Repair and Replacement Strategy for Optimizing Cost and Time of Warranty Process using Integer Programming

Warranty is an assurance issued by a company as the manufacturer to guarantee that its product is damage-free within a specified period. The warranty process is usually carried out when a complaint or damage regarding the product is received. The warranty process consists of two decisions that the company establishes to handle the process. The occurring problem is in the warranty process; there is not any standard established to determine the cost to incur for the warranty process. In this research, integer programming method was used to do optimization on repair and replacement strategy in warranty process. Before doing optimization, mathematical model must be created. Using that mathematical model, the results show that the costs of the warranty process decrease by 16.97%, while the time increases by 13.9%. So, with this method company will be increase the profit.


Introduction
Warranty is an assurance issued by a company as the manufacturer to guarantee that its product is damage-free within a specified period (warranty period) [1,2]. Warranty is usually used as a contract between the manufacturer and the customer [3] to gain customer's trust, so that it can be used as a means to attract customers [4]. In this research, the problem used is the warranty process on the distributor of wireless devices, since distributor is considered to be the connector between producer and customer. As a matter of fact, the distributor cannot suppress the cost of goods in the warranty process because it is predetermined by the manufacturer. In the warranty process, there are two choices: repair and replace. In the process of selecting whether to repair or to replace, there are advantages and disadvantages to each choice. The replacement versus repair is a classic problem that has long occurred [5]. The problem is based on two criteria: cost and time. To obtain the maximum decision result, it requires optimization between costs and time. Optimization is the activity conducted to produce the best result in accordance with the requirement. In the optimization process, the formulation is considered to be essential because with precise formulation produces an efficient and optimal decision [6]. One of the methods which can be used for optimization to solve the problem is linear programming method [7,8]. With various alternatives available, the method can determine the optimal decision [9] by minimizing or maximizing objective functions with the existing constraint variables. Thus, it can solve problems using the available/limited resources [10]. Linear programming has several types, one of which is integer programming. Integer programming is an optimization method that provides limits of the results of decision variables are integers [11,12,13].
In previous research, many researchers use problems in the warranty. In [4], goal programming method is employed for warranty optimization in manufacturing companies with multi-objective optimization. In other previous research [14], repair and replacement strategy decision is under Markov Deterioration; in [15], AHP is used to decide priority improving parts in automotive industry to decrease warranty. All of that previous research, the problem they examined is manufacturing side. In this paper, the problem on warranty process is distributor side. In distributor side, they cannot change the goods of cost. But, the manufacturing can change the goods of cost to minimize production. Integer programming method is opted to optimize costs and time because it is in accordance with the problems formulated. The result of this research is the choice of the decision to repair or replace which is in contrast to previous studies [4,6] indicating reduced costs.
In this research, optimization is conducted to optimize process warranty. In previous research [16], optimization problem aims to determine which items are replaced or repaired by generating the value of 0 or 1. It means that if the result of repair or replace is 0, the process is not choosed, but if the decision result is 1, the process is choosed. The decision is based on two options whether to replace or to repair meaning that the decision is obliged to opt one of the modeled decisions. The previous method [16] uses the operational cost variable from repair and replaces process. In this paper, the researcher added the customer satisfaction variable. In reality, customer satisfaction is in terms of grading; however, the researcher converted customer satisfaction into cost. Customer satisfaction is assessed in terms of the time spent for the warranty process. By conversing to cost, the longer the warranty process is the company is more likely to lose the assumed costs, vice versa; when the warranty process is finished quickly, the company is more likely to reduce the cost incurred. It means that time is the influential factor in the warranty process. In other words, time affects customer satisfaction. In this research, the process taken is divided into three procedures. The first one is setting limit resource for optimization; the second is making a model optimization with integer programming method. The final procedure is result and analysis.

Research Method 2.1. Return on Investment (ROI)
Profit has to do with investment. To determine the advantages there are two methods of measurement. By measuring Return on Investment (ROI) and Return on Asset (ROA). The result of ROI is that it can produce an evolutionary measure that shows how large a company is able to generate profits from used assets [17]. Results generated from the size of the ROI is the size of the ratio. The ratio can also be used as a benchmark how big a company in generating payback [18]. Besides, the ROI size can also be used to compare the efficiency of a number of different investments in the company. The formula ROI [19] as (1).

Integer Programming
Integer programming is one type of optimization method used to solve problems to generate optimal decisions. Integer programming is part of a linear type programming. Many types of optimization methods of linear part programming are used for optimization with various problems. For example, one of the types of methods is Goal programming, goal programming can be used to optimize the time and cost on the container port [20]. Besides that, goal programming can also be combined with fuzzy method which can also be used to optimize time and cost so as to maximize total production, production cost and maximize sales [21]. In the case to be examined in this paper. Integer programming is chosen because the decision result of the method is integer value. Because the problem is to choose between repair or replacing with notation 0 and 1 as a result of a decision. The decision will be forced to produce integer numbers [22].
To optimize a problem, an optimization model is needed. Optimization models must match the problems that occur. the model contains variables that will be used for optimization. To create mathematical model using integer programming method in need of three main parts. That is decision variable, constraint function and objective function.
Decision variables are variables that are the results generated by the integer programming method and will be the optimal solution. For this paper the decision variable denoted by and (i = 1,2,3 ……i) where R is repair and P is replaced. The constraint function is a function used to limit the decision result to be used. In this study the limit used is 65% of ROI. The decision is obtained from the company's needs to be studied. The model constraint as (2).
where: = cost of replace items as many as i (i … n) = cost of operational items as many as i (i … n) = cost operational of replace items as many as i (i … n) = cost of repair items as many as i (i … n) = cost operational of repair items as many as i (i … n) = cost of customers satisfaction repair items as many as i (i … n) = cost of customers satisfaction replacement items as many as i (i … n) In the model described above there are several variables used such as operational costs for administration warranty process, replacement costs, repair costs, operational costs for the repair process, operational costs for the process of replacing and the cost of customer satisfaction conversion. After the constraint model is created, the next are to make the function objective. Objective function serves to obtain optimal results in decision making. Objective function model is described as (3) where: X : number of items to be in service.
: the amount of optimization results of items in the repair : the amount of optimization results of items in the replacement In the objective function model explained that the result of the objective function is the total of the resulting decision result

Results and Analysis 3.1. Set Limit Resource of Optimization
Limitation is very important to limit the resources that will be used for mathematical models in optimizing problems. The limitations that will be used are the results of the company's ROI used in this study. In this case it is known that the profit from the sale in the company is From the above calculation, it is known ROI of the company is 46% from the provit of sales. The result of limit resource is 9.782.469,19 IDR.

Optimize using Integer Programming Method
Before doing the optimization process. The first thing is to collect data that will be used for the optimization process. The data is based on the results of the mathematical model that was made previously from (2).
In this paper the data used is the overall data process warranty in December 2017. The data collected is data from the monitoring service that is in the warranty process. The data explains what data goes into the warranty process of the customer.
In Table 1, there are five columns, namely type, mac address, description, solution and process. For example, in the first data type RB SXT-5nDr2 ROUTERBOARD with mac address 6C:3B: 6B:9D:0E:56 has been damaged in phy ic, then the solution for replacing AR9344-BC2A Network Processor components and process status is repair.
First, determine collect data operating Costs Company. The cost includes the costs incurred by the company for the administration process in the process of warranty process. In the process of administration of the warranty process there are several activities as follows. Table 2 describes the types of tasks in the operational warranty process. In each task there are resources, descriptions, time and total costs incurred.  Second, the next is to collect how much the company will cost to replace the goods received from customers for the warranty process. The replace cost used is equal to the price of the item. In Table 3, there are some replacement costs for each item. For example, in the first data, the price of the DISC Lite 5 MIKROTIK cost of replace is 558.900,00 IDR. Third, determine the costs incurred for the repair process. in this paper the repair process is divided into three parts according to the level of difficulty in process repair. Table 4 explain the more difficult the repair process, the more expensive costs will be. whereas, the easier the repair process is, the costs will be cheap. In this contex, salary is the salary of the technician and the component is the cost of replacing the damaged part.
After the cost of the repair process in three parts according to the level of difficulty. The rules will be entered according to the level of difficulty repair to the goods that enter the warranty process. The results of the repair costs are shown in Table 5.
In Table 5, can be seen more in detail the cost of the warranty process. By adding colom criteria for difficulties. The total cost is obtained from calculations based on Table 4. Fourth, convert customer satisfaction into a value. Customer satisfaction is also a consideration in the selection between repair and replace. The conversion is done so that the calculation in the mathematical model in the integer programming into one unit with variables used before. unit in the method to be used is to generate cost, then customer satisfaction is changed in unit cost.   How to convert customer satisfaction into cost is by referring to company regulation. in the company rules mentioned that the replacement deadline is 12 days. 12 days will be converted to time units to be balanced with units multiplied by the cost used to calculate the cost of the replace and repair process in (5).
Where CC is cost customer satisfaction per item. Then the cost is multiplied by how long the process from customer until the warranty process is complete, the calculation is described as (6).
Where T is time of work on repair or replacement process. In the process the repair process takes 2 days, while the replace process requires a faster time that is only one day. From the formula above obtained the following results.
In Table 6, there are conversion results for customer satisfaction in each type of item. the results of the calculation are based on (5) and formula (6). handles the replace process. there is an RMA admin as a resource with a description of costs including salary and computer as the device used. and the time needed for the replace process. The total costs for technical replace is 9.600,00 IDR. Sixth, the cost for the repair process, the cost of the repair process is the cost incurred by the company in the process of repairing the goods. These costs include technician equipment and computer technicians. Table 8 explain that the technician takes 226 minutes to process. In this case it is from the total component checking activity, analyzing what is going on, replacing and installing the components and in the final stages of testing the repaired items. So the technician can repair the repair process completely completed or there are still obstacles in the repair process. So the costs incurred for technical repair amounted to 18.620,00 IDR After determining the data. Then, apply the entire data that has been described above into the model that has been made before. Here are the results of mathematical models that have been applied with the data already described as (7) for objective function, (8) and (9) for constraint function. Minimize: Subject to: