In the ISSA, a Hybrid Search (HS) method is used to produce an initial high-quality population; a Quantum Rotation Gate (QRG) and a Sine–Cosine Algorithm (SCA) are integrated to intensify the ability of the ISSA to coordinate exploration and exploitation; the adaptive adjustment strategy and Variable Neighborhood Search (VNS) are applied to strengthen diversification of the ISSA to move away from local optima. Extensive computational experiments validate that the ISSA outperforms other existing algorithms in solving the EFJSP due to the advantages of intensification and diversification mechanisms in the ISSA.

Modelling is an effective way of designing, understanding, and analysing bio-refinery supply chain systems. The supply chain is a complex process consisting of many systems interacting with each other. It requires the modelling of the processes in the presence of multiple autonomous entities (i.e. biomass producers, bio-processors and transporters), multiple performance measures and multiple objectives, both local and global, which together constitute very complex interaction effects. In this paper, simulation models for recovering biomass from the field of the biorefinery are developed and validated using some industry data and the minimum biomass recovery cost is established based on different strategies employed for recovering biomass. Energy densification techniques are evaluated for their net present worth and the technologies that offer greater returns for the industry are recommended. In addition, a new scheduling algorithm is also developed to enhance the process flow of the management of resources and the flow of biomass. The primary objective is to investigate different strategies to reach the lowest cost delivery of sugarcane harvest residue to a sugar factory through optimally located bio-refineries. A simulation /optimisation solution approach is also developed to tackle the stochastic variables in the bioenergy production system based on different statistical distributions such as Weibull and Pearson distributions. In this approach, a genetic algorithm is integrated with simulation to improve the initial solution and search the near-optimal solution. A case study is conducted to illustrate the results and to validate the applicability for the real world implementation using ExtendSIM Simulation software using some real data from Australian Mills.

Nowadays, rapid urbanization causes a wide-range of congestion and pollution in megacities worldwide, which bears an urgent need for micromobility solutions such as electric scooters (e-scooter). Many e-scooter firms use freelancers to charge the scooter where they compete to collect and charge the e-scooters at their homes. This competition leads the chargers to travel long distances to collect e-scooters. In this paper, we developed a mixed-integer linear programming (MILP) model for a real-world e-scooter -Chargers Allocation (ESCA) problem. The proposed model allocates the e-scooters to the chargers with an emphasis on minimizing the chargers’ average travelled distance to collect the e-scooters. The MILP returns optimal solutions in most cases; however, the ESCA is identified as a generalized assignment problem which classifies as an NP-complete combinatorial optimization problem. Moreover, we modelled the charging problem as a game between two sets of disjoint players, namely e-scooters and chargers. Then we adapted the college admission algorithm (ACA) to solve the ESCA problem. For the sake of comparison, we applied the black hole optimizer (BHO) algorithm to solve this problem using small and medium cases. The experimental results show that the ACA solutions are close to the optimal solutions obtained by the MILP. Furthermore, the BHO solutions are not as good as the ACA solutions, but the ACA solution consumes more time to solve large-scale real cases. Based on the obtained results, we recommend applying the ACA1 to find the near-optimal solution for large-scale instances, as the MILP is inapplicable to find the exact solution in comparison.

In Australia, Bioenergy plays an important role in modern power systems, where many biomass resources provide greenhouse gas neutral and electricity at a variety of scales. By 2050, the Biomass energy is projected to have a 40-50 % share as an alternative source of energy. In addition to conversion of biomass, barriers and uncertainties in the production, supply may hinder biomass energy development. The sugarcane is an essential ingredient in the production of Bioenergy, across the whole spectrum ranging from the first generation to second generation, e.g., production of energy from the lignocellulosic component of the sugarcane initially regarded as waste (bagasse and cane residue). Sustainable recovery of the Lignocellulosic component of sugarcane from the field through a structured process is largely unknown and associated with high capital outlay that have stifled the growth of bioenergy sector. In this context, this paper develops a new scheduler to optimise the recovery of lignocellulosic component of sugarcane and cane, transport and harvest systems with reducing the associated costs and operational time. An Optimisation Algorithm called Limited Discrepancy Search has been adapted and integrated with the developed scheduling transport algorithms. The developed algorithms are formulated and coded by Optimization Programming Language (OPL) to obtain the optimised cane and cane residues transport schedules. Computational experiments demonstrate that high-quality solutions are obtainable for industry-scale instances. To provide insightful decisions, sensitivity analysis is conducted in terms of different scenarios and criteria.

Road crash fatality is a universal problem of the transportation system. A massive death toll caused annually due to road crash incidents, and among them, vulnerable road users (VRU) are endangered with high crash severity. This paper focuses on employing machine learning-based classification approaches for modelling injury severity of vulnerable road users—pedestrian, bicyclist, and motorcyclist. Specifically, this study aims to analyse critical features associated with different VRU groups—for pedestrian, bicyclist, motorcyclist and all VRU groups together. The critical factor of crash severity outcomes for these VRU groups is estimated in identifying the similarities and differences across different important features associated with different VRU groups. The crash data for the study is sourced from the state of Queensland in Australia for the years 2013 through 2019. The supervised machine learning algorithms considered for the empirical analysis includes the K-Nearest Neighbour (KNN), Support Vector Machine (SVM) and Random Forest (RF). In these models, 17 distinct road crash parameters are considered as input features to train models, which originate from road user characteristics, weather and environment, vehicle and driver condition, period, road characteristics and regions, traffic, and speed jurisdiction. These classification models are separately trained and tested for individual and unified VRU to assess crash severity levels. Afterwards, model performances are compared with each other to justify the best classifier where Random Forest classification models for all VRU modes are found to be comparatively robust in test accuracy: (motorcyclist: 72.30%, bicyclist: 64.45%, pedestrian: 67.23%, unified VRU: 68.57%). Based on the Random Forest model, the road crash features are ranked and compared according to their impact on crash severity classification. Furthermore, a model-based partial dependency of each road crash parameters on the severity levels is plotted and compared for each individual and unified VRU. This clarifies the tendency of road crash parameters to vary with different VRU crash severity. Based on the outcome of the comparative analysis, motorcyclists are found to be more likely exposed to higher crash severity, followed by pedestrians and bicyclists.

[This corrects the article DOI: 10.1371/journal.pone.0229289.].

In this work, we proposed a hybrid pointer network (HPN), an end-to-end deep reinforcement learning architecture is provided to tackle the travelling salesman problem (TSP). HPN builds upon graph pointer networks, an extension of pointer networks with an additional graph embedding layer. HPN combines the graph embedding layer with the transformer's encoder to produce multiple embeddings for the feature context. We conducted extensive experimental work to compare HPN and Graph pointer network (GPN). For the sack of fairness, we used the same setting as proposed in GPN paper. The experimental results show that our network significantly outperforms the original graph pointer network for small and large-scale problems. For example, it reduced the cost for travelling salesman problems with 50 cities/nodes (TSP50) from 5.959 to 5.706 without utilizing 2opt. Moreover, we solved benchmark instances of variable sizes using HPN and GPN. The cost of the solutions and the testing times are compared using Linear mixed effect models. We found that our model yields statistically significant better solutions in terms of the total trip cost. We make our data, models, and code publicly available https://github.com/AhmedStohy/Hybrid-Pointer-Networks.

Maritime management is a crucial concern for movable bridge safety. Irregular management of water vehicles near movable bridges may lead to collision among ships and bridge infrastructures, causing massive losses of life and property. The paper presents a theoretical framework and simulation of an intelligent water vehicle management system for movable bridges corresponding to vehicle traffic responses. The water regime around the bridge is considered in virtually separated domains to estimate the desired safety actions based on the position of the approaching ships. An emergency clash avoidance control system is represented to prevent ship-infrastructure collision and ensure transportation safety. In addition, a simulation platform is developed specifically adaptable for movable bridge maritime and dynamic traffic management. The proposed theory is experimented using the simulation platform for different ship speeds and bridge-vehicle traffic volumes. Based on analyzing the velocity profile of approaching ships at different incidents, the bridge is found incapable of evacuating vehicles and unable to open promptly in case of speeding ships and high traffic density of vehicles on the bridge. Computational results show that the emergency control system is effective in reducing ship speed and prevent certain collisions. Lastly, the transportation policy for the newly proposed maritime management system is validated by real-world implementation in movable bridges across the world.

Substantial research is required to ensure that micro-mobility ride sharing provides a better fulfilment of user needs. This study proposes a novel crowdsourcing model for the ride-sharing system where light vehicles such as scooters and bikes are crowdsourced. The proposed model is expected to solve the problem of charging and maintaining a large number of light vehicles where these efforts will be the responsibility of the crowd of suppliers. The proposed model consists of three entities: suppliers, customers, and a management party responsible for receiving, renting, booking, and demand matching with offered resources. It can allow suppliers to define the location of their private e-scooters/e-bikes and the period of time they are available for rent. Using a dataset of over 9 million e-scooter trips in Austin, Texas, we ran an agent-based simulation six times using three maximum battery ranges (i.e., 35, 45, and 60 km) and different numbers of e-scooters (e.g., 50 and 100) at each origin. Computational results show that the proposed model is promising and might be advantageous to shift the charging and maintenance efforts to a crowd of suppliers.

The freight rail systems have an essential role to play in transporting the commodities between the delivery and collection points at different locations such as farms, factories and mills. The fright transport system uses a daily schedule of train runs to meet the needs of both the harvesters and the mills (An Integrated Approach to Optimise Cane Rail Operations (M. Masoud, E. Kozan, G. Kent, Liu, Shi Qiang, 2016b) [1]). Producing an efficient daily schedule to optimise the rail operations requires integration of the main elements of harvesting, transporting and milling in the value chain of the Australian agriculture industry. The data utilised in this research involve four main tables: sidings, harvesters, sectional rail network and trains. The utilised data were collected from Australian sugar mills as a real application. Operations Research techniques such as metaheuristic and constraint programming are used to produce the optimised solutions in an analytical way.

As the Autonomous Vehicle (AV) industry is rapidly advancing, the classification of non-motorized (vulnerable) road users (VRUs) becomes essential to ensure their safety and to smooth operation of road applications. The typical practice of non-motorized road users’ classification usually takes significant training time and ignores the temporal evolution and behavior of the signal. In this research effort, we attempt to detect VRUs with high accuracy be proposing a novel framework that includes using Deep Transfer Learning, which saves training time and cost, to classify images constructed from Recurrence Quantification Analysis (RQA) that reflect the temporal dynamics and behavior of the signal. Recurrence Plots (RPs) were constructed from low-power smartphone sensors without using GPS data. The resulted RPs were used as inputs for different pre-trained Convolutional Neural Network (CNN) classifiers including constructing 227 × 227 images to be used for AlexNet and SqueezeNet; and constructing 224 × 224 images to be used for VGG16 and VGG19. Results show that the classification accuracy of Convolutional Neural Network Transfer Learning (CNN-TL) reaches 98.70%, 98.62%, 98.71%, and 98.71% for AlexNet, SqueezeNet, VGG16, and VGG19, respectively. Moreover, we trained resnet101 and shufflenet for a very short time using one epoch of data and then used them as weak learners, which yielded 98.49% classification accuracy. The results of the proposed framework outperform other results in the literature (to the best of our knowledge) and show that using CNN-TL is promising for VRUs classification. Because of its relative straightforwardness, ability to be generalized and transferred, and potential high accuracy, we anticipate that this framework might be able to solve various problems related to signal classification.

In this essay, we sought to infer the method to design the most fitting geometrical shape for the plan of a ‘Salat’ space in the prayer hall in a mosque, from relevant scripture, and from textbooks of A’emah of Fiqh, making use of basic rules of analytic geometry. We established that any shape for the ‘Salat space’ plan besides the Orthogonal Polygon which takes the complete undivided ‘Musalliah unit’ for a strict module in its composition, would yield juristically unfavorable effects in the way rows of Musalleen are lined up behind the Imam, and would diminish the use that can be made of Waqf money in hosting the largest possible number of ‘Musalleen’ within the bounds of available space.