Fuzzy Linear Programming Dalam Optimalisasi Pelayanan Air Bersih Perusahaan Daerah Air Minum (PDAM) Kab. Jeneponto Menggunakan Metode Sabiha

Abstrak. Fuzzy linear programing merupakan pengembangan model program linear dalam menentukan nilai optimal yang mengandung bilangan fuzzy. Metode yang dapat digunakan dalam menyelesaikan fuzzy linear programing yaitu metode Sabiha. Penggunaan metode Sabiha didasarkan pada bilangan linear fuzzy real yang berbentuk bilangan triplet. Pada penelitian ini digunakan model Fuzzy linear programing dalam menentukan nilai optimal pelayanan PDAM Kab. Jeneponto dengan metode sabiha. Menyusun setiap indikator fungsi tujuan (Z) dan fungsi kendala untuk dioptimalkan.. Hasil penyelesaian model diperoleh nilai optimal total pelanggan 9075,999999999990. Untuk setiap variabel tujuan dengan nilai optimal 8896, 999999999990 untuk jenis pelanggan rumah tangga, 96,0000000000112 untuk jenis pelanggan sosial khusus, dan 82,9999999999982 untuk jenis pelanggan sosial umum. Dengan total pendapatan optimal Rp. 4.753.125.000 dan total permintaan air 1.082.303 m3.Kata Kunci : Program Linear, Fuzzy Linear Programing, Linear Fuzzy Number. Metode Sabiha, Optimalisasi.Abstract. Linear fuzzy programing is advance model for linear programing to determin the optimal result that contains fuzzy numbers. Linear Fuzzy programing can be solved using Sabiha’s method. Which is based on real linear fuzzy numbers in triplet numbers form. This paper used linear fuzzy programming model and Sabiha’s method, to determin the optimal solution on PDAM Kab. Jeneponto’s operation plan. Each indicator constructed to optimized objective function and constraint function. Results of this research have optimal solution for each objective variable was obtained with an optimal value for total costumer are 9075,999999999990 from 8896,999999999990 the type of household customer, 96,0000000000112 the type of special social customer, and 82,9999999999982 the type of public social costumer. With an optimal total revenue Rp. 4,753,125,000 and total water demand 1,082,303 m3.Keywords: Linear Programing, Linear Fuzzy Programing, Linear Fuzzy Number, Sabiha’s Method, Optimalization.

A Fuzzy Programming Model for Positioning Customer Order Decoupling Point Based on QFD in Logistics Service with Mass Customization

Mass customization logistics service mode provides a new way to maintain the sustainable cooperative relationship between customers and integrators. One of the key factors to maintain the sustainable development of logistics service supply chain under MC mode is to locate a suitable customer order decoupling point (CODP) location. This paper investigates the problem of CODP in the logistics service supply chain based on the fuzzy set theory under the mass customization mode. With the help of a fuzzy QFD method and a new service quality function that we constructed, this paper quantifies the quality of a logistics service when the LSI selects a different CODP. Then, the fuzzy set of the high-quality logistics service and the fuzzy set of the satisfactory delivery time are built. Based on those two new fuzzy sets, this paper builds a new fuzzy programming model on CODP positioning. The solving methods of this model under different conditions are given. Finally, the influence of some important parameters on the optimal CODP position is studied by sensitivity analysis on a specific numerical case.

Methodology for Solving Multi-Objective Quadratic Programming Problems in a Fuzzy Stochastic Environment

This chapter presents two methodologies for solving quadratic programming problems with multiple objectives under fuzzy stochastic environments. The right side parameters of the chance constraints of both the models are chosen as fuzzy random variables (FRVs) following different probability distributions. Like the previous chapters, chance constrained programming (CCP) methodology is employed to the fuzzy chance constraints to develop fuzzy programming model. In the first model, cut of fuzzy sets and fuzzy partial order relations are incorporated to the fuzzy programming model to develop an equivalent deterministic model. For the second model, defuzzification method of fuzzy numbers (FNs), which are presented in Chapter 2, are taken into consideration to generate equivalent quadratic programming model in a crisp environment. As the objective functions are quadratic in nature, it is easy to understand that the membership functions obtained through methodological development process are also quadratic in nature. To linearize the quadratic membership functions, linearization techniques are employed in this chapter. Finally, for achieving the maximum degree of each of the membership goals of the objectives, a fuzzy goal programming (FGP) approach is developed for the linearized membership goals and solved by minimizing under-deviational variables and satisfying modified system constraints in fuzzy stochastic decision-making environments. To illustrate the acceptability of the developed methodology presented in this chapter, some numerical examples are included.