Mathematical modelling
Seyyed Mostafa Mousavi; Majid Motamedi; Rasoul Karimi
Abstract
A supply chain is a network that creates and delivers products and services to customers. In this research, the four-level supply chain in the field of food products, including the levels of supplier, customer, and central and secondary warehouses, has been investigated. A mixed integer mathematical ...
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A supply chain is a network that creates and delivers products and services to customers. In this research, the four-level supply chain in the field of food products, including the levels of supplier, customer, and central and secondary warehouses, has been investigated. A mixed integer mathematical model of the research problem is presented to minimize chain costs, including the setting up and preparation of warehouses, transportation between transfer levels, and holding products. The proposed model is developed based on constraints such as inventory, warehouse capacity, vehicle capacity, and multi-period multi-product. The decision variables are determined after solving the model, which includes the optimal number of central and secondary warehouses, the optimal amount of product transferred between the factory and central warehouse, the central warehouse and secondary warehouse, and the secondary warehouse and customer, the optimal amount of product storage in secondary warehouses, the type of vehicle for transportation between levels, and the capacity level of each product in each central warehouse. To validate the proposed model, experiments were conducted using the Kaleh company's real data in GAMS software. Finally, the sensitivity analysis of the model was carried out on two critical parameters influencing decision-making: demand and the cost of increasing the capacity of the central warehouse. The output results confirmed the validity and efficiency of the proposed model.
Mathematical modelling
Eshetu Dadi Gurmu; Boka Kumsa Bole; Purnachandra Rao Koya
Abstract
In this paper, optimal control theory is applied to Human Papillomavirus (HPV) and Human immunodeficiency viruses (HIV) coinfection model given by using a system of ordinary differential equations. Optimal control strategy was employed to study the effect of combining various intervention strategies ...
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In this paper, optimal control theory is applied to Human Papillomavirus (HPV) and Human immunodeficiency viruses (HIV) coinfection model given by using a system of ordinary differential equations. Optimal control strategy was employed to study the effect of combining various intervention strategies on the transmission dynamics of HPV-HIV coinfection diseases. The necessary conditions for the existence of the optimal controls were established using Pontryagin’s Maximum Principle. Optimal control system was performed with help of Runge-Kutta forward-backward sweep numerical approximation method. Finally, numerical simulation illustrated that a combination of prevention, screening and treatment is the most effective strategy to minimize the disease from the community.
Scheduling
B. Naderi
Abstract
This paper considers the problem of university course timetabling. In this problem, there are a set of courses, lecturers and classrooms. The objective is to assign schedule courses so as to maximize the total preference of lecturer-course, lecturer-day and course-day. The paper first formulates the ...
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This paper considers the problem of university course timetabling. In this problem, there are a set of courses, lecturers and classrooms. The objective is to assign schedule courses so as to maximize the total preference of lecturer-course, lecturer-day and course-day. The paper first formulates the problem in form of linear integer programming model. Using the model and commercial software, the small sized instances are optimally solved. Then, the paper proposes three different algorithms based on imperialist competitive algorithm, simulated annealing and variable neighborhood search. The algorithms employ several novel procedures such as encoding scheme, move operator, crossing operators. The algorithms are tuned and evaluated with optimal solutions found by the model. Then, they are evaluated by comparing their performance. The results show that imperialist competitive algorithm outperforms the other algorithms.
A. Jafari; P. Chiniforooshan; F. Mousavinejad; Sh. Shahparvari
Volume 1, Issue 3 , December 2012, , Pages 1-25
Abstract
In this paper, we consider the fuzzy open shop scheduling problem with parallel machines in each working stage where processing times are vague and are represented by fuzzy numbers. An open shop scheduling problem with parallel machines in each working stage under this condition is close to the real ...
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In this paper, we consider the fuzzy open shop scheduling problem with parallel machines in each working stage where processing times are vague and are represented by fuzzy numbers. An open shop scheduling problem with parallel machines in each working stage under this condition is close to the real production scheduling conditions. A mixed-integer fuzzy programming (MIFP) model is presented to formulate this problem with the objective of minimizing makespan. To solve small-sized instances, an interactive fuzzy satisfying solution procedure is applied. Since this problem is known as a class of NP-hard, a novel discrete electromagnetism-like (DEM) is proposed to solve medium to large size examples. The DEM algorithm employs a completely difference approach. It makes use the crossover operators to calculate force and move particle is used. We employ Taguchi method to evaluate the effects of different operators and parameters on the performance of DEM algorithm. Finally to assess the performance of the algorithm, the results are compared with an existing EM algorithm from the literature and benchmark problems. The result exhibited the ability of the proposed DEM algorithm to converge to the efficient solutions.
M. Seyedrezaei; S.E. Najafi; A. Aghajani; H. Bagherzadeh Valami
Volume 1, Issue 2 , July 2012, , Pages 40-57
Abstract
Distribution centers (DCs) play an important key role in supply chain. Delivering the right items to the right customers at the right time, at the right cost is a critical mission of the DCs. Today, customer satisfaction is an important factor for supplier companies in order to gain more profits. Optimizing ...
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Distribution centers (DCs) play an important key role in supply chain. Delivering the right items to the right customers at the right time, at the right cost is a critical mission of the DCs. Today, customer satisfaction is an important factor for supplier companies in order to gain more profits. Optimizing the number of fulfilled orders (An order that the required quantity of all items in that order are available from the inventory and can be send to the customer) in a time period may lead to delay some major orders; and consequently lead to dissatisfaction of these customers, ultimately loss them and lead to lower profits. In addition, some inventory may remain in the warehouse in a time-period and over the time become corrupt. It also leads to reduce the benefit of supplier companies in the supply chain. Therefore, in this paper, we will present a dynamic mathematical model to flow process /storage process of goods for order picking planning problem (OPP) in DCs. And we will optimize the number of fulfilled orders in this problem with regard to a) the coefficient of each customer, b) to meet each customer's needs in the least time c) probabilistic demand of customers, and d) taking inventory to send to customers at the earliest opportunity to prevent their decay. After presenting the mathematical model, we use Lingo software to solve small size problems. Complexity of the mathematical model will intensify by increasing the numbers of customers and products in distribution center, Therefore Lingo software will not able to solve these problems in a reasonable time. Therefore, we will develop and use a genetic algorithm (GA) for solving these problems.