Dissertation for M.Sc degree
Field: Industrial Engineering
Tension: System Management and Productivity
Winter 1392
Abstract
The location problem is one of the emerging and recently flourishing fields in theory. The location of classic facilities is that supply chain managers of organizations and companies should pay special attention to these issues when designing their supply chain network as part of the decision-making process. In strategic planning, decisions may have long-term effects and implementation of plans may take considerable time. Also, the input data is not exactly known in advance. Hence, uncertainty should be considered in the decisions made. Uncertainty can be considered as a property of the system that describes the imperfection of human knowledge about a system and its state of progress. In this research, special models of location-based problems under the title of simple and multiple allocation considered. First model General simple and multiple allocation modes of limited capacity are introduced, and in the following, the proposed model of this research is presented for how to deal with the uncertainty of parameters, which includes simple and multiple allocation modes of limited capacity based on location-based optimization approach. At the end, the uncertainty of parameters such as the fixed cost of axis setup and the capacity of each axis on the data set of Iran Airlines IAD [1] is investigated using the Minimax Regret approach [2] and the obtained results are analyzed. The obtained results indicate that not taking into account the uncertainty in the design of supply chain networks sometimes causes huge damages and costs, which in turn cause delays in the implementation of long-term plans and the suspension of all The activities of organizations or companies are analyzed.
Key words: facility location, location-based, uncertainty, simple and multiple allocation of limited capacity, robust optimization, Minimax Regret
Introduction
Facility location is a well-known term in the field of applied studies in operations research. A large number of published articles and researches are proof of this claim. However, the application of location models is always questioned. Of course, the usefulness and applicability of location, especially in logistics, has never been doubted. The most notable logistics in this field is supply chain management. In fact, the development of supply chain management was carried out independently of operations research, and operations research entered supply chain topics step by step. As a result, facility location models gradually entered the supply chain literature and a very attractive and useful field was created. In the process of this development, many questions naturally arise, some of which are: What features should the facility location model have in order to be in the supply field Should it be accepted?
Are there models of facility location that have already worked in the supply chain field?
Does supply chain management basically need facility location?
One of the problems of facility location is knowing a set of customers with different physical distances and a set of facilities to meet demand. That is it. The distances, times and costs of customers and facilities should be measured with a specific criterion. The questions that need to be answered include the following:
Which one of the facilities should be used (in terms of location)?
Which customer should receive services from which facility in order to minimize the cost?
Facility location models play an important role in the design and planning of the supply chain.Basically, in the design and planning of the supply chain, there are 3 levels based on the time horizon, including strategic, tactical and operational. The strategy level is related to decisions that have long-term effects on your organization. These cases include decisions regarding: number, location, storage capacity, production capacity or flow of raw materials in the logistics network. Location of facilities includes many other areas. One of the newest and most widely used is location-based. Hubs are facilities that have been created in the direction of providing services to people, meeting demands, circulating information and consumer goods between pairs of origin and intended destination. Hubs are used to reduce the number of transport connections between origin and destination nodes (Zanjirani Farahani et al., 2013).
After the initial articles of O’Kelly (1986, 1987), many researches have been done in this field. Especially, issues with different goals and characteristics, which have been given more attention. The median p-axis problem and the location problems of limited capacity and unlimited capacity are among the topics that have the most repetition in published articles. In the central p-axis problem, the goal is to minimize the operational costs of the network (demand routing costs), on the other hand, in the limited and unlimited capacity axis location problems, the fixed costs of setting up the axes are also considered in the objective function (Alumur et al., 2012).
In location problems; Based on the search, there are usually a number of nodes with the corresponding amount of demands, and the flow is being transferred between these nodes. In the simple allocation model of axis location, a number of nodes are selected as axes, and other nodes, i.e., non-axis nodes (rods), are each connected to only one axis. In this model, there is no direct connection between non-axis nodes and the flow is transmitted only through the communication axes and the flow is distributed throughout the network by connecting the axes to each other. In the multiple allocation model, as in the case of simple allocation, there is no connection between the non-axis nodes and the flow of the non-axis nodes is transmitted through the axes, but with the difference that here the non-axis nodes are allowed to be connected with more than one axis and through them deliver the flow to other nodes of the network. Certain types of simple and multiple assignment of location-oriented problems are presented. Issues in which the capacity of each service center or service delivery is limited. Despite the fact that the ultimate goal of this type of problems is to minimize network costs and optimal allocation of nodes to the created axes, due to the limited capacity of axes when assigning non-axis nodes, it is possible that the policy of assigning each node to the nearest available axis may be disrupted and nodes may send their requests to other axes in the network due to the fact that their demand is not met by a particular axis. do Usually, real world problems are analyzed by assuming that the input parameters are immutable. However, in practice, the input data often differ from the assumptions of the mathematical models. Therefore, these assumptions lead to solutions that are far from optimal and even feasible in the real world. Demand, types of costs, capacities, etc. There are things that change over time in the problems of location of network design facilities. As a result of the investigation and development of the limited capacity model for the location of network design facilities in the state of uncertainty, it is considered one of the existing research gaps in this field, and an attempt will be made to investigate this gap. Optimization under uncertainty is usually investigated from two perspectives. (1) stochastic programming and (2) robust optimization. In stochastic programming, the uncertain parameters are controlled by the probability distribution function and the model seeks to provide a solution that minimizes the expected cost of the objective function. But in robust optimization, probabilities are uncertain and random parameters are estimated through discrete scenarios or intervals.