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Data Envelopment Analysis (DEA) is a methodology to compare efficiency of Decision Making Units (DMUs). DEA is an extension of Charnes, Cooper and Rhodes work by introducing CCR model in 1978. Ranking DMUs is one of the main purposes of DEA in management and engineering. DEA evaluates some DMUs with efficiency score one as efficient DMUs and we therefore need to produce a reliable method for fully ranking DMUs. Some methods have been proposed in this concept and newly Khodabakhshi and Aryavash (2012) ranked DMUs relative to their combined maximum and minimum efficiency scores where efficiency is defined as ratio of weighted sum of outputs to weighted sum of inputs. Due to some obtained weights (multipliers) in DEA may be zero, previous methods have low ability in ranking DMUs because of eliminating the effect of corresponding input and outputs on DEA evaluations. We expand their method by assigning lower bounds on multipliers using facet analysis and then we propose an equitable and precise method for ranking all DMUs based on the modified CCR. Keywords: Data envelopment analysis, decision making unit, rank.
Data Envelopment Analysis (DEA) was introduced under the name of a deterministic model assuming all the deviations from the estimated production frontier were one sided indicating technical inefficiency. Biased estimations of inefficiency and production are provided by the model when deviations do not originate only from inefficiency but also from measurement errors. In 1988, Banker developed Data Envelopment Analysis as a stochastic model to reflect inefficiency and statistical noise simultaneously. However, from deterministic to stochastic, the problem with weak efficient frontiers and related biased results stayed the same. This dissertation proposes a modification over Banker’s stochastic DEA (SDEA) model by applying a limitation on the coefficients of inputs in the original model in order to change weak efficient hyperplane(s) while keeps general assumptions behind production function unaffected. This can change the production possibility set (PPS) while the frontier has the potential to give a better representation of the true production frontier. Comparing the results from the stochastic model and suggested modified model shows that the achieved model is providing a new benchmark for relative efficiency evaluation and production frontier estimation. Keywords: Data Envelopment Analysis (DEA), Stochastic Data Envelopment Analysis (SDEA), Modified Model, Weak Efficient Frontier.
Changes of today’s firm’s competitiveness strategies from firms level to improved Supply Chain level causes increases in number and importance of Supply Chain studies in the literature. Variation between demand and orders is became the most important problem and most studied Supply Chain topic. This problem named in literature as Bullwhip Effect, is studied in this thesis with possible 11 factors effect on bullwhip. By using the improved Bullwhip Effect formula; lead time, review period, demand distribution, ordering cost, numbers of forecast periods are found as the factors which have significant effect on Bullwhip. In addition to this, for the use of similar Supply Chain researches, or real Supply Chain members, an improved spreadsheet simulation tool is prepared to test the proposed Supply Chain structures effects on different Supply Chain performance measures.
In recent times, there has been a growing concern regarding environmental issues. This has resulted in increased pressure on companies and producers from government regulations, while also striving to maintain customer satisfaction by addressing environmental concerns. Green Supply Chain Management (GSCM) has emerged as a means to enhance efficiency and reduce environmental impact for firms collaborating with clients and suppliers. GSCM encompasses various aspects such as green purchasing, design, manufacturing, distribution, packaging, marketing, and reverse logistics within supply chains, to improve environmental performance. The use of nonparametric models, specifically Data Envelopment Analysis (DEA), has been prevalent in assessing the efficiency and proficiency of supply chains as decisionmaking units (DMUs). However, the earliest research on efficiency fulfilment in GSCM has not thoroughly explored the combined effect of economic and environmental factors, such as service level, CO2 emissions, and supply chain size (arcs), on the overall efficiency of the supply system. These principles are crucial as they can impact a manager's capability to accurately evaluate the performance of a green supply chain. Therefore, it is imperative to evaluate GSCM efficiency using DEA models while incorporating green principles to identify efficient DMUs and potential DMUs that can be improved with less cost and effort. This study aims to address this research gap by developing a benchmark approach to identify efficient DMUs and potentially efficient DMUs, which can be enhanced through minor adjustments. The study utilizes DEA standard models to determine benchmarks and potentially efficient DMUs and modifies their inputs to achieve an efficient status. Additionally, the impact of green elements on the efficiency of DMUs is assessed using Tobit regression analysis pre and post adjustment. Pragmatic outcomes obtained from the case study demonstrate the practicality of the proposed procedure in prioritizing potential DMUs for modification. Keywords: Green supply chain management, Performance evaluation, Efficiency, Benchmarking, Data envelopment analysis, Tobit regression
This thesis has two main objectives. The first objective is to analyze whether the classification of countries provided by the World Bank (WB) can be reconstructed with a linear and/or integer-programming model known as Multi-Group Hierarchical Discrimination method, using only data published by the WB. The model’s parameters were determined for a collection of 44 countries, and the model was verified using another 39 countries. Moreover, the study examines the relative importance of factors in classification of countries. The second purpose of this study is applying Logical Analysis of Data for country risk rating to provide an approximate rating method. The employed data is available in World Bank and International Monetary Fund and the results are compared with Moody’s rating scale on year 2010. The country risk rating model was established for a collection of 71 countries, and the model was verified using another 34 countries. Furthermore, the study examines the relative importance of economical, environmental, educational, and infrastructure criteria in determining countries risk rating. Keywords: Multi-Group Hierarchical Discrimination, Classification of countries, Country Risk Rating, Logical Analysis of Data
In the last decades, the simultaneous scheduling of production and preventive maintenance has been receiving a considerable attention. Initially, in most researches, maintenance activities were treated as tasks with a fixed period. However, this assumption leads to create a hole in the time horizon. Recently, the variations in maintenance times were addressed, but the starting time is still fixed and known in advance in most of the works. There are few researches that consider the maintenance starting times as decision variables, especially in the non-preemptive case. In this study, the expected total completion time is minimized in the case of a single machine and random failures. The probability of machine failure is an increasing function of the age and the length of the time interval, and preventive maintenance reduces the machine age to zero. The problem is represented by a nonlinear integer programming model which is reduced later to an unconstrained 0-1 optimization problem. Subsequently, a method for solving the unconstrained model by identifying the preventive maintenance decisions is proposed. Moreover, the problem for minimizing the expected makespan on the single machine for the same above mentioned maintenance conditions is addressed and two heuristics methods were proposed to solve the problem. Additionally, the problem of parallel machines which are under the same reliability conditions, but they may have different values of maintenance parameters is discussed. An approximation method based on the bin packing‟s first fit algorithm as well as an exact branch and bound method were introduced to solve the problem. Finally, numerical examples were provided to illustrate each solution procedure of the proposed methods and some analysis was performed. The results show the benefits of integrating both decisions of production and maintenance, because some savings in the values of the discussed performance measures were obtained.
Facility layout problems are applied to find the best arrangement of facilities in manufacturing and service environments. The main goal of these problems is to minimize the total weighted travelled distance of the facilities by the travelled frequency of them. The difficult part is how to measure these distances. A frequently used approximation is the Manhattan distance. However, it is significantly shorter than the real distance in many cases. This thesis suggests an exact mathematical model for closed loop layout that uses real distances instead of Manhattan distance. Many feasible solutions are generated for benchmark problems that are competitive with the solutions provided by metaheuristics. A generalization of multi-dimensional scaling (MDS) method is developed to reconstruct the layout problems from their distance matrix. MDS is a well-known method used in statistics to explore the hidden dependency among data. The reconstruction done by MDS is completely successful if the distance used in layout problems is of Euclidean type. Therefore the generalized MDS provides the opportunity to reconstruct the layout problems with any distance type. The results show that only the Quadratic Assignment Problems which are the models of real layout problems can be reconstructed successfully. The thesis also suggests a mathematical model based on Travelling Salesman Problem and its Dantzig-Fulkerson-Johnson formulation to rearrange the departments of a supermarket in order to increase the travelled path of customers and motivate them to buy more items. The study was done in one of the biggest supermarket chain of Hungary by considering the purchasing items of more than 13,000 customers. The computational experiences show that the total travelled distance can be increased by approximately 4 percent.Öz:Tesis içi yerleşim, tesislerin üretim ve hizmet ortamlarında en iyi iç düzenlemesini bulmak için uygulanmaktadır. Bu problemlerin temel amacı seyahat sıklığına göre tesislerin toplam ağırlıklı seyahat mesafesini en aza indirmektir. Zor olan kısmı bu mesafelerin nasıl ölçüldüğü ile bağlantılıdır. Manhattan mesafesi sık kullanılan bir yaklaşıklamadır. Ancak birçok durumda gerçek mesafeden anlamlı derecede kısadır. Bu tez, kapalı döngü iç yerleşimi için Manhattan mesafesi yerine gerçek mesafe kullanmakta olan kesin sonuç veren bir matematiksel model önermektedir. Birçok uygulanabilir çözüm sezgi ötesi yöntemlerle sağlanan çözümlere rakip olabilecek denektaşı problemler için oluşturulmuştur. Genelleştirilmiş bir çok boyutlu ölçekleme metodu, tesis içi yerleşim problemlerini mesafe matrislerinden yeniden kurmak için geliştirilmiştir. Çok boyutlu ölçekleme, veriler arasındaki gizli bağlantıyı keşfetmek için istatistikte kullanılan bilinen bir yöntemdir. Çok boyutlu ölçekleme ile yeniden kurma, iç yerleşim probleminin öklit türü olması durumunda tamamen başarılıdır. Bu nedenle genelleştirilmiş çok boyutlu ölçekleme herhangi bir mesafe tipi olan iç yerleşim problemlerinin yerinden kurulması fırsatı yaratır. Sonuçlar göstermektedir ki sadece gerçek iç yerleşim problemlerinin modeli olan karesel atama problemleri başarılı bir şekilde yeniden kurulabilmektedir. Bu tez ayni zamanda müşterilerin süpermarkette daha fazla ürün almaları yönünde motive olmaları amacıyla katettikleri mesafeyi artırmak için gezgin satıcı problemi ve onun Dantzig-Fulkerson-Johnson biçimlendirmesini baz alarak süpermarket departmanlarının yeniden düzenlemesini sağlayan bir matematiksel model önermektedir. Bu çalışma Macaristanda bulunan en büyük süpermarket zincirlerinden birinde, 13000‘den fazla müşterinin satın aldığı ürünler dikkate alınarak yapılmıştır. Hesaplamalı denemeler göstermektedir ki toplam seyahat edilen mesafe yaklaşık yüzde 4 oranında artırılabilmektedir.
This thesis deals with two different flexible manufacturing cells. Both cells contain m identical computer numerical control (CNC) machines that are able to perform all the processes to produce a final product. The CNC machines are set up in a line layout. In the both cases, one input station and one output station exists at the beginning and at the end of the line, respectively. The items to be processed are kept in the input station, and the finished items are kept in the output station. In the second case, in addition to the input station, there is an individual input buffers attached to each machine. Using these buffers, each machine can be consecutively loaded twice in a cycle. In the both cells, a robot serves the machines and transports parts from the input station to a machine, loads the machine, and unloads the machine, after finishing its process, and puts the processed part in the output station. In these cells, m different parts will be processed in every cycle. Each part is processed completely by one machine. If the system is at a specific state at the beginning of a cycle, it reaches the same state at the end of the cycle, and then repeats the same actions in the same order in the subsequent cycles. To show all of the possible cycles in such cells, a sequential part production matrix is presented considering a general case. The duration of a cycle is called cycle time. The objective function of both cell types is to find the order of robot operations that minimizes the cycle time which maximizes the long-run average throughput rate of each cell. For the first case, a new mathematical model is presented to optimize the system. A reduced version of the new model is also provided. The reduced version is still an exact model of the minimization of the cycle time, however it does not determine the waiting times of the robot directly. These two models are more effective than the previous existed exact models in the literature. The solution of the reduced model requires significantly less CPU time comparing to the other models. A metaheuristic algorithm based on simulated annealing algorithm is proposed. In order to compute the minimum cycle time in each iteration of the algorithm, a linear programming model is needed to be solved which is the first case in the literature to the best of our knowledge. A new proof is provided for the lower bound of cycle time. This new proof facilitates the optimality analysis of several sequences of the robot movements. For the second case, a mathematical model is presented to optimize the cyclic production. A two-machine cell is discussed in details. In addition to some lower bounds of the cycle time for different orders of robot movements, the optimal cycles and upper bounds for the cases with different activities are also investigated.
There are many papers which emphasize on the benefits of radio frequency identification (RFID) technology implementation in the management and the production. This technology is used in many fields such as inventory, logistics, return management, order picking in a warehouse, assembly and testing and health care Etc. The existing literature examined the efficiency of RFID based on one of the following factors: accuracy, reliability, service enhancement, cost, time, work efficiency, flexibility, interactivity, risk management, emergency, privacy, energy and big Data. In this research, we will shed the light on the failure modes of this technology by using FMEA Approach, then we will measure the efficiency of solving each of these failures according to their severity, occurrence, detection, cost and time; using data envelopment analysis (DEA). DEA is a non-parametric method that evaluates the efficiency of the collection of decision making units (DMUs) when all of them consume and produce the same inputs and outputs respectively. A DMU can be efficient when it is able to produce more outputs by consuming fewer inputs. This economical point of view transforms the issue into a linear programming problem. Based on DEA concept, each failure mode of the RFID technology will be considered as a DMU, and the above mentioned criteria as inputs/outputs. Then the efficiency of these DMUs will be evaluated by DEA models.
The closed-loop supply chain network (CLSC) includes all operations related to recyclable products. The CLSC consists of vendors, producers, warehouses, retail stores, clients, garbage dumps, and recycling facilities. Understandably, the manufacturer has a crucial function to play in this logistical ecosystem. After providing consulting services for several manufacturers in the CLSC, we have helped avoid issues like inadequate manufacturing capacity, high transportation costs, longer delivery times, and higher production prices. This study presents a mathematical planning model for creating a closed-loop supply chain system that includes several electronics manufacturers. The objective function of this optimization model minimizes the amount of costs as well as optimizes (maximizes) the amount of affordable and efficient transportation. General Algebraic Modeling Language software (GAMS) is used to solve this optimization model. Our simulated and realworld results demonstrate that the number of production decreases as demand decreases. Thus, given that the objective function of manufacturers is to minimize costs, whenever demand tends to zero, production does not occur. In such cases, shortage of products (the model’s shortage variable) also approaches zero, and the value of the objective function (i.e. minimizing costs) will also approach zero. In this paradigm, rising demand generally does not increase the value of the objective function. Our model also demonstrates that increasing the production capacity does not worsen the value of the objective function. Building upon an assumed multiproduct model, this study identifies a method to increase the efficiency of the proposed supply chain.