Supplier Selection Analysis Using Minmax Multi Choice Goal Programming Model

Production control, inventory and distribution is an important factor in trading activities. These three factors are discussed in a system called Supply Chain Management (SCM). Procurement of goods from a company or trading business related to suppliers. In some cases, there are several suppliers that can be assessed by considering certain factors. In certain cases, the data from several factors that are considered are uncertainty, so the fuzzy approach can be used. The MINMAX Multi Choice Goal Programming model can be used to solve fuzzy supplier selection problems with linear membership function. It can be applied to selecting supplier of Brastagi Oranges. There are four suppliers, namely Jaya, Mako, Baros. Gina. There are three factor to consider, cost, quality and delivery. The decision maker selects the best supplier for ordering 17000 kg Brastagi oranges. The results, the best supplier is Gina with an order quantity of 10000 kg and Mako with a total order of 7000 kg.


INTRODUCTION
Supply chain management has three main components, namely the process of obtaining suppliers of raw materials, the process of changing raw materials into finished products and the product distribution process. The first stage in the supply chain is supplier selection. Selection of suppliers aims to get products with good quality and competitive prices. Supplier selection is related to the process of procuring goods to meet customer demands. price and quality, time of delivery is a consideration in supplier's selection, especially for perishable products. Fruit is a type of product that does not last long if not stored in the refrigerator.
Research related to supply chains with application in various fields and solutions have been carried out with several approaches. The application of fuzzy TOPSIS in supplier selection was introduced by [1]. The fuzzy approach is also used by [2] in the selection of suppliers in manufacturing companies. The application of the supply chain concept to inventory control and supplier selection for planning new product production in several planning horizons was carried out by [3]. Discussion of supply chain problems by considering price, supply and demand factors is carried out by [4] and an efficient Lagrangian relaxation algorithm is proposed to solve the model. A discussion of bioethanol supply chain network problems with a robust approach was introduced [5]. A deterministic approach to solving the supply chain problem of food product distribution is discussed by [6]. The application of the mix integer programming model to the distribution and supply chain problems of liquid helium is given by [7]. The research of the [8] is combines the concepts of siting, inventory and routing in the supply chain.
There are two main studies related to the supplier selection model to be used, namely the concept of fuzzy and fuzzy goal programming. The Goal Programming (GP) model is used in problems with several objectives to be achieved simultaneously. The GP model with fuzzy numbers is called the Fuzzy Goal Programming (FGP) model. The concept of FGP with random variables was introduced by [9]. Fuzzy and probabilistic approaches to the FGP model are discussed by [10]. Completion of the FGP model with a genetic algorithm is discussed by [11]. Research [12] uses a multi-choice goal programming model to determine energy renewal facilities. [13] used the FGP model in production planning. The choice of waste transportation mode using the FGP model was introduced by [14]. The application of the Weighted Goal Programming model in the urban planning process is given by [15]. The application of the GP model in capital management is given by [16]. The use of the FGP model in transportation problems with several modes of transportation is given by [17].
The research that has been mentioned is the implementation of the supply chain concept to supplier, inventory and distribution components. This research will discuss the problem of selecting suppliers of Brastagi oranges using MINMAX Multi Choice Goal Programming models (Minmax MCGP). The research focus is on component suppliers. This research is a basic research by developing the MINMAX Multi Choice Goal Programming introduced by [2]. In [2], the fuzzy number used is the trapezoid fuzzy number by considering the factors of price, quality and technology offered. In this study, price, quality and time of delivery are considering. Linear membership function is used to define these tree factor.

METHODS
The steps for completing the supplier selection using the MINMAX MCGP method are: 1

. Data Collection and Description
The data used in this study is primary, consist of data on the purchase with the parameters of cost, quality and delivery. The data collection period is from 18 February to 18 March 2020. 2. Determine the fuzzy triangular membership value for the goal of price, quality and delivery. Following are given fuzzy membership functions for the respective three goals, in order of price, quality and timeliness of delivery which are formulated based on the data in step 1. The restriction value of variable , , is determined based on the data in step 1. (2) Where ( ) is the membership function for the cost.
( ) is the membership function for the quality.

RESULTS AND DISCUSSION
This research discusses supplier selection problem of citrus fruits for the type of Brastagi oranges. The data used are primary data with a data collection period of 30 ordering periods. The research was conducted at a fruit shop in Palembang . The following is given the research data.  Table 1 can determine the percentage of on-time delivery, the variable price offered, and the varying percentage of quality citrus in good condition with the total of all oranges sent by the supplier. The price value of each supplier is obtained by adding up each price in purchases divided by the number of investments, determined the average value for each data cost, quality, and timeliness. The calculation results are given in Table 2 below. Determined the degree of membership for the level of satisfaction of the Decision Maker (DM) of each goal using (1), (2), (3). The calculation results are given in Table 3 below: The value of the level of satisfaction is in the interval [0,1]. Based on Table 3, it is known that for the lowest decision value, DM gives a satisfaction level value of 0. For the highest decision value, DM gives a satisfaction level value 1. The level of satisfaction for each goal of cost, quality, and time delivery is determined based on equations (1), (2), and (3). The results are given in Table 4 below. Solving the linear model (5) uses LINGO 13 software and the solution is obtained in Table  5 below.

Supplier Selection Analysis Using Minmax Multi Choice Goal Programming Model
Novi Rustiana Dewi 103 In Table 5, for a maximum total order of 17000 kg, an order is recommended for 2 (Supplier Mako) and 4 (Supplier Gina). The values of 1 (Aspiration Rate G1) = 39463.88,