استفاده از الگوريتم ژنتيك و تحليل پوششي داده‌ها براي انتخاب كاراترين چيدمان مبتني بر ساختار نواري منعطف

USING A GENETIC ALGORITHM AND DATA ENVELOPMENT ANALYSIS FOR SELECTING EFFICIENT LAYOUT BASED ON FLEXIBLE BAY STRUCTURE

«چيدمان تسهيلات» مسيله‌يي است كه به تعيين موقعيت دپارتمان‌ها در كف كارخانه مي‌پردازد. رايج‌ترين هدف در اين مسيله كمينه‌سازي هزينه‌هاي حمل‌و‌نقل مواد است. بيشتر محققين به چندمنظوره‌ بودن ماهيت مسايل چيدمان اذعان دارند و بنابراين، در تعيين مكان مناسب تسهيلات در نظر گرفتن‌ِ اهداف مختلف ضرورت مي‌يابد. از اين‌رو در اين نوشتار با در نظر گرفتن اهداف مختلف و به‌كارگيري يك رويكرد چندمرحله‌يي ــ شامل الگوريتم ژنتيك، الگوريتم 2-opt و شيوه‌ي تحليل پوششي داده‌ها ــ يك چيدمان كارا براي مسيله‌ي چيدمان‌ِ مبتني بر ساختار نواريِ منعطف تعيين مي‌شود. در اين نوع چيدمان، دپارتمان‌ها به‌صورت پيوسته به نوارهايي موازي با عرض‌هاي مختلف اختصاص مي يابند. رويكرد پيشنهادي براي چندين مسيله‌ي موجود در ادبيات موضوع آزمايش شده است. نتايج به دست آمده نشان‌گر موثر‌ بودن رويكرد پيشنهادي است.

The facility layout problem (FLP) involves determining the position of department plant floors. The most common objective in this problem is minimizing material handling costs. This paper presents a multistage approach for the facility layout problem based on flexible bay structure. This structure, proposed by Tong (1991) for the first time, is the limited state of the continuous layout problem. In a plant layout, based on flexible bay structure, departments are assigned to parallel bays on a plant floor. Departments could be free oriented and may have unequal areas. The width of each bay is flexible and dependent on the number of departments located in that bay. The width of each bay is obtained by dividing the area of departments located in the bay by minimum sides of the plant floor. In addition, the numbers of bays and departments set in each bay are changeable or flexible. It should be noted that in problems based on flexible bay structure, due to control department shapes, the factor of the maximum aspect ratio is used. Due to complexity, only small-size problems could be solved in logical time, while using exact methods. Thus, at the first stage, a genetic algorithm (GA) was proposed to solve this optimization problem. Genetic algorithms are meta-heuristic methods for solving problems based on evolution mechanisms and the nature of genes. The main idea in this regard was introduced by Holland in 1975, and for three decades has been introduced as an effective optimization and search method. In the genetic code used in this paper, each chromosome is formed by N genes, each of which is a random number between 1 and B, the integer part of which represents the number of bays, and the decimal part of which represents the department sequence in each bay. The proposed GA algorithm uses FBS to represent the facility layout with the unequal area department. The proposed algorithm tries to find the optimum value for the number of bays, the number of departments contained in each bay, and the department’s placement order, which could minimize the objective function value. The majority of researchers believe that the facility layout problems are naturally multi-objective. Therefore, considering various objectives in determining the proper position of facilities is essential. The proposed approach is that, after creating a primary layout using the genetic algorithm, a 2-opt algorithm has been applied to generate layout alternatives. Then, using the DEA approach, the most efficient layout from alternatives will be chosen. This paper improves the integrated data envelopment analysis (DEA) model introduced by Amin (2009) for finding the most efficient decision making units. The proposed approach was tested on some test problems of the FLP literature. The results show the effectiveness of the proposed algorithm.