Published at : 04 Apr 2023
Volume : IJtech
Vol 14, No 2 (2023)
DOI : https://doi.org/10.14716/ijtech.v14i2.5105
Nur Faizatus Sa’idah | Doctoral Program in Industrial Engineering and Management, Faculty of Industrial Engineering, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia |
Andi Cakravastia | Industrial Engineering, Faculty of Industrial Engineering, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia |
Udjianna Sekteria Pasaribu | Statistics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia |
Bermawi Priyatna Iskandar | Industrial Engineering, Faculty of Industrial Engineering, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia |
In this paper, we study a two- dimensional Maintenance Service Contract (MSC) characterized by two limits (dimensions) of age and usage. It is considered that an agent offers a two-dimensional MSC by guaranteeing a certain level of equipment available to consumers. The agent needs to reduce the total maintenance cost to offer competitive MSC prices. Preventive maintenance actions (PM) are periodically carried out, and each PM action is considered to improve reliability modeled by reducing the failure rate function. Two decision variables (the PM interval (T) and the reduction in the intensity function are obtained by considering two performance measures that are relevant to agents and consumers (i.e., availability and total maintenance cost). A numerical example is presented by considering three types of equipment usage rates: low, medium, and high. The optimization of the two performance measures can ensure availability targets and, at the same time, minimize total maintenance costs.
Availability; Imperfect preventive maintenance; Maintenance service contract Total cost; Two-dimensional
Maintenance Service Contract (MSC) is defined as
an equipment maintenance contract that agents offer to
consumers within a certain period. Maintenance contracts, generally, are characterized
by a time limit (e.g., 1 year), called an MSC with one dimension. However, for
equipment such as dump trucks whose failure patterns are affected by age and
use, it is necessary to include a usage limit (e.g., 100,000 km) in
addition to the age limit. Different types of equipment may have different ways
of measuring usage. For example, a photocopier's usage can be measured by the
number of copies made, while a machine tool's usage can be measured by the
hours it is used. This MSC is referred to as an MSC with two dimensions. To
appeal to consumers, the MSC may include promised equipment performance (e.g.,
Target 94% equipment availability) in addition to the price charged. A
comprehensive review of MSC can be found in Murthy
and Jack (2014), and MSC is studied
From
the consumer side, equipment used to support business processes will
deteriorate with age and use, and eventually, failure will occur (Jiang and Murthy, 2008). Maintenance is an effective way to slow down
the deterioration of equipment so that failure can be minimized and
availability can be kept high (Pariaman et
al., 2017; Suthep and Kullawong, 2015; Jackson and Pascual, 2008). Consumers who own equipment,
generally need MSC because maintenance activities are not their main business
(core business), so they do not need to be done in-house.
Using an agent to maintain equipment through a
Maintenance Service Contract (MSC) is more cost-effective and reliable than
in-house maintenance, which requires expensive investments in human resources,
equipment and technology. MSC offers consumers the benefits of saving on
maintenance costs and improving equipment performance. Many studies have
explored MSC from the consumer's perspective, including research conducted by Huber and Spinler (2012) and Jensen and
Stonecash (2009). In general,
research from the consumer’s point of view always wants (i)
minimum cost or maximum profit, with additional considerations of other
performance measures such as (ii) service quality (eg. delivery time) (De-Almeida, 2007) (iii) product reliability (Laksana and
Hartman, 2010), or (iv) availability (Datta and Roy, 2010). Due to the important role of maintenance in
maintaining the condition of equipment, the agents respond proactively to the
consumers’ needs by offering MSCs that promise high availability. In addition to getting regular income, agents
can also build good relationships with consumers, which positively impacts the agent’s image (brand building).
From the agent’s point of view, research was
carried out by Tarakci et al. (2006), where the agent offers specific incentives
based on the combination of target uptime and bonuses in the contract to
attract consumers. In addition, reliability improvement is also considered.
Generally, the agent looks for the optimal PM time interval to fulfill the
performance promise to the customer, which maximizes the profit. MSC can be
grouped into two categories: one-dimension MSC and two-dimension MSC.
One-dimensional MSC is characterized by a one-time limit (age). For example,
the MSC of a piece of equipment is for one year, while the two-dimension MSC is
characterized by an area of a two-dimensional plane where one dimension
describes a time limit and the other a usage limit (Iskandar et al., 2014). One-dimensional MSC research has considered several important
performance measures for agents (i.e., total cost and benefit) as well as
consumers (i.e., reliability and availability). First, many MSC studies
consider profit performance measures (Darghouth, Ait-kadi,
and Chelbi, 2017; Hamidi, Liao, and Szidarovszky, 2013; Chang and Lin, 2012). Second, the reliability performance measure is
considered in addition to the benefits (Laksana and
Hartman, 2010). Third, the
availability performance measure is also involved (Su and Cheng, 2018; Iskandar et al., 2014). The effect of PM's actions on increasing
reliability can be represented through a reduction in (i) failure rate or (ii)
virtual age. Some of them are researched by Darghouth, Ait-kadi, and Chelbi (2017) and Pasaribu, Husniah, and
Iskandar (2012), who specifically examined one-dimensional MSC with periodic PM
policies and the impact of PM reducing a virtual age. Other works are the
research of Husniah et al. (2019) and Yeh and
Chang (2007), which examine
one-dimensional MSC with a periodic PM policy model using an intensity
reduction function. There is also research by Iskandar
and Husniah (2017) and Yeh, Kao, and Chang (2009), who investigate one-dimensional contracts
using a PM policy that ensures equipment reliability.
Meanwhile, two-dimensional MSC
studies have not received much attention. As in one-dimensional MSC, the most
commonly used performance measure in two-dimensional MSC is profit (Huang, Gau, and Ho, 2015; Husniah et al., 2014). No studies have considered the availability
of two-dimensional MSCs. At the same time, consumers want high equipment
availability to be guaranteed. The motivation to prioritize availability is
because the losses (costs) due to equipment downtime are very large. For
example, the breakdown of equipment such as draglines (in the mining business)
and airplanes (in the transportation business) will result in huge losses for
the company operating the equipment. Performance in two-dimensional MSC can be
achieved by implementing various preventive maintenance (PM) policies, which
can be divided into two categories, namely periodic and non-periodic (Jiang and Murthy, 2008).
In this paper, we propose a two-dimensional MSC that implements the imperfect PM policy carried out periodically. The effect of the PM action on the two-dimensional MSC will be developed by extending the formulation of the one-dimensional MSC. As in the one-dimensional MSC studied by Yeh and Chang (2007), It is assumed that the effect of PM reduces the intensity function. Furthermore, this paper focuses on two-dimensional MSC, The study is carried out from the agent's point of view, considering two performance measures, namely: (i) equipment availability and (ii) total maintenance costs, and involving two decision variables, i.e., the PM time interval (T), and the failure rate reduction value for each PM. As a result, the main contributions of this paper are (i) developing a PM policy that ensures the equipment availability target with minimum costs and (ii) obtaining optimal solutions of PM policies for a two-dimensional MSC with two objective functions, namely maximizing availability and minimizing total cost. This is in accordance with the goals desired by consumers for MSC, which are to ensure high availability (for example, 94%) and simultaneously meet the agency's goal of minimizing total maintenance costs. This paper is organized as follows: The model formulation is given in Section 2, which includes a discussion of the two-dimensional MSC formulation, failure modeling, and PM impact modeling. Section 3 describes an optimization to find the optimal solution that guarantees target availability with the minimum total cost. Section 4 provides numerical examples and a discussion of the results. Finally, we present conclusions and further research topics in Section 5.
Model
Formulation
This section will detail the two-dimensional MSC under study, failure
modeling, and PM effect modeling.
2.1. Two-dimensional
MSC
Consider
a two-dimensional MSC for equipment (e.g. dump trucks), which is characterized
by two parameters, L (time limit) and U (usage limit). For example, a
maintenance contract for a dump truck with a time limit of 1 year and a usage
limit of 100,000 km. Thus, these two contract limits form a rectangular area (Iskandar et al.,
2014). Suppose that the equipment with the rate of use is said to be moderate (normal) usage rate, low usage rate, and high usage rate . The contract will end at
2.2. Failure Modeling
Equipment failures that occur randomly during the
contract period are considered random points that fall in the maintenance
contract area (which is rectangular). There are three approaches to modeling
random points (equipment failure) on a two-dimensional plane (Murthy and Jack, 2014). In this paper, we shall use the formulation of a one-dimensional point process as has been done by
Iskandar, Murthy, and Jack (2005). Let
Equipment is repairable, and the
equipment failure over time is modeled with an intensity function (Iskandar and Murthy, 2003).
Suppose
2.3. PM Policy
The agent requires a proper PM
policy to reduce failures and downtime, and this will increase availability. In
this paper, two PM policies are considered.
2.3.1. PM Policy 1
PM
actions are carried out periodically or at the time of
2.4.1. PM Policy 1
2.4.2. PM Policy 2
In this PM policy, whenever PM (if the failure rate reaches ), failure rate will be reduced by . For a given Y = y, number of PM actions
throughout the period L
2.5. Availability and Total Maintenance Cost
2.5.1.
Availability
2.5.2. Total Maintenance Cost
PM Policy 1: Total maintenance costs include minimal repair costs (including expected downtime penalties) and PM action costs. The total expected cost of a two-dimensional MSC over the period is given by:
Optimal Decision
This section discusses the optimization scheme
(Optimization Schema) of the two-dimensional MSCs under consideration.
3.1. Two-dimensional MSC with PM 1 Policy
(Proposed)
Optimization Scheme 3: Find the value of by considering availability and total cost together. This is done using optimization with two objective functions. Using the Weighted Sum method from the study of Grodzevich and Romanko (2006), the structure of the optimization function with two objectives is given below.
3.2. Two-dimensional MSC with PM Policy 2
Again, the three optimization schemes are also used to find the optimal solution.
Optimization
Scheme 1:
(i) First, using the algorithm proposed by Yeh and Chang (2007) finding the optimal value of which
minimizes the expected total cost. (ii) Second, based on the optimal
value of (i), then calculate the availability with the equation in (2).
Consider that is Weibull distribution
with , where is the scale parameter and is the shape parameter. Suppose that each
failure incurs costs (including the minimal repair cost and possible penalty
cost) and the cost for performing a PM action with maintenance degree . A similar form of maintenance cost is used by Supriatna et al.
(2020). These parameter values were used in Yeh and Chang (2007) and will be considered in this section given
in Table 1.
In this
section, we shall evaluate the performance of two-dimensional MSC with PM Policy 1
(proposed PM) and two-dimensional with PM Policy 2.
4.1. Discussion of MSC 2D results with PM 1
Tables 2 and 3 show the results for low usage (y=0.9), comparing results with Schemes 1 and 2 and then results with Schemes 2 and 3. From Tables 2 and 3, we have the following findings. Increasing the parameter value of gives the same or increased availability for Schemes 1-3. This is expected because larger means higher reliability (this agrees with the result of Yeh and Chang (2007) for a 1D MSC case). The results with Scheme 2 always give higher availability values than Scheme 1. In addition, Scheme 2 also provides a lower total cost of up to 71.70% (see Table 2, for the parameter ) than the results of Scheme 1. The total cost is smaller because the PM Policy 1 improves reliability by optimizing (is not constant). Furthermore, Scheme 3 also provides an availability value that is as large as the results of Scheme 2. The advantage of Scheme 3 is that the total cost obtained is lower than the total cost with Schemes 1 and 2. Total maintenance costs can be reduced by up to 71.70% (see Table 2 on parameters ). Thus, the best optimization scheme for PM 1 policy is Scheme 3, and this pattern also holds for medium and high usage rates (Note: the results cannot be included due to the number of page limitations of a paper).
In this paper, a two-dimensional
Maintenance Service Contract (MSC) study is conducted with (1) periodic and (2)
non-periodic PM policies by considering availability performance measures and
total maintenance costs. The two-dimensional MSC with periodic PM policy
provides the best performance – in terms of availability (can guarantee an
availability target) and low total costs at any rate of usage considered. Here, a two-dimensional MSC study was
conducted from the agent's point of view. One of the further research topics is
a two-dimensional MSC study that takes into account the two parties- i.e., the
agent and the consumer, who are very concerned about the price of MSC. This
topic can be modeled by a game theory formulation and provides optimal results for
both parties. In addition, from an equipment maintenance perspective, MSC can
also consider condition-based preventive maintenance options so equipment
performance can be even better. Furthermore, as the maintenance services can be
provided by the Original Equipment Manufacturer (OEM) or the agent, another
interesting topic is to study a 2D MSC involving three parties– i.e., the
Original Equipment Manufacturer (OEM), the agent, and the consumer. The
integration of three-party decision problems is an interesting topic because it
can mathematically describe the relationship of competition or cooperation
between agents. The formulation can be done using two-level game theory and it
is expected to choose the optimal option for consumers as well as the optimal three-party
coordinated option. The findings will be very beneficial for the parties
involved with the following details: (i) the agent can achieve the availability
target with minimum total maintenance costs, and (ii) the consumer benefits
from the optimal target of equipment availability and MSC price to maximize
profit. Research on these topics is on the way.
The research and study were supported by the
Ministry of Research, Technology, and Higher Education (Kementrian Ristek-Dikti)
Indonesia through the Program Magister menuju Doktor untuk Sarjana Unggul (PMDSU).
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