Search results for: integer%20programming

Authors: Khaled S. Abdallah, Abdel-Aziz M. Mohamed

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Moving industries consume numerous resources and dispose masses of used packaging materials. Proper sorting, recycling and disposing the packaging materials is necessary to avoid a sever pollution disaster. This research paper presents a conceptual model to propose sustainable truck rental operations instead of the regular one. An optimization model was developed to select the locations of truck rental centers, collection sites, maintenance and repair sites, and identify the rental fees to be charged for all routes that maximize the total closed supply chain profits. Fixed costs of vehicle purchasing, costs of constructing collection centers and repair centers, as well as the fixed costs paid to use disposal and recycling centers are considered. Operating costs include the truck maintenance, repair costs as well as the cost of recycling and disposing the packing materials, and the costs of relocating the truck are presented in the model. A mixed integer model is developed followed by a simulation model to examine the factors affecting the operation of the model.

Keywords: modeling, truck rental, supply chains management.

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Authors: Tao Yin, Zeqiang Zhang, Wei Liang, Yanqing Zeng, Yu Zhang

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To accelerate the remanufacturing process of electronic waste products, this study designs a partial disassembly line with the multi-robotic station to effectively dispose of excessive wastes. The multi-robotic partial disassembly line is a technical upgrade to the existing manual disassembly line. Balancing optimization can make the disassembly line smoother and more efficient. For partial disassembly line balancing with the multi-robotic station (PDLBMRS), a mixed-integer programming model (MIPM) considering the robotic efficiency differences is established to minimize cycle time, energy consumption and hazard index and to calculate their optimal global values. Besides, an enhanced NSGA-II algorithm (HNSGA-II) is proposed to optimize PDLBMRS efficiently. Finally, MIPM and HNSGA-II are applied to an actual mixed disassembly case of two types of computers, the comparison of the results solved by GUROBI and HNSGA-II verifies the correctness of the model and excellent performance of the algorithm, and the obtained Pareto solution set provides multiple options for decision-makers.

Keywords: waste disposal, disassembly line balancing, multi-robot station, robotic efficiency difference, HNSGA-II

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Authors: Mohsen S. Sajadieha, Danyar Molavia

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In this paper, a truck scheduling problem is investigated at a two-touch cross-docking center with due dates for outbound trucks as a hard constraint. The objective is to minimize the total cost comprising penalty and delivery cost of delayed shipments. The sequence of unloading shipments is considered and is assumed that shipments are sent to shipping dock doors immediately after unloading and a First-In-First-Out (FIFO) policy is considered for loading the shipments. A mixed integer programming model is developed for the proposed model. Two meta-heuristic algorithms including genetic algorithm (GA) and variable neighborhood search (VNS) are developed to solve the problem in medium and large sized scales. The numerical results show that increase in due dates for outbound trucks has a crucial impact on the reduction of penalty costs of delayed shipments. In addition, by increase the due dates, the improvement in the objective function arises on average in comparison with the situation that the cross-dock is multi-touch and shipments are sent to shipping dock doors only after unloading the whole inbound truck.

Keywords: cross-docking, truck scheduling, fixed due date, door assignment

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Authors: Billel Kenidra, Mohamed Benmohammed

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Data mining technique used in the field of clustering is a subject of active research and assists in biological pattern recognition and extraction of new knowledge from raw data. Clustering means the act of partitioning an unlabeled dataset into groups of similar objects. Each group, called a cluster, consists of objects that are similar between themselves and dissimilar to objects of other groups. Several clustering methods are based on partitional clustering. This category attempts to directly decompose the dataset into a set of disjoint clusters leading to an integer number of clusters that optimizes a given criterion function. The criterion function may emphasize a local or a global structure of the data, and its optimization is an iterative relocation procedure. The K-Means algorithm is one of the most widely used partitional clustering techniques. Since K-Means is extremely sensitive to the initial choice of centers and a poor choice of centers may lead to a local optimum that is quite inferior to the global optimum, we propose a strategy to initiate K-Means centers. The improved K-Means algorithm is compared with the original K-Means, and the results prove how the efficiency has been significantly improved.

Keywords: microarray data mining, biological pattern recognition, partitional clustering, k-means algorithm, centroid initialization

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Authors: Wen-Tsung Ho, Ku-Kuang Chang, Hsin-Yuan Chang

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In this study, we consider an economic lot-size batch-shipment scheduling problem (ELBSP) with extended basic period (EBP) and power-of-two (PoT) policies. In this problem, the supplier using a single facility to manufacture multiple products and equally sized batches are then delivered by the supplier to buyers over an infinite planning horizon. Further, the extended basic period (EBP) and power-of-two (PoT) policy are utilized. Relaxing the production schedule converts the ELBSP to an economic lot-size batch-shipment problem (ELBP) with EBP and PoT policies, and a nonlinear integer programming model of the ELBP is constructed. Using the replenishment cycle division and recursive tightening methods, optimal solutions are then solved separately for each product. The sum of these optimal solutions is the lower bound of the ELBSP. A proposed heuristic method with polynomial complexity is then applied to figure out the near-optimal solutions of the ELBSP. Numerical example is presented to confirm the efficacy of the proposed method.

Keywords: economic lot-size scheduling problem, extended basic period, replenishment cycle division, recursive tightening, power-of-two

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Authors: Homa Ghave, Parmis Shahmaleki

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This paper presents a new multi-criteria stochastic mathematical model for a single machine scheduling with outsourcing allowed. There are multiple jobs processing in batch. For each batch, all of job or a quantity of it can be outsourced. The jobs have stochastic processing time and lead time and deterministic due dates arrive randomly. Because of the stochastic inherent of processing time and lead time, we use the chance constrained programming for modeling the problem. First, the problem is formulated in form of stochastic programming and then prepared in a form of deterministic mixed integer linear programming. The objectives are considered in the model to minimize the maximum tardiness and outsourcing cost simultaneously. Several procedures have been developed to deal with the multi-criteria problem. In this paper, we utilize the concept of satisfaction functions to increases the manager’s preference. The proposed approach is tested on instances where the random variables are normally distributed.

Keywords: single machine scheduling, multi-criteria mathematical model, outsourcing strategy, uncertain lead times and processing times, chance constrained programming, satisfaction function

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Authors: Elham Jelodari Mamaghani, Christian Prins, Haoxun Chen

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In this paper, there is concentration on collaborative transportation planning (CTP) among multiple carriers with pickup and delivery requests and time windows. This problem is a vehicle routing problem with constraints from standard vehicle routing problems and new constraints from a real-world application. In the problem, each carrier has a finite number of vehicles, and each request is a pickup and delivery request with time window. Moreover, each carrier has reserved requests, which must be served by itself, whereas its exchangeable requests can be outsourced to and served by other carriers. This collaboration among carriers can help them to reduce total transportation costs. A mixed integer programming model is proposed to the problem. To solve the model, a hybrid algorithm that combines Genetic Algorithm and Simulated Annealing (GASA) is proposed. This algorithm takes advantages of GASA at the same time. After tuning the parameters of the algorithm with the Taguchi method, the experiments are conducted and experimental results are provided for the hybrid algorithm. The results are compared with those obtained by a commercial solver. The comparison indicates that the GASA significantly outperforms the commercial solver.

Keywords: centralized collaborative transportation, collaborative transportation with pickup and delivery, collaborative transportation with time windows, hybrid algorithm of GA and SA

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Authors: Muhammad Abdullah, Asma Rashid Butt, Nauman Raza

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Biomagnetic fluids like blood play key role in different applications of medical science and bioengineering. In this paper, the magnetohydrodynamic flow of a viscous fluid with magnetic particles through a cylindrical tube is investigated. The fluid is electrically charged in the presence of a uniform external magnetic field. The movement in the fluid is produced due to the cylindrical tube. Initially, the fluid and tube are at rest and at time t=0⁺, the tube starts to move along its axis. To obtain the mathematical model of flow with fractional derivatives fractional calculus approach is used. The solution of the flow model is obtained by using Laplace transformation. The Simon's numerical algorithm is employed to obtain inverse Laplace transform. The hybrid technique, we are employing has less computational effort as compared to other methods. The numerical calculations have been performed with Mathcad software. As the special cases of our problem, the solution of flow model with ordinary derivatives and flow without magnetic particles has been procured. Finally, the impact of non-integer fractional parameter alpha, Hartmann number Ha, and Reynolds number Re on flow and magnetic particles velocity is analyzed and depicted by graphs.

Keywords: viscous fluid, magnetic particles, fractional calculus, laplace transformation

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Authors: Prashant Pandey

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In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

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Authors: Nusrat T. Chowdhury, M. F. Baki, A. Azab

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The production planning problem is concerned with specifying the optimal quantities to produce in order to meet the demand for a prespecified planning horizon with the least possible expenditure. Making the right decisions in production planning will affect directly the performance and productivity of a manufacturing firm, which is important for its ability to compete in the market. Therefore, developing and improving solution procedures for production planning problems is very significant. In this paper, we develop a Dantzig-Wolfe decomposition of a multi-item hierarchical production planning problem with capacity constraint and present a column generation approach to solve the problem. The original Mixed Integer Linear Programming model of the problem is decomposed item by item into a master problem and a number of subproblems. The capacity constraint is considered as the linking constraint between the master problem and the subproblems. The subproblems are solved using the dynamic programming approach. We also propose a multi-step iterative capacity allocation heuristic procedure to handle any kind of infeasibility that arises while solving the problem. We compare the computational performance of the developed solution approach against the state-of-the-art heuristic procedure available in the literature. The results show that the proposed heuristic-based decomposition approach improves the solution quality by 20% as compared to the literature.

Keywords: inventory, multi-level capacitated lot-sizing, emission control, setup carryover

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Authors: Masoud Shahmanzari

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The aim of this paper is to present a Variable Neighborhood Search (VNS) with Tabu Search (TS) conditions for the Roaming Salesman Problem (RSP). The RSP is a special case of the well-known traveling salesman problem (TSP) where a set of cities with time-dependent rewards and a set of campaign days are given. Each city can be visited on any day and a subset of cities can be visited multiple times. The goal is to determine an optimal campaign schedule consist of daily open/closed tours that visit some cities and maximizes the total net benefit while respecting daily maximum tour duration constraints and the necessity to return campaign base frequently. This problem arises in several real-life applications and particularly in election logistics where depots are not fixed. We formulate the problem as a mixed integer linear programming (MILP), in which we capture as many real-world aspects of the RSP as possible. We also present a hybrid metaheuristic algorithm based on a VNS with TS conditions. The initial feasible solution is constructed via a new matheuristc approach based on the decomposition of the original problem. Next, this solution is improved in terms of the collected rewards using the proposed local search procedure. We consider a set of 81 cities in Turkey and a campaign of 30 days as our largest instance. Computational results on real-world instances show that the developed algorithm could find near-optimal solutions effectively.

Keywords: optimization, routing, election logistics, heuristics

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Authors: Antonin Ponsich, Eric Alfredo Rincon Garcia, Roman Anselmo Mora Gutierrez, Miguel Angel Gutierrez Andrade, Sergio Gerardo De Los Cobos Silva, Pedro Lara Velzquez

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The electoral zone design problem consists in redrawing the boundaries of legislative districts for electoral purposes in such a way that federal or state requirements are fulfilled. In Mexico, this process has been historically carried out by the National Electoral Institute (INE), by optimizing an integer nonlinear programming model, in which population equality and compactness of the designed districts are considered as two conflicting objective functions, while contiguity is included as a hard constraint. The solution technique used by the INE is a Simulated Annealing (SA) based algorithm, which handles the multi-objective nature of the problem through an aggregation function. The present work represents the first intent to apply a classical Multi-Objective Evolutionary Algorithm (MOEA), the second version of the Non-dominated Sorting Genetic Algorithm (NSGA-II), to this hard combinatorial problem. First results show that, when compared with the SA algorithm, the NSGA-II obtains promising results. The MOEA manages to produce well-distributed solutions over a wide-spread front, even though some convergence troubles for some instances constitute an issue, which should be corrected in future adaptations of MOEAs to the redistricting problem.

Keywords: multi-objective optimization, NSGA-II, redistricting, zone design problem

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Authors: Ons Sassi, Wahiba Ramdane Cherif-Khettaf, Ammar Oulamara

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In this paper, we consider a new real-life Heterogenous Electric Vehicle Routing Problem with Time Dependant Charging Costs and a Mixed Fleet (HEVRP-TDMF), in which a set of geographically scattered customers have to be served by a mixed fleet of vehicles composed of a heterogenous fleet of Electric Vehicles (EVs), having different battery capacities and operating costs, and Conventional Vehicles (CVs). We include the possibility of charging EVs in the available charging stations during the routes in order to serve all customers. Each charging station offers charging service with a known technology of chargers and time-dependent charging costs. Charging stations are also subject to operating time windows constraints. EVs are not necessarily compatible with all available charging technologies and a partial charging is allowed. Intermittent charging at the depot is also allowed provided that constraints related to the electricity grid are satisfied. The objective is to minimize the number of employed vehicles and then minimize the total travel and charging costs. In this study, we present a Mixed Integer Programming Model and develop a Charging Routing Heuristic and a Local Search Heuristic based on the Inject-Eject routine with three different insertion strategies. All heuristics are tested on real data instances.

Keywords: charging problem, electric vehicle, heuristics, local search, optimization, routing problem

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Authors: Maryam Haghi, Ivan Contreras, Nadia Bhuiyan

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Chemotherapy is one of the most popular and effective cancer treatments offered to patients in outpatient oncology centers. In such clinics, patients first consult with an oncologist and the oncologist may prescribe a chemotherapy treatment plan for the patient based on the blood test results and the examination of the health status. Then, when the plan is determined, a set of chemotherapy and consultation appointments should be scheduled for the patient. In this work, a comprehensive mathematical formulation for planning and scheduling different types of chemotherapy patients over a planning horizon considering blood test, consultation, pharmacy and treatment stages has been proposed. To be more realistic and to provide an applicable model, this study is focused on a case study related to a major outpatient cancer treatment clinic in Montreal, Canada. Comparing the results of the proposed model with the current practice of the clinic under study shows significant improvements regarding different performance measures. These major improvements in the patients’ schedules reveal that using optimization techniques in planning and scheduling of patients in such highly demanded cancer treatment clinics is an essential step to provide a good coordination between different involved stages which ultimately increases the efficiency of the entire system and promotes the staff and patients' satisfaction.

Keywords: chemotherapy patients scheduling, integer programming, integrated scheduling, staff balancing

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Authors: Rabiatu Bonku, Faisal Alkaabneh

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Inspired by a food banks distribution operation for non-profit organization, we study a variant synchronized vehicle routing problem for equitable resource allocation. This research paper introduces a Mixed Integer Programming (MIP) model aimed at addressing the complex challenge of efficiently distributing vital resources, particularly for food banks serving vulnerable populations in urban areas. Our optimization approach places a strong emphasis on social equity, ensuring a fair allocation of food to partner agencies while minimizing wastage. The primary objective is to enhance operational efficiency while guaranteeing fair distribution and timely deliveries to prevent food spoilage. Furthermore, we assess four distinct models that consider various aspects of sustainability, including social and economic factors. We conduct a comprehensive numerical analysis using real-world data to gain insights into the trade-offs that arise, while also demonstrating the models’ performance in terms of fairness, effectiveness, and the percentage of food waste. This provides valuable managerial insights for food bank managers. We show that our proposed approach makes a significant contribution to the field of logistics optimization and social responsibility, offering valuable insights for improving the operations of food banks.

Keywords: food banks, humanitarian logistics, equitable resource allocation, synchronized vehicle routing

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Authors: Alvaro Javier Ortega

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A large number of companies face the challenge of matching highly-skilled professionals to high-end positions by human resource deployment professionals. However, when the professional list and tasks to be matched are larger than a few dozens, this process result is far from optimal and takes a long time to be made. Therefore, an automated assignment algorithm for this workforce management problem is needed. The majority of companies are divided into several sectors or departments, where trained employees with different experience levels deal with a large number of tasks daily. Also, the execution order of all tasks is of mater consequence, due to some of these tasks just can be run it if the result of another task is provided. Thus, a wrong execution order leads to large waiting times between consecutive tasks. The desired goal is, therefore, creating accurate matches and a near-optimal execution order that maximizes the number of tasks performed and minimizes the idle time of the expensive skilled employees. The problem described before can be model as a mixed-integer non-linear programming (MINLP) as it will be shown in detail through this paper. A large number of MINLP algorithms have been proposed in the literature. Here, genetic algorithm solutions are considered and a comparison between two different mutation approaches is presented. The simulated results considering different complexity levels of assignment decisions show the appropriateness of the proposed model.

Keywords: employees, genetic algorithm, industry management, workforce

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Authors: Omar A. Abuobidalla, Mingyuan Chen, Satyaveer S. Chauhan

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Railroad transportation of hazardous materials freights is important to the North America economics that supports the national’s supply chain. This paper introduces various extensions of the dynamic hazardous materials trip plan problems. The problem captures most of the operational features of a real-world railroad transportations systems that dynamically initiates a set of blocks and assigns each shipment to a single block path or multiple block paths. The dynamic hazardous materials trip plan policies have distinguishing features that are integrating the blocking plan, and the block activation decisions. We also present a non-linear mixed integer programming formulation for each variant and present managerial insights based on a hypothetical railroad network. The computation results reveal that the dynamic car scheduling policies are not only able to take advantage of the capacity of the network but also capable of diminishing the population, and environment risks by rerouting the active blocks along the least risky train services without sacrificing the cost advantage of the railroad. The empirical results of this research illustrate that the issue of integrating the blocking plan, and the train makeup of the hazardous materials freights must receive closer attentions.

Keywords: dynamic car scheduling, planning and scheduling hazardous materials freights, airborne hazardous materials, gaussian plume model, integrated blocking and routing plans, box model

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Authors: Amirhossein Chambari

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This article proposes a bi-objective model for the facility location problem subject to congestion (overcrowding). Motivated by implementations to locate servers in internet mirror sites, communication networks, one-server-systems, so on. This model consider for situations in which immobile (or fixed) service facilities are congested (or queued) by stochastic demand to behave as M/M/1/K queues. We consider for this problem two simultaneous perspectives; (1) Customers (desire to limit times of accessing and waiting for service) and (2) Service provider (desire to limit average facility idle-time). A bi-objective model is setup for facility location problem with two objective functions; (1) Minimizing sum of expected total traveling and waiting time (customers) and (2) Minimizing the average facility idle-time percentage (service provider). The proposed model belongs to the class of mixed-integer nonlinear programming models and the class of NP-hard problems. In addition, to solve the model, controlled elitist non-dominated sorting genetic algorithms (Controlled NSGA-II) and controlled elitist non-dominated ranking genetic algorithms (NRGA-I) are proposed. Furthermore, the two proposed metaheuristics algorithms are evaluated by establishing standard multiobjective metrics. Finally, the results are analyzed and some conclusions are given.

Keywords: bi-objective, facility location, queueing, controlled NSGA-II, NRGA-I

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Authors: Zekang Lan, Yan Xu, Yingkun Huang, Dian Huang, Shengzhong Feng

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Jobs on high-performance computing (HPC) clusters can suffer significant performance degradation due to inter-job network interference. Topology-aware job allocation problem (TJAP) is such a problem that decides how to dedicate nodes to specific applications to mitigate inter-job network interference. In this paper, we study the window-based TJAP on a fat-tree network aiming at minimizing the cost of communication hop, a defined inter-job interference metric. The window-based approach for scheduling repeats periodically, taking the jobs in the queue and solving an assignment problem that maps jobs to the available nodes. Two special allocation strategies are considered, i.e., static continuity assignment strategy (SCAS) and dynamic continuity assignment strategy (DCAS). For the SCAS, a 0-1 integer programming is developed. For the DCAS, an approach called neural simulated algorithm (NSA), which is an extension to simulated algorithm (SA) that learns a repair operator and employs them in a guided heuristic search, is proposed. The efficacy of NSA is demonstrated with a computational study against SA and SCIP. The results of numerical experiments indicate that both the model and algorithm proposed in this paper are effective.

Keywords: high-performance computing, job allocation, neural simulated annealing, topology-aware

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Authors: Ming-Yang Guo, Cheng-Xian Wu, Wei-Xiang Chen, Chun-Yuan Lin, Yen-Jen Lin, Ann-Shyn Chiang

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With more and more Drosophila Driver and Neuron images, it is an important work to find the similarity relationships among them as the functional inference. There is a general problem that how to find a Drosophila Driver image, which can cover a set of Drosophila Driver/Neuron images. In order to solve this problem, the intersection/union region for a set of images should be computed at first, then a comparison work is used to calculate the similarities between the region and other images. In this paper, three encoding schemes, namely Integer, Boolean, Decimal, are proposed to encode each image as a one-dimensional structure. Then, the intersection/union region from these images can be computed by using the compare operations, Boolean operators and lookup table method. Finally, the comparison work is done as the union region computation, and the similarity score can be calculated by the definition of Tanimoto coefficient. The above methods for the region computation are also implemented in the multi-core CPUs environment with the OpenMP. From the experimental results, in the encoding phase, the performance by the Boolean scheme is the best than that by others; in the region computation phase, the performance by Decimal is the best when the number of images is large. The speedup ratio can achieve 12 based on 16 CPUs. This work was supported by the Ministry of Science and Technology under the grant MOST 106-2221-E-182-070.

Keywords: Drosophila driver image, Drosophila neuron images, intersection/union computation, parallel processing, OpenMP

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Authors: Amit Kumar Baghel, Sisir Kumar Nayak

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The proposed metamaterial design help to increase the radiation efficiency at 2.9 GHz by reducing the side and back lobes by making the phase difference of the waves emerging from the phase center of the horn antenna same after passing through metamaterial array. The unit cell of the metamaterial is having concentric ring structure made of copper of 0.035 mm thickness on both sides of FR4 sheet. The inner ring diameter is kept as 3 mm, and the outer ring diameters are changed according to the path and tramission phase difference of the unit cell from the phase center of the antenna in both the horizontal and vertical direction, i.e., in x- and y-axis. In this case, the ring radius varies from 3.19 mm to 6.99 mm with the respective S21 phase difference of -62.25° to -124.64°. The total phase difference can be calculated by adding the path difference of the respective unit cell in the array to the phase difference of S21. Taking one of the unit cell as the reference, the total phase difference between the reference unit cell and other cells must be integer multiple of 360°. The variation of transmission coefficient S21 with the ring radius is greater than -6 dB. The array having 5 x 5 unit cell is kept inside the pyramidal horn antenna (L X B X H = 295.451 x 384.233 x 298.66 mm3) at a distance of 36.68 mm from the waveguide throat. There is an improvement in side lobe level in E-plane by 14.6 dB when the array is used. The front to back lobe ration is increased by 1 dB by using the array. The proposed antenna with metamaterial array can be used in beam shaping for wireless power transfer applications.

Keywords: metamaterial, side lobe level, front to back ratio, beam forming

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Authors: Y. Sunecher, N. Mamode Khan, V. Jowaheer

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This paper considers the modelling of a non-stationary bivariate integer-valued autoregressive moving average of order one (BINARMA(1,1)) with correlated Poisson innovations. The BINARMA(1,1) model is specified using the binomial thinning operator and by assuming that the cross-correlation between the two series is induced by the innovation terms only. Based on these assumptions, the non-stationary marginal and joint moments of the BINARMA(1,1) are derived iteratively by using some initial stationary moments. As regards to the estimation of parameters of the proposed model, the conditional maximum likelihood (CML) estimation method is derived based on thinning and convolution properties. The forecasting equations of the BINARMA(1,1) model are also derived. A simulation study is also proposed where BINARMA(1,1) count data are generated using a multivariate Poisson R code for the innovation terms. The performance of the BINARMA(1,1) model is then assessed through a simulation experiment and the mean estimates of the model parameters obtained are all efficient, based on their standard errors. The proposed model is then used to analyse a real-life accident data on the motorway in Mauritius, based on some covariates: policemen, daily patrol, speed cameras, traffic lights and roundabouts. The BINARMA(1,1) model is applied on the accident data and the CML estimates clearly indicate a significant impact of the covariates on the number of accidents on the motorway in Mauritius. The forecasting equations also provide reliable one-step ahead forecasts.

Keywords: non-stationary, BINARMA(1, 1) model, Poisson innovations, conditional maximum likelihood, CML

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Authors: Abhishek Jain, Kavish Kejriwal, V. Balaji Rao, Abhigna Chavda

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Increasing environmental and social concerns are forcing companies to take a fresh view of the impact of supply chain operations on environment and society when designing a supply chain. A challenging task in today’s food industry is the distribution of high-quality food items throughout the food supply chain. Improper storage and unwanted transportation are the major hurdles in food supply chain and can be tackled by making dynamic storage facility location decisions with the distribution network. Since food supply chain in India is one of the biggest supply chains in the world, the companies should also consider environmental impact caused by the supply chain. This project proposes a multi-objective optimization model by integrating sustainability in decision-making, on distribution in a food supply chain network (SCN). A Multi-Objective Mixed-Integer Linear Programming (MOMILP) model between overall cost and environmental impact caused by the SCN is formulated for the problem. The goal of MOMILP is to determine the pareto solutions for overall cost and environmental impact caused by the supply chain. This is solved by using GAMS with CPLEX as third party solver. The outcomes of the project are pareto solutions for overall cost and environmental impact, facilities to be operated and the amount to be transferred to each warehouse during the time horizon.

Keywords: multi-objective mixed linear programming, food supply chain network, GAMS, multi-product, multi-period, environment

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Authors: Mohammed Abdulhameed, Sagir M. Abdullahi

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In this paper, based on the applications of nanoparticle, the blood flow along with nanoparticles through stenosed artery is studied. The blood is acted by periodic body acceleration, an oscillating pressure gradient and an external magnetic field. The mathematical formulation is based on Caputo-Fabrizio fractional derivative without singular kernel. The model of ordinary blood, corresponding to time-derivatives of integer order, is obtained as a limiting case. Analytical solutions of the blood velocity and temperature distribution are obtained by means of the Hankel and Laplace transforms. Effects of the order of Caputo-Fabrizio time-fractional derivatives and three different nanoparticles i.e. Fe3O4, TiO4 and Cu are studied. The results highlights that, models with fractional derivatives bring significant differences compared to the ordinary model. It is observed that the addition of Fe3O4 nanoparticle reduced the resistance impedance of the blood flow and temperature distribution through bell shape stenosed arteries as compared to TiO4 and Cu nanoparticles. On entering in the stenosed area, blood temperature increases slightly, but, increases considerably and reaches its maximum value in the stenosis throat. The shears stress has variation from a constant in the area without stenosis and higher in the layers located far to the longitudinal axis of the artery. This fact can be an important for some clinical applications in therapeutic procedures.

Keywords: nanoparticles, blood flow, stenosed artery, mathematical models

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Authors: Aydin Sipahioglu, Gokhan Celik

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Helicopter routing problem (HRP) is finding good tours for helicopter so as to pick up and deliver personnel or material among specified nodes, mutually. It can be encountered in case of being lots of supply and demand points for different commodities and requiring delivering commodities with helicopter. For instance, to deliver personnel or material from shore to oil rig is a good example. In fact, HRP is a branch of vehicle routing problem with pickup and delivery (VRPPD). However, it has additional constraints such that fuel capacity, performance of helicopter in different altitude and temperature, and the number of maximum takeoff and landing allowed. This kind of pickup and delivery problems can be classified into 3 groups, basically. 1-1 (one to one), M-M (many to many) and 1-M-1 (one to many to one). 1-1 means each commodity has only one supply and one demand point. M-M means there can be more than one supply and demand points for each kind of commodity. 1-M-1 means commodities at depot are delivered to demand points and commodities at customers are delivered to depot. In this case helicopter takes off from its own base, complete its tour and return to its own base. In this study, we define 1-M-M-1 type HRP. That means helicopter takes off from its home base, deliver commodities among the nodes as well as between depot and customers and return to its home base. These problems have NP-hard nature. Therefore, obtaining a good solution in a reasonable time is not easy. In this study, a model is offered for 1-M-M-1 type HRP. It is shown on small scale test instances that the model can find the optimal solution.

Keywords: helicopter routing problem, vehicle routing with pickup and delivery, integer programming

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Authors: Ming-Jong Yao, Chin-Sum Shui, Chih-Han Wang

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This paper is developed based on a real-world decision scenario that an industrial gas company that applies the Vendor Managed Inventory model and supplies liquid oxygen with a self-operated heterogeneous vehicle fleet to hospitals in nearby cities. We name it as a Joint Replenishment and Heterogeneous Vehicle Routing Problem with Cyclical Schedule and formulate it as a non-linear mixed-integer linear programming problem which simultaneously determines the length of the planning cycle (PC), the length of the replenishment cycle and the dates of replenishment for each customer and the vehicle routes of each day within PC, such that the average daily operation cost within PC, including inventory holding cost, setup cost, transportation cost, and overtime labor cost, is minimized. A solution method based on genetic algorithm, embedded with an encoding and decoding mechanism and local search operators, is then proposed, and the hash function is adopted to avoid repetitive fitness evaluation for identical solutions. Numerical experiments demonstrate that the proposed solution method can effectively solve the problem under different lengths of PC and number of customers. The method is also shown to be effective in determining whether the company should expand the storage capacity of a customer whose demand increases. Sensitivity analysis of the vehicle fleet composition shows that deploying a mixed fleet can reduce the daily operating cost.

Keywords: cyclic inventory routing problem, joint replenishment, heterogeneous vehicle, genetic algorithm

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Authors: Hao Wang, Shuguo Pan

Abstract:

The Global Navigation Satellite System (GNSS) signal received by the dynamic vehicle in the harsh environment will be frequently interfered with and blocked, which generates gross error affecting the positioning accuracy of the GNSS/Inertial Navigation System (INS) integrated navigation. Therefore, this paper put forward an improved robust Cubature Kalman filter (CKF) algorithm for single-frequency GNSS/INS tightly coupled system ambiguity resolution. Firstly, the dynamic model and measurement model of a single-frequency GNSS/INS tightly coupled system was established, and the method for GNSS integer ambiguity resolution with INS aided is studied. Then, we analyzed the influence of pseudo-range observation with gross error on GNSS/INS integrated positioning accuracy. To reduce the influence of outliers, this paper improved the CKF algorithm and realized an intelligent selection of robust strategies by judging the ill-conditioned matrix. Finally, a field navigation test was performed to demonstrate the effectiveness of the proposed algorithm based on the double-differenced solution mode. The experiment has proved the improved robust algorithm can greatly weaken the influence of separate, continuous, and hybrid observation anomalies for enhancing the reliability and accuracy of GNSS/INS tightly coupled navigation solutions.

Keywords: GNSS/INS integrated navigation, ambiguity resolution, Cubature Kalman filter, Robust algorithm

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Authors: Dibakar Chakrabarty, Mebada Suiting

Abstract:

Rapid urbanization coupled with changes in land use pattern results in increasing peak discharge and shortening of catchment time of concentration. The consequence is floods, which often inundate roads and inhabited areas of cities and towns. Management of storm water resulting from rainfall has, therefore, become an important issue for the municipal bodies. Proper management of storm water obviously includes adequate design of storm water drainage networks. The design of storm water network is a costly exercise. Least cost design of storm water networks assumes significance, particularly when the fund available is limited. Optimal design of a storm water system is a difficult task as it involves the design of various components, like, open or closed conduits, storage units, pumps etc. In this paper, a methodology for least cost design of storm water drainage systems is proposed. The methodology proposed in this study consists of coupling a storm water simulator with an optimization method. The simulator used in this study is EPA’s storm water management model (SWMM), which is linked with Genetic Algorithm (GA) optimization method. The model proposed here is a mixed integer nonlinear optimization formulation, which takes care of minimizing the sectional areas of the open conduits of storm water networks, while satisfactorily conveying the runoff resulting from rainfall to the network outlet. Performance evaluations of the developed model show that the proposed method can be used for cost effective design of open conduit based storm water networks.

Keywords: genetic algorithm (GA), optimal design, simulation-optimization, storm water network, SWMM

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Authors: Abdulrahman Abdulrahman

Abstract:

A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.

Keywords: analytical solution, combined channel, exponential channel, side weirs, trapezoidal channel, water surface profile

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Authors: Zeinab Haji Abolhasani, Romeo Marian, Lee Luong

Abstract:

This paper and its companions (Part II, Part III) will concentrate on optimizing a class of supply chain problems known as Multi- Commodities Consumer Supply Chain (MCCSC) problem. MCCSC problem belongs to production-distribution (P-D) planning category. It aims to determine facilities location, consumers’ allocation, and facilities configuration to minimize total cost (CT) of the entire network. These facilities can be manufacturer units (MUs), distribution centres (DCs), and retailers/end-users (REs) but not limited to them. To address this problem, three major tasks should be undertaken. At the first place, a mixed integer non-linear programming (MINP) mathematical model is developed. Then, system’s behaviors under different conditions will be observed using a simulation modeling tool. Finally, the most optimum solution (minimum CT) of the system will be obtained using a multi-objective optimization technique. Due to the large size of the problem, and the uncertainties in finding the most optimum solution, integration of modeling and simulation methodologies is proposed followed by developing new approach known as GASG. It is a genetic algorithm on the basis of granular simulation which is the subject of the methodology of this research. In part II, MCCSC is simulated using discrete-event simulation (DES) device within an integrated environment of SimEvents and Simulink of MATLAB® software package followed by a comprehensive case study to examine the given strategy. Also, the effect of genetic operators on the obtained optimal/near optimal solution by the simulation model will be discussed in part III.

Keywords: supply chain, genetic algorithm, optimization, simulation, discrete event system

Procedia PDF Downloads 277