Multiobjective Optimization of Aircraft Maintenance in Thailand Using Goal Programming: A Decision-Support Model

The purpose of this paper is to develop the multiobjective optimization model in order to evaluate suppliers for aircraft maintenance tasks, using goal programming. The authors have developed a two-step process. The model will firstly be used as a decision-support tool for managing demand, by using aircraft and flight schedules to evaluate and generate aircraft-maintenance requirements, including spare-part lists. Secondly, they develop a multiobjective optimization model by minimizing cost, minimizing lead time, and maximizing the quality under various constraints in the model. Finally, the model is implemented in the actual airline’s case.


Introduction
With severe competition and under the current global uncertainty, airlines have to generate new strategies in order to enhance their competitive advantages in the current marketplace 1-4 . Currently, an individual airline mainly focuses on its existing business function, while impacts from supply chain efficiency have been neglected. Consequently, the aviation supply chain management is not well understood and effectively implemented like other industries for example, automobiles, electronics, and so forth 5 . Thus, the effective management of the aviation supply chain must be considered 6 . Major findings show that there is information about new trends in the aviation supply chain that correlate with existing problems 7 . The supply chain in aircraft maintenance includes the flow of materials or services from many suppliers through airline maintenance 8 . The airline must fulfill air travelling demand as committed to in their flight schedule.
The supply chain in Thai Aviation starts from the aircraft owner requesting services to commercial maintenance centers or internal maintenance department. The maintenance manager buys the materials or outsources services from overseas suppliers. There are more

Literature Review
There are several studies in performance measurement methods in the aviation supply chain 8,11 . Most of them used a single factor to measure their systems. However, in a practical environment, the system composes several important factors, which relate to an enterprise's success. The authors specify key factors in aircraft maintenance to be cost, time, quality, reliability, maintainability, availability, and flexibility or replace ability.

Cost
The cost is the primary factor of firms, especially in a highly competitive industry. Researchers mention unsatisfactory global sourcing costs 12 . Airline operations directly affect the costs of the products or services and their purchase price. These costs are generated directly or Advances in Decision Sciences 3 indirectly from the supply chain. Consequently, higher costs and prices decrease airline competitiveness 13 . Choy et al. studied the costs of aircraft parts and developed a performance measurement system to monitor the effectiveness of the logistics flow in handling various components for rework, maintenance or replacement, and benchmark with the best-in-class practice 8 . However, the process analysis or cost-reduction strategy provides insights into the inefficiencies which exist within current processes and place more emphasis on demand pulltype processes which require forecasting operational schedules 14 .
Nevertheless, aircraft fuel is the most important issue to airlines cash flow. It is the highest operating cost portion 26.5% of the total cost 3 . Airlines separately manage fuel cost and maintenance. Aircraft climb technique results in a 5 per cent fuel saving 15 . Thai Airways International tries to manage high fuel price risk by hedging, but they are not successful 16 . Other airlines in Thailand face a fuel crisis and share the risk with passengers under a fuel surcharge.

Times
Time refers to maintenance time and material procurement lead time. Maintenance time is the job-processing time since the service was requested by a customer up to completely fulfilling that requirement 11, 17 . Procurement lead time begins from an order issued until the part's arrival at the promised location 18 . Lead times include transport time, custom clearance time, and other unexpected delays. Moreover, the supplier relationship possibly affects procurement lead time 19 .
Chen studied the minimization of completion time, subject to maintenance and the proposed integer linear programming model 20 . This model only applies to jobs performed in a serial fashion, but in aircraft maintenance, practical operations are continuously performed in both parallel and serial fashions.

Quality
Aircraft parts must be manufactured by factories, which are officially approved by the civil aviation organization of the state. Also, inspection, repair, altering, or overhauls of aircraft parts must performed by an approved factory 21 . The worldwide-accredited auditors are the Federal Aviation Administration FAA and the European Aviation Safety Agency EASA . The Department of Civil Aviation DCA of Thailand is also an approved auditor for repairing factories, which are located in Thailand 22 . On the other hand, the quality of aircraft maintenance is related to approval organization. Airlines trust FAA/EASA-certified repair stations as top quality and DCA-certified repair station as lower quality. However, both FAA/EASA and DCA are acceptable as explained in ICAO annex 6 23 .

Reliability
Langford explained the meaning of reliability as "the probability that a system will perform its intended function for a specified interval under stated conditions" 11 and expressed as an equation as follows:  where R t probability that the system will successfully preform as required over the interval of time t. λ failure rate 1/mean time between failures MTBF , t specified operation interval. e 2.7182818. Figure 1, the longer mean time between failures MTBF results in higher reliability. In order to increase aircraft reliability, maintenance managers must reduce aircraft downtime due to maintenance, which is related to aircraft-part-procurement lead time and repairing time 11 .
The failure rate dictates the frequency of unscheduled corrective maintenance or repair of a system affected by random malfunction. Low reliability indicates frequent failures, which trigger more frequent corrective maintenance. Consequently, the reliability can be improved by enhancing maintenance support in forms of facilities, skilled technicians, tools, and supporting stocks of spare components, and repair parts 24 . Increased system reliability based on high-quality components can greatly extend the intervals of operation between failures and eliminate or minimize corrective maintenance support requirements 25 .

Maintainability
The maintainability measures ability of a system to be restored to a specified level of operational readiness within defined intervals with the use of the aforementioned facility, and equipment resources 11, 26 . The maintainability, ii , is related to scheduled and unscheduled maintenance. The minimization of related factors time, procurement lead time, corrective/preventive time results in maximization of maintainability.
Advances in Decision Sciences 5 where M mean active maintenance time, λ corrective maintenance frequency, M ct mean time between corrective maintenance, f pt schedule maintenance frequency, and M pt mean preventive maintenance time.
Maintainability refers to ease and speed at which any maintenance activity can be carried out on any equipment. Maintenance can be measured by mean time to repair MTTR 27 . It is a function of equipment design, and maintenance task design including use of appropriate tools, jigs, work platforms, and so forth 28 . Once a piece of equipment has failed, it must be possible to get it back into an operating condition as soon as possible 11 .

Availability
Availability measures the readiness of a system to fulfill its assigned function 29 . Airlines try to obtain high utilization to maximize their income. The aircraft must be available before next scheduled flight; otherwise, the flight delay may be costly 30 . Maintenance managers must predict unforeseen troubles and preplan materials, skilled technicians, and facilities 31 . They seek possible solutions for minimizing aircraft-maintenance times which results in maximized availability 32 . Thus, aircraft availability relates to flight hours per period. Higher flight hours lower ground time results in higher availability.

Flexibility/Replace Ability
Operation managers frequently experience problems of material shortage or malfunction of equipment. Flexibility is an ability of production plant or service provider by which he switches the planned operation to another process or solution to meet the customer expectation 33 .
Supply chain flexibility is an ability to reconfigure the supply chain and alter the supply of product in line with customer demand 34 . It is composed of two dimensions: 1 resource flexibility refers to a resource that can be applied to a range of alternative uses with low costs and low difficulties are associated with the switching from one resource to another as well as a short time is required for the switch 35 , 2 coordination flexibility is a flexibility of process that redefines product strategies in reconfiguring the chain of resources to produce the product, and re-deploy those resources needed to produce the product 36, 37 . In this research, the three factors of aircraft maintenance cost, aircraft downtime, and quality are considered, since the reliability, maintainability, and availability relate to aircraft downtimes in an adverse direction. On the other hand, flexibility, and replace ability relate to the choice of alteration, material sources, or outsource maintenance centers. In the next section, the authors formulate an optimization aircraft maintenance model by using these three factors.

Multiobjective Optimization Model
In order to formulate the model, an aircraft supply chain is first explained. The supply chain of an aircraft can be illustrated as Figure 2. The suppliers deliver materials or maintenance services to an airline. Later, the airline delivers services to passengers, tour agencies, and 6  air cargo agencies with a promised quantity and specified time. The airline must prepare its aircraft with effective and efficient maintenance 38 . Back office has to plan future maintenances, which conform to a flight plan. The manager must make a decision whether to insource or outsource maintenance services as well as material suppliers in advance.

Advances in Decision Sciences
These activities need powerful and impacting decision tools for aircraft maintenance and relevant supply chain. The planner has to survey aircraft flying requirements and  transform them to a flight plan, which indicates exactly the aircraft registration number and flight schedule. Then, the planner reviews the aircraft maintenance planning data along with the aircraft use. The results provide the maintenance scope of works and an individual maintenance schedule. The next process is the resource preparation for future inspection. There are different types of inspection for example, A-check aircraft inspection 600 flight hours interval and C-Check aircraft inspection 6000 flight hours interval . The aircraft maintenance plan can be depicted in Figure 3.

Advances in Decision Sciences
The quality of aircraft parts must be high realized, which conform to an aviation organization's certificate. In this research, quality is classified as follows: i the value of OEM original equipment manufacturer equals 4; ii FAA Federal Aviation Administration or EASA European Aviation Safety Agency equals 3; iii Thai DCA Department of Civil Aviation equals 2; iv other state aviation organizations approval equal 1; v the Bogus part no accepted document or cannibalized part equal 0.
The Airlines should accept at least Thai DCA approval quality. The mathematical model is formulated for maintenance planning decision support in preparation of the material sources. Figure 3 illustrates an Aircraft Maintenance Planning Document APMD issued by an aircraft manufacturer. The manual declares inspection, service, and repair procedures in several intervals related to flight hours. The airline must perform A-check every 600 flight hours and C-Check in every 6,000 flight hours the different aircraft models may have different intervals . Each check includes several task cards, which indicate manpower, tools, materials, and procedures. The maintenance manager must prepare internal capability economically. The airline hires external services for any checks that are cheaper than investing their own capability. The aircraft material procurement process is separated from man powers and tools. The manager surveys material suppliers and approves them. The aircraft part procurement criteria are prices, lead time, and quality. The mathematical model of multiobjective optimization can be formulated as follows: There are three binary decision variables which are valued 0 and 1. The X ij represent a decision of buying the material. It equals "1" when the manager chooses buy and "0" otherwise. The Y ij represents a decision of loaning the material. It equals "1" when the manager chooses loan and "0" otherwise. The Z ij represents a decision of repairing the material. It equals "1" when the manager chooses repair and "0" otherwise. The a ij , b ij , and c ij represent a sell price, loan price, and repair price of material respectively. The d ij , e ij , and f ij represent a lead time of buying material, a lead time of loan material, and a lead time of repairing material consecutively. The p ij , q ij , and r ij represent a quality value of buying material, a quality value of loan material, and quality value of repairing material. The values of material's qualities are scored by referring to the certificate of approval of the factory issued by an aviation organization as follows: 1 the Bogus part no certificate 0; 2 the other state aviation organization approval 1; 3 the Thai DCA 2, FAA or EASA 3; the OEM 4 .

Constraints
Constraint 3.5 ensures that each task card chooses at least one choice. If the system chooses loan, it must choose a repair constraint 3.6 . In normal repair, repair price of the item should not higher 85% of current buying price. If it is higher than 85%, maintenance manager mostly chooses buying constraint 3.7 . Technically, the quality of purchasing items should be higher than repairing in overall constraint 3.8 . Flexible and replaceable channels of material sources are loan and repair but it should receive spare parts at least thirty days faster constraint 3.9 . Decision variables are binary Constraints 3.10 -3.12 . Constraint 3.13 ensures that parameters are not negative.

Solution Algorithm
In this research, goal programming is used to solve multiobjective optimization. The problem will be solved by generating decision variables as follows: There are six decision variables which are: 1 an underachievement deviation from the minimum total cost; 2 an overachievement deviation from the minimum total cost; 3 an underachievement deviation from the minimum total lead time; 4 an overachievement deviation from the minimum total lead time; 5 an underachievement deviation from the minimum total quality; 6 an overachievement deviation from the minimum total quality.

Variables
TC total cost of a single minimized object 1 TLT total lead time of a single minimized object 2 TQ total quality of a single maximized object 3 The equation 4.1 is a single-objective optimization from a previous problem. After solving 4.1 using the X-press program of cost optimization, total cost is 58,418,000 US dollars.
The equation 4.2 is a single-objective optimization from a previous problem. Solving 4.2 using the X-press program of time optimization, total lead time is 151,000 days.
The equation 4.3 is a single-objective optimization from a previous problem. Solving 4.3 using the X-press program of quality optimization, the total quality is 57,670 points.
This problem can be formulated as a linear goal programming model. The new objective function minimizes the sum of undesirable deviations. In goal programming, a specific numeric goal is established for each goal function constraint , and then a solution is derived that minimizes the weighted sum of deviations of these goal functions from their respective goals.

Objective Function
where, d 1 , d 2 , and d − 3 are the overachievement and underachievement deviations from the goals.

Case Study
The AAA airline in Thailand flies from Bangkok to Chiang Mai, Phuket, Udon Thani, and other airports, which are two-hour flights. The AAA airline maintenance manager plans five years' maintenance of 15 aircraft with 10,000 spare-part requirements. He must indicate the upcoming aircraft scheduled maintenance with service centers and suppliers. The mathematical algorithms are used in AAA airline's case. The different lead time deviations and different quality deviations are used on each solving. The results are cost deviations. Each solution is shown in each row of Tables 1, 2, and 3. The minimum-cost solutions do not meet the minimum lead time and the maximum quality. Then, the authors apply 154,500 deviations to the total time and −25,000 deviations to quality. Therefore, the solution is 107,810 higher costs as shown in Table 1 Row 1. The first solutions are 58,525,810 total material costs, 154,500 total waiting days, and 32,671 total quality points. For the second row, the total lead time is changed to 3,400 deviate days and −25,000 deviate qualities. The result is a higher total cost than row 1 s solution. The testing changes several lead time deviations. This table illustrates fifteen different parameter sets which result in different cost deviations. Then, it is concluded that the shorter lead time produces higher cost at the same quality level.    The maintenance manager may tradeoff between reducing the waiting time and higher material expenses. In practical exercise, the AAA airline generates average income at US$33,000 per day. Thus, the maintenance manager can make technical decisions to overpay aircraft recovery up to US$16,500 50% from income to reduce a single AOG Aircraft on ground day. Table 2 shows the results as an average 2.84 quality points and different lead time periods. This table illustrates thirteen different parameter sets which result in different cost deviations. However, the trend of data is similar to Table 1. It is only different in longer lead time at equal prices. Thus, the maintenance manager can use the data from two tables for making decisions among expected quality, lead time, and increasing/decreasing prices. In Table 2, if the maintenance manager aims to increase material's average quality, he must pay higher material costs. Furthermore, if he wants shorter procurement lead time, it will result in higher material expenses, which indicate in Table 2. Table 3 shows the results under a higher average quality and different lead time periods compare with Table 2 . This table illustrates nine different parameter sets which result in different cost deviations. The AAA airline maintenance manager confirms that these results are valid by reviewing empirical results with their operational records. Therefore, the data from Tables 1, 2, and 3 are created in a single chart, which is used for comparisons between total cost, total lead time, and average quality. Figure 4 shows a graphical comparison of Tables 1, 2, and 3. The high total cost at an early stage produces shorter lead time with a high negative slope. Each point on the three curves explains three objective dimensions: cost, lead time, and quality. Line B represents when airlines increase average quality, they pay a higher cost for the same lead time in order to buy, repair, or loan higher-quality aircraft parts. The arrow position points are the limit points to increase costs for a shorter time. It is not worth to pay a higher price for a small reduction of time beyond the arrows.
The solutions of the multiobjective optimization are not only three factors beneficial but also reliability, availability, and maintainability. Meanwhile, the material lead time is shorter, it reduces the aircraft downtime, which results in a shorter mean time to repair higher maintainability , the longer MTBF higher reliability , and the higher availability of the aircraft. The solutions are beneficial to the airlines that aim to fulfill travelling demand. The cost minimization results in lower airfare. Hence, the airlines gain a higher competitive advantage. The time minimization results in a higher flight time. Then, there are higher available flight hours of the airlines in responding to the market demand. Thus, this model is beneficial to the airlines on competitive advantage.

Conclusions
A multiobjective optimization using goal programming is particularly useful to aircraft maintenance organizations in simultaneous reduction of cost and aircraft downtime, as well as for increasing quality. Also, it is valuable to the improvement of supplier flexibility/replace ability, aircraft availability, and aircraft reliability. For airlines in Thailand, the results of the model with AAA airline's data are used as a decision-support strategy of multi-factors in aircraft maintenance, which generates the best solution among 7.8 × 10 5 possible solutions.
There are six contributions in this paper. First, the mathematic model supports the commercial aviation industry or the military aircraft fleet in survival under limited cost or certain budgets in Thailand by developing the supply chain. Second, this research illustrates the critical factors to aviation performance measurement. Third, the model assists the aircraft maintenance manager in decision support of resources selection. Fourth, the airline maintenance manager could develop the mathematical algorithm in their maintenance to optimize relative benchmarking and continue their best operation to enhance their competitive advantage. Fifth, the outcome of this research can be applied in aircraft operational risk management. Finally, it is beneficial to future research in performance analysis of other industries for example, ship, train, truck, and so forth.
However, aircraft fuel price is a vital factor that is related to operating costs and this needs to be carefully watched, thus future research may review and add the fuel cost factor into the optimization model.