Layout of facilities pdf

Genetic algo- ship functions as shown in Figs. Also, each of these variables is assumed to have a C. Proposed Approach weight factor WF that affects the closeness between each pair As discussed earlier in this section, in the layout problem the of facilities [24]. These relationships are following four steps. Membership functions of material flow MF.

Membership functions of information flow IF. Membership functions of equipment flow EF. Each linguistic variable with its weight factor are used as input to the fuzzy decision-making system.

This program is used to perform fuzzification, fuzzy inferencing, and defuzzifica- tion. The final crisp values obtained by the defuzzification process are then used to generate the facility relationship chart.

In the literature [11], [5], chart and a genetic algorithm program. In this study, the weight values used are output variable. This is performed through pairwise assessments shown in Table I and can be used as a guide to draw the close- of the relationships between each two facilities. Membership functions of closeness relationship R. If the relationship and, accordingly, the distance between them should be small.

A between facilities 1 offices and 2 warehouse is under con- weight value of unity also means that the two facilities have no sideration, for example, the planner is assigning a value of two interaction between them and the distance separating them is ir- for the importance of factor 2 over factor 3.

This means that there relevant. It is noted that the values in Table I are presented for is a range between an equal and a weak importance of factor 2 illustration only and the planner can set other values based on over factor 3. Considering the relationship between facilities 1 his own judgement or using a quantitative measure.

The mem- and 6 , as another example, the value of nine assigned for the bership functions of the closeness relationships are shown importance of factor 2 over factor 3 indicates an absolute im- in Fig. The information shown in Table II, however, are based on the D.

Considering the relationship between facility tion, the input values for the three linguistic variables are as- 1 offices and facility 3 batch plant , for example, the in- sumed along with the intensity importance of factors for each tensity importance of factors listed in Table II are used to calcu- pair of facilities as shown in Table II. These values are needed late the weights of factors shown in Table IV below.

These to generate the overall membership functions. These numbers represent the true pref- of factors and equals to three in this study. The result is. The result is the weight factor. This process is repeated for all pairs of facilities to calculate E. The weight factor is considered one of the input factors that will influence At this point, the fuzzification process is complete.

The next the layout. The higher the weight factor is, the more important step is to establish the decision-making logic decision rules. Membership functions of weight factor WF. These values are then used to develop the best layout scheme. This fuzzy decision-making process is repeated for each pair of fa- cilities i. Appendix A-1 shows the -values of Since we are considering three input variables that will affect the membership function low of the material flow varible; 4 the decision of the planner, the total number of rules between the input value of the material flow variable for example, each two facilities is equal to rules.

These rules between facilities 2 and 4, as given in Table II and the input are generated by considering the membership functions of each value of the corresponding weight factor for example, 0. These rules are com- terial flow and its weight factor ; 6 the membership function of piled in Fig. For example, rule number 1 shown previous experience in construction projects.

The input values for each variable shown in Table II were F. Generation of the Facility Relationship Chart FRC then entered to the program for each pair of facilities along with A program using spreadsheet visual basic is developed to deal its corresponding weight factor to get the overall membership with the inference of the generated IF-THEN decision rules. The functions and their output crisp values.

For example, Fig. It also allows the user to chose any of the The average of output crisp values closeness relationship defuzzification methods such as the centroid of the area COA , for each pair of facilities is calculated in Table VI.

Overall membership functions of facilities 2—5 for material flow, information flow, and equipment flow. Facility relationship chart. The figure shows that construction site is divided into square units selected as 19 22 units. Each unit has an area of 20 m. As shown in Table VII, the user is required to enter the start unit number for fixed facilities in the site such as roads, building to be constructed, etc.

The program also requires that fixed facilities should be given the number 1 , while other facilities to be given the number 0. Table VII also summarizes the required inputs for each facility in the construction site. Due to the shape of the building to be constructed in the site, it is divided into two parts building 1 and building 2.

This is to enable the program to place the building in its required location. The genetic algorithms technique involves three main steps: 1 deciding the objective function; 2 generating an initial pop- ulation of genes; and 3 selecting an offspring generation. First, the objective function is generated by multiplying the desired closeness relationship values between each two facilities by the actual distance between them, and summing them up for all fa- cilities.

This objective function, therefore, represents the total travel distance for a given site layout. In order to arrive at the optimum layout that brings the least travel distance and, accord- ingly, to ensure that facilities with higher closeness relationship G. Developing the Physical Layout of Facilities values will be placed close to each other, the objective function Once the facility relationship chart is generated as outlined in should be minimized.

The program is structured in a way as it volves determining the centroids of all facilities and then calcu- requires the user to enter the number of facilities to be located in lating the distances between them.

The user interface of the genetic algorithm program. Third, jective function of a site layout with facilities can be calcu- the reproduction process among the population members takes lated as follows: place by crossover to produce an offspring. Once an offspring Total travel distance objective function is generated, it is evaluated in turn and can be retained only if its fitness is higher than that of others in the population.

This process is continued for a large number of offspring genera- tions until an optimum gene is generated. In the program, the user is given the flexibility to input the number of offspring where is the desired closeness relationship value between generations.

Throughout the process, the entire population soon facilities and. In the Second, a population of parent genes is generated randomly. Once the population is generated, The first step is to provide as input all pertinent facilities data. Distance between facilities. The selected layout. On the other hand, the spectively.

Following this, the genetic algorithm program gen- workshop facility number 4 is placed far from the building, erates different solutions layouts with their corresponding fit- which is also considered to be a logical placement. This is be- ness values scores. The best solution, basically, is the one with cause there is no strong relation between the workshop and the the minimum score minimum fitness value.

In this application building to be constructed. The shaded area in the figure represents IV. As shown in the figure, it is noticed that facility number 1 the The main features of the proposed approach that makes it offices is placed near the building to be constructed in the site.

Screen interface for inference rules. Screen interface for membership function data. On the other hand, one of the drawbacks of the proposed ap- proach is the difficulties encountered in generating the mem- bership functions of the variables affecting the decision of the Fig. However, newly developed tools of neuro-fuzzy infer- encing [13] have been introduced in recent years and should a construction site. An example application is also presented to be promising in this regard as they have the potential of au- demonstrate the practicality and potential capabilities of the ap- tomating the process of generating the membership functions proach andthe results are then discussed.

Integrating the proposed from a set of experiential data. Another issue is the problem of approach with newly developed tools of neuro-fuzzy inferencing establishing the decision rules, which requires a great deal of systems should make it an even more versatile and powerful tool care and experience. In some particular cases, the planner may for dealing with facilities layout planning. The screen interface for membership function data is shown in Fig.

Wivhelm, W. Karwowski, and G. Production Res. Armour, E. Buffa, and T. Computing Civil Engrg. ASCE, vol. Texas—Austin, TX, Dweiri and F. SMC-3, —, Francis and J. Michigan, Ann Arbor, Sets Syst. Hegazy and E. Lee and J. Lin and C. Linkens and S. His areas of expertise span the fields of advanced pt.

D, vol. He has published Large Scale Syst. Mamdani and S. Studies, vol. Kitchener-Waterloo area, which he cofounded. Raoot and A. Florida, Gainesville, Essam Zaneldin is working toward the Ph. Rodriguez-Ramos and R. He participated in the design and construction super- [23] J. Ross, Fuzzy Logic with Engineering Applications. New York: Mc- vision of many large projects with a number of international companies.

He has Graw-Hill, Saaty, The Analytical Hierarchy Process. New York: McGraw- mation management, change management, collaboration, and simulation.

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