# Development of a Decision Support Interface for Optimal Maintenance Scheduling in Food Manufacturing Industries

Nkemakonam Igbokwe

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## To cite this version:

Nkemakonam Igbokwe. Development of a Decision Support Interface for Optimal Maintenance Scheduling in Food Manufacturing Industries. Tertiary Trust Fund (TETFUND), Abuja, Nigeria; Nnamdi Azikiwe University, Awka, Nigeria. 2023. [hal-04348924](https://hal.science/hal-04348924v1).

HAL Id: hal-04348924

https://hal.science/hal-04348924v1

Submitted on 17 Dec 2023

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FINAL RESEARCH REPORT

ON

Development of a Decision Support Interface for Optimal Maintenance

Scheduling in Food Manufacturing Industries

NAU/TETFC/IBR/2022/VOL. IV/61

NNAMDI AZIKIWE UNIVERSITY, AWKA.

BY

ENGR. DR. NKEMAKONAM CHIDIEBUBE IGBOKWE (LEAD
RESEARCHER)

NOVEMBER 2023
Executive Summary

The importance of maintenance is ever increasing as a result of the widespread automation of manufacturing systems and the capital expenditure allocated to it, thus making maintenance of manufacturing equipment an investment opportunity to be maximized and not a cost center. The economic downturn continuously drives manufacturing organizations to seek for more efficient strategies to manage assets maintenance. Thus in this study a decision support system was developed and presented in this study, of which the aim is to develop a schedule for future maintenance actions for each manufacturing component that is repairable over the period time. This is obtained through the optimization of a bi-model-based multi-criteria optimization model. The developed system was validated using an industrial case study and it proved to be highly effective and less cumbersome in obtaining the optimal maintenance strategy from any manufacturing setting.
# Contents

<table><tr><td>Executive Summary</td><td>2</td></tr><tr><td>1.0 Background of the Study</td><td>5</td></tr><tr><td>1.1 Statement of the Problem</td><td>6</td></tr><tr><td>1.2 Research Aim and Objectives</td><td>6</td></tr><tr><td>1.3 Scope of Study</td><td>7</td></tr><tr><td>1.4 Significance of the Study</td><td>7</td></tr><tr><td>2.0 Materials</td><td>7</td></tr><tr><td>2.1.1 Data Collection</td><td>8</td></tr><tr><td>2.2 Validation Case Study</td><td>9</td></tr><tr><td>2.3 Collection, evaluation and categorization of relevant data from case study for the optimal maintenance strategy</td><td>13</td></tr><tr><td>2.4 Development of a decision support interface system</td><td>14</td></tr><tr><td>2.5 Ethical Consideration</td><td>15</td></tr><tr><td>3.0 Results and Discussions</td><td>15</td></tr><tr><td>3.1 Definition and identification of the variables, constraints and objectives for the optimal maintenance strategy</td><td>15</td></tr><tr><td>3.1.1 Maintenance Actions</td><td>16</td></tr><tr><td>3.1.2 Cost of Maintenance</td><td>17</td></tr><tr><td>3.1.3 System Reliability</td><td>20</td></tr><tr><td>3.2. Formulation and Development of Optimization Model for an Optimal Maintenance Strategy Based on Cost and Reliability</td><td>22</td></tr><tr><td>3.2.1 Optimization Algorithm Variables</td><td>24</td></tr><tr><td>3.2.2 Assumptions</td><td>25</td></tr><tr><td>3.3 Validation of the developed Optimization Model with an Industrial Application</td><td>27</td></tr><tr><td>3.4 Lingo Solver Computational Results</td><td>29</td></tr><tr><td>3.5 Development of a Decision Support Interface</td><td>37</td></tr><tr><td>3.5.1 General Considerations in User Interface Support Systems</td><td>37</td></tr><tr><td>3.5.2 System Development</td><td>38</td></tr><tr><td>3.5.3 Data Preparation</td><td>39</td></tr><tr><td>3.5.4 System Walk Through</td><td>39</td></tr><tr><td>4.0 Conclusions and Recommendations</td><td>44</td></tr><tr><td>4.1 Summary of Findings</td><td>44</td></tr><tr><td>4.2 Specific Conclusion</td><td>44</td></tr><tr><td>4.3 Achievement of Research Aim</td><td>45</td></tr></table>
<table><tr><td>4.4 Contribution to Knowledge</td><td>45</td></tr><tr><td>5.0 References</td><td>45</td></tr></table>
## 1.0 Background of the Study

The pressure on businesses and organizations to function in the most productive and cost-effective manner has intensified as a result of globalization. In all industries worldwide, maintenance optimization presents a chance for greater economic advantage and profit generation (Syan and Ramsoobag, 2019). Through optimization efforts, savings of 20-30% of the total operational cost have been attained (Regattieri et al., 2015).

Achieving high dependability in the context of manufacturing systems is essential and may be sought by putting in place appropriate maintenance plans, even taking into account its substantial effects on a company's competitiveness and cost-effectiveness (Pisacane et al., 2021). The importance of maintenance is ever increasing as a result of the widespread automation of manufacturing systems and the capital expenditure allocated to it, thus making maintenance of manufacturing equipment an investment opportunity to be maximized and not a cost centre (Horenbeek, Pintelon, and Muchiri, 2011). The economic downturn continuously drives manufacturing organizations to seek for more efficient strategies to manage assets maintenance.

According to Turuna Seecharan, Ashraf Labib (2016) the effective maintenance of assets is a vital strategic task given the increasing demand on sustained availability of those assets used for manufacturing. This is essential as sudden failures of manufacturing equipment can be prohibitively expensive because they result in immediate lost production outcome, inefficient quality characteristics and poor customer satisfaction. In the food manufacturing sector, asset maintenance is one of the most important essentials for an efficient manufacturing in the sector as this sector continuously face challenges that makes asset maintenance very critical due to the nature of manufacturing, as a result manufacturing companies in the sector must add or modify these assets to keep it running efficiently thus enhancing production. This is causing food manufacturers to invest more on manufacturing assets than any other manufacturing sector (Betts, 2018).

The main focus for food manufacturers is to improve efficiency and profitability through the reduction of total manufacturing costs by optimizing operation processes and maintenance activities achieved through continuously improved machine reliability and a hands-on maintenance culture. However, few manufacturers have the internal resources to implement such practical culture hence this research intends to contribute by developing an optimal maintenance method for improved cost and machine reliability in food manufacturing.
**1.1 Statement of the Problem**

In manufacturing, every sector faces its own individual problems or issues, but it can be said
that the food manufacturing sector face more stringent issues than any other sector because
their product is intended for human consumption, thus dealing with a wide range of
regulations regarding food safety and maintaining complex machineries and equipment so
that production is not affected to the detriment of the manufacturer. In other to stay
competitive, production lines are sometimes run 24 hours a day. Hence when manufacturing
equipment are not kept in good working condition, it can be prone to microbiological and
physical contamination. Debris from worn or broken parts can contaminate the production
line or even enter the product directly.

Furthermore, manufacturing equipment that do not meet operating parameter specifications
can impact product quality as well as safety. Critical goals or targets can be missed, processes
can be interrupted, and unwanted substances and chemicals can enter the production stream.
It is apparent that the maintenance team in any food manufacturing company has a lot to
handle under such conditions, and to maintain these highly automated systems and keep
equipment running optimally, food production and maintenance managers must stay on top of
new techniques. There is a need to research, provide ideas and adopt newer and better
maintenance strategies.

Trying to run such a sensitive system on reactive maintenance alone where components are left to fail
before repairs are carried out is detrimental as downtime would be disproportionately high and the
enterprise runs the risk of shortening the lifespan of their assets. Thus a proactive maintenance
strategy is the most straightforward way to improve overall maintenance operations that will keep
downtime and the associated stress of loss of revenue to the minimum.

**1.2 Research Aim and Objectives**

The aim of this study was to develop a decision support interface for optimal maintenance
scheduling in food manufacturing. This was achieved via the following specific objectives:

1. To collect, evaluate and categorize relevant data obtained from relevant industrial studies for the optimal maintenance scheduling.

2. To develop a multi-objective optimization model for an optimal maintenance scheduling based on cost and reliability.
3. To validate the developed optimization model with an industrial application.

4. To develop a user interface support system capable of providing an optimal maintenance schedule from the multi-objective optimization model developed in objective two.

## 1.3 Scope of Study

This study focused on maintenance and maintenance strategy, cost of maintenance and equipment reliability

The developed optimization model and programming execution codes were validated using the maintenance process at Tummy Tummy Foods Industry limited as an industrial applied case study.

## 1.4 Significance of the Study

An enhanced manufacturing system is key to sustaining the competitive nature of an economy. Thus it is crucial manufacturing systems in Nigeria continue to manufacture high quality products in an efficient and timely manner hence keeping the end user satisfied. Hence this study will be significant in the sense that it:

* Presented new multi-objective maintenance optimization and cost forecasting models for use in manufacturing systems

* Provided a basis for short and long term performance evaluation of maintenance management in manufacturing systems

* Contributed to the enhancement of knowledge in the academic world as well as in industrial practice.

## 2.0 Materials

The basic materials used in this study, comprise the data sets and the software tools for accomplishing statistical analysis, simulation and optimization techniques. Their nature and sources are described as follows:
### 2.1.1 Data Collection

Data used within this study is categorised under two data source, primary data source and secondary data source.

* **Primary data source:** Necessary data was collected for three years (2015 -2017) historical maintenance records (cost data, records of equipment faults and failures, and factory maintenance compliance sheet) and through twelve months' direct observation of manufacturing machines and maintenance activities at tummy tummy industries Limited.

* **Secondary data source:** data and information were obtained from the following sources:

* Academic thesis and dissertations, Journal publications and conference reports

* Research outputs and project reports.

* Published textbooks.

The use of this source was cost effective and provided a platform for building the foundation of this study and carrying out optimization analysis.

### 2.1.2 Software Packages for Data Analysis

The following software packages were used for data analysis in this study:

* Witness 14 Simulation software was used to develop and simulate a discrete event simulation of the maintenance process in this study.

* Lingo was used to test and solve the multi-objective algorithm.

* GaNetXL a decision support system generator for multi-objective optimization of spreadsheet based models by Savić, Bicik, and Morley (2011) was used to solve multi-objective optimization algorithm in the study. GANetXL uses genetic algorithms to solve complex optimization and search problems.

* Matlab was used to optimize the genetic algorithm fitness functions.

* Minitab software was used for statistical analysis and graphical representation.
## 2.2 Validation Case Study

The validation of this study was carried out in a food and beverage manufacturing company "Tummy Tummy Foods Industries limited" located at Chicason Drive, Umudim, Nnewi, Anambra State, Nigeria. The company was incorporated in December 2008 (with RC No: 793032.) as a manufacturer and marketer of Tummy-Tummy Instant Noodles for human consumption, with production starting in October 2009. The organisational structure is shown in figure 3.1. The production line is connected in series as illustrated in figure 3.2
<figure><img src="image_3.png" /><figcaption>Fig 2.1 Organizational Structure at Tummy Tummy Foods Industries Limited</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Figure 2.2: Illustration of the Production line**</figcaption></figure>

The line consists of the following components:

**Mixer:** Mixing and kneading occurs at this process, in which the mixing machine stirs up wheat flour and the mixing water. Normally 0.3-0.4kg of the mixing water at a temperature of 20-30°C is kneaded into the flour for 15-20 minutes. This process gives the dough textiform tissue that generates noodle's elasticity.

**Compounding machine:** The dough is put through two rotating rollers, which compounds two noodle belts into one single belt. This process helps distribute ingredients evenly. Occasionally the dough is left for a certain period of time to mature.

**Rollers:** With the help of pressing rollers, the 10mm thick noodles is flattened repeatedly using four rollers and finally becomes thin at 1mm thickness. This process strengthens the textiform tissue and gives elasticity to the noodles.

**Slitter machine:** After the rolling process, noodles are put into the slitter, where a rolling blade slits the noodle belt into thin noodles. Most of the instant noodles are wavy. Being pressed up and down gently, the noodles cut out by the slitter become wavy. The wavy-shape gives space in between noodles, which prevent the noodles from sticking together.

**Steamer:** Pregelatinization process occurs here in the steamer, where the instant noodles are steamed for one to five minutes.

**Dipping Bath:** The steamed noodles are dipped in seasoning.
**Flash Fryer:** dehydration process occurs here, most instant noodles are dehydrated either by oil-frying or air-drying.

**Fried noodles:** Noodles in a metal mold go through frying oil of 140-160°C for a minute or two. The moisture content of 30-40% in the dough is reduced to 3-6%, and pregelatinization is accelerated. Non-fried noodles: Noodles in a metal mold are placed into air-drier and dehydrated with hot air of approximately 80°C for more than 30 minutes. "Raw-type instant noodles" are the steamed noodles, which are sterilized with organic acid.

**Cooler:** After the dehydration process, the noodles, which are at 100°C, are cooled with air. This cooling process is followed by a series of careful inspection for weight, shape, color, dryness, frying condition, cooling temperature, etc.

**Casing:** The ready instant noodles are then put into firm bags or containers as required along with the garnish and seasonings and then sealed with aluminium foils.

The company runs a computerized manufacturing process for the manufacturing and processing of noodles for human consumption and adopts corrective maintenance as its preferred maintenance strategy only, which can be described as a reactive, firefighting strategy. The information obtained from the maintenance team of the organisation was that most faults and failures can be fixed manually by the maintenance team in a relatively short period of time. But, there have been incidents and occasions where breakdowns resulted in long unavailability of the manufacturing physical assets. Also observed was the effect of faults and failures on the manufacturing process as depicted in figure 3.1.
<figure><img src="image_5.png" /><figcaption>Fig 2.3: Faults/Failures and implications</figcaption></figure>

Source: Igbokwe and Godwin, (2021)

The implications observed are in contradiction of the maintenance goals and objectives of the organization which is that in the long run maintenance should ensure equipment availability in order to produce products at the compulsory quantity and quality levels.

## 2.3 Collection, evaluation and categorization of relevant data from case study for the optimal maintenance strategy.

In order to develop the optimal maintenance strategy, it is necessary to define and identify key essential attributes for the method. The flowchart in figure 3.2 describes the process by which it was achieved.
<figure><img src="image_6.png" /><figcaption>**Fig 2.4:** Flowchart for collection, evaluation and categorization of relevant data from case study for the optimal maintenance strategy</figcaption></figure>

**2.4 Development of a decision support interface system**

A decision support interface system was developed through the following steps:
<figure><img src="image_7.png" /><figcaption>Fig 2.5: User interface support system development flowchart</figcaption></figure>

**2.5 Ethical Consideration**

The following considerations were upheld during the study:

* The participating manufacturing firm was informed of the purpose and expected benefits of this research study.

* The participating manufacturing firm was offered the choice to indicate whether they would like to receive a report about this research study upon conclusion. A contact detail was provided.

**3.0 Results and Discussions**

**3.1 Definition and identification of the variables, constraints and objectives for the optimal maintenance strategy.**

The goal is to develop a schedule for future maintenance actions for each manufacturing component that is repairable over the period T, where T is the length of the planning scope. The length of planning scope is subsequently divided into J separate intervals of length during which at the end of each interval $\frac{T}{J}$, either preventive maintenance, corrective
maintenance action is carried out, or nothing is done. Thus three strategic maintenance schedule are proposed for a multi-component system of N components over T time periods, has N x 3^T possible maintenance schedules. It is assumed that at the end of each interval, the activities (Preventive or corrective actions) carried on each of the components will have a positive effect on the age and the rate of occurrence of failure of the components.

An assumption is made in this study that if preventive maintenance is performed on any component, the effective age of the component is reduced by 30% thus the age reduction factor of preventive maintenance on a component i ($\alpha_{pmi}$) is assigned a fixed value of 0.7.

To account for the changes in age and rate of failure and if the initial age for each component is equal to zero, let $X_{i,j}$ represent the effective age of component i at the start of period j and $XX_{i,j}$ represent the effective age of component i at the end of period j, then:

$$XX_{i,j} = X_{i,j} + \frac{T}{j} \quad \text{For } i=1,...,N; j=1,...,T \quad (3.1)$$

### 3.1.1 Maintenance Actions

In a scenario where maintenance action is carried out on component i at the end of period j and the preventive maintenance action effectively reduces the age of the component i for the start of the next period then:

$$X_{i,j+1} = \alpha_{pmi} \times X_{i,j} \quad \text{For } i = 1, ..., N; j = 1, ..., T \text{ and } (0 \le \alpha_{pmi} \le 1) \quad (3.2)$$

$\alpha_{pmi}$ indicates the effects of maintenance on the component i thus if $\alpha_{pmi} = 0$ the maintenance action improved the component i to a state of "good-as-new" and if $\alpha_{pmi} = 1$ maintenance action has no effect, and the component i remains in a state of "bad-as-old".

If at the end of period j component i is replaced with another new component, and the component is returned to a state of "good-as-new" then:

$$X_{i,j+1} = 0 \quad \text{For } i = 1, ..., N; j = 1, ..., T \quad (3.3)$$

If no action takes place at the end of period j and the rate of occurrence of failure of component i remains the same as that of the previous period, then:
$$ XX_{i,} = X_{i,j + T/J} \quad \text{for } i = 1, \dots, N; j = 1, \dots, T \quad (3.4) $$

$$ X_{i,j+1} = XX_{i,j} \quad \text{for } i = 1, \dots, N; j = 1, \dots, T \quad (3.5) $$

### 3.1.2 Cost of Maintenance

The model developed by Igbokwe and Godwin, (2022) was adopted in this study. Taking into account that any maintenance or replacement action that is carried out is associated with cost, the cost of maintenance or replacement of component i at the end of period j include the total sum of failure cost, cost of preventive maintenance, cost of replacement of component and downtime cost.

To calculate for failure cost, the expected number of failures for component i in period j is calculated and multiplied by the cost of failure for component i

$$ FC_i = F_i \times [N_{i,}] \quad \text{for } i = 1, \dots, N; j = 1, \dots, T \quad (3.6) $$

Where

$F_i$ = cost of failure for component i

$[N_{i,j}]$ = expected number of failures for component i in period j

From equation 3.6

$$ [N_{i,j}] = \int_{x_{i,j}}^{x_{i,j}} u_i(t) dt \quad \text{for } i = 1, \dots, N; j = 1, \dots, T \quad (3.7) $$

$$ E[N_{i,j}] = \int_{x_{i,j}}^{x_{i,j}} \lambda_i \beta_i t^{\lambda_i - 1} dt = \lambda_i [(xx_{i,j})^{\beta_i} - (x_{i,j})] \quad \text{for } i = 1, \dots, N; j = 1, \dots, T \quad (3.8) $$

Therefore $FC_i$

$$ FC_i = F_i \times \lambda_i [(xx_{i,j})^{\beta_i} - (x_{i,j})] \quad \text{for } i = 1, \dots, N; j = 1, \dots, T \quad (3.9) $$

Cost of preventive maintenance $PMC_i$ refers to the cost incurred while component i is maintained. It includes cost of consumables (CCC$_i$), cost of condition based maintenance (CCBM$_i$), and cost of time based maintenance (CTBM$_i$). Where cost of consumables includes the cost of consumable material and equipment used while carrying out preventive
maintenance activities such as cost of lubricating oil (CLOij), cost of component wires (CCWij), cost of replacement vital parts (screw nuts, belts etc) (CRVPij), cost lubricating grease (CLGi). The cost of condition based maintenance includes cost of inspections (CIij), cost of diagnostic actions (CDAij), travel cost (CTij), labour cost (CLij) and cost of delayed production (CDPij). While cost of time based maintenance includes the cost of preventive oil change (CPOCij), cost of equipment material change (CEMCij).

Thus $PMC_i = CLO_{ij} + CCW_{ij} + CRVP_{ij} + CLG_{ij} + CI_{ij} + CDA_{ij} + CT_{ij} + CL_{ij} + CDP_{ij} + CPOC_{ij} + CEMC_{ij}$

$$CPOC_{ij} + CEMC_{ij} \quad \text{for } i = 1... N; j = 1,..., T \quad (3.10)$$

Where $CCC_{ij} = CLO_{ij} + CCW_{ij} + CRVP_{ij} + CLG_{ij}$

$$CCBM_{ij} = CI_{ij} + CDA_{ij} + CT_{ij} + CL_{ij} + CDP_{ij}$$

$$CTBM_{ij} = CPOC_{ij} + CEMC_{ij}$$

Thus $PMC_i = CCC_{ij} + CCBM_{ij} + CTBM_{ij}$ for $i = 1... N; j = 1,..., T$ (3.11)

Where $PMC_i = PMC_{ij}$ for $i = 1... N; j = 1,..., T$ (3.12)

$$\text{Where } PMC_{ij} = \begin{cases} 1 & \text{maintained at } j \\ 0 & \text{Otherwise} \end{cases}$$

Cost of corrective maintenance of component i is the cost $CRC_i$ incurred when component i is replaced at the end of period j with a new component i. It includes cost of diagnostic actions, Cost of repair actions, Cost and equipment hire and travel expenses, labour cost and administrative cost.

Thus $CMC_i = CDA_{ij} + CRA_{ij} + CEH_{ij} + TEC_{ij} + LC_{ij} + AC_{ij}$

$$\text{for } i = 1... N; j = 1,..., T \quad (3.13)$$

$$CMC_i = CMC_{ij} \quad \text{for } i = 1... N; j = 1,..., T \quad (3.14)$$

$$\text{Where } CMC_{ij} = \begin{cases} 1 & \text{replaced at } j \\ 0 & \text{Otherwise} \end{cases}$$

The cost of downtime of the manufacturing system $DC_{ij}$ is the cost lost when component i is maintained or replaced at period j
$$DC = DT \times PL \qquad (3.15)$$

Where

DT: Average duration for downtime

PL: estimated profit loss per month by the company due to downtime.

For a multi-component manufacturing system, the main issue is to find the optimal maintenance strategy for each component independent of the other components. For example, while the manufacturing system is shut down to carry out an appropriate maintenance action on one component, it may make sense to go ahead and perform preventive maintenance corrective maintenance of some other components, even if they are not at their individual optimum point where maintenance actions would have ordinarily be performed.

Thus from the definitions of each types of cost, the total cost of maintenance is the sum of all the cost defined for component *i* at period *j* and is expressed as follows:

Total Maintenance cost =

$$\sum_{i=1}^{N} \sum_{j=1}^{T} \left\{ F_i \times \lambda_i \left[ (XX_{i,j})^{\beta_i} - (X_{i,j})^{\beta_i} \right] + CLO_{ij} + CCW_{ij} + CRVP_{ij} + CLG_{ij} + CI_{ij} + CDA_{ij} + CT_{ij} + CL_{ij} + CDP_{ij} + CPOC_{ij} + CEMC_{ij} + CDA_{ij} + CRA_{ij} + CEH_{ij} + TEC_{ij} + LC_{ij} + AC_{ij} \right\} + \sum_{j=1}^{T} \left[ DC \left( 1 - (PMC_{ij} + CMC_{ij}) \right) \right]$$

$$\text{for } i = 1 \dots N; j = 1, \dots, T \qquad (3.16)$$

This objective function calculates for the total cost of maintenance as a summation of component costs in each period based on any preventive maintenance or corrective maintenance cost, the system downtime cost, and the cost of the expected number of unexpected failures.
### 3.1.3 System Reliability

Based on the failure time reliability distributions and system configuration, the system reliability is a function of probability of operating without failure over the planning scope. That is the probability of surviving component *i* to the end of period *j* given survival to the start of period *j*. Four reliability distribution models are used in modelling reliability (weibull, lognormal, exponential and normal) in this study, in conjunction with series and parallel system configurations

For weibull distributed failure times, the reliability of the system at the end of period *j* is as

$$R_j = e^{-\lambda t^\beta}$$

$$\text{Where } t = ((xx_{i,j}) - (x_{i,j}))$$

Thus *Rseries* is

$$R_j = \prod_{i=1}^{N} e^{-[\lambda_i [(xx_{i,j})^{\beta_i} - (x_{i,j})^{\beta_i}]]}$$

And *Rparallel* is

$$R_p = 1 - (1 - R_j)^N$$

$$R_p = 1 - (1 - \prod_{i=1}^{N} e^{-[\lambda_i [(xx_{i,j})^{\beta_i} - (x_{i,j})^{\beta_i}]]})^N$$

$$\text{for } i = 1... N; j = 1,..., T \qquad (3.17)$$

For exponential distributed failure times, the reliability of the system at the end of period *j* is as

$$R_j = e^{-\lambda t}$$

$$\text{Where } t = ((xx_{i,j}) - (x_{i,j}))$$

Thus *Rseries* is
$$R_j = \prod_{i=1}^{N} e^{-[\lambda_i [(xx_{i,j}) - (x_{i,j})]]}$$

And $R_{\text{parallel}}$ is

$$R_p = 1 - (1 - R_j)^N$$

$$R_p = 1 - \left(1 - \prod_{i=1}^{N} e^{-[\lambda_i [(xx_{i,j}) - (x_{i,j})]]}\right)^N$$

$$\text{for } i = 1... N; j = 1,..., T \quad (3.18)$$

For normal distributed failure times, the reliability of the system at the end of period $j$ is as

$$R_j = \int_t^\infty f(x)dx$$

$$R_j = \int_t^\infty \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(t - \frac{\mu}{\sigma}\right)^2} dx$$

Where $t = ((xx_{i,j}) - (x_{i,j}))$

$\mu$ = Mean of normal time to failure

$\sigma$ = standard deviation of times to failure

Thus $R_{\text{parallel}}$ is

$$R_p = 1 - (1 - R_j)^N$$

$$= 1 - \left(1 - \left(\int_t^\infty \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(t - \frac{\mu}{\sigma}\right)^2} dx\right)\right)^N$$

$$\text{for } i = 1... N; j = 1,..., T \quad (3.19)$$

For lognormal distributed failure times, the reliability of the system at the end of period $j$ is as

$$R_j = \int_t^\infty f(x)dx$$

$$R_j = \int_{\ln(t)}^\infty \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(t - \frac{\mu}{\sigma}\right)^2} dx$$
Where $t = ((xx_{i,j}) - (x_{i,j}))$

$\mu$ = Mean of normal time to failure

$\sigma$ = standard deviation of times to failure

Thus $R_{\text{parallel}}$ is

$$R_p = 1 - (1 - R_j)^N$$

$$= 1 - \left(1 - \left(\int_{\ln(t)}^{\infty} \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(t - \frac{\mu}{\sigma}\right)^2} dx\right)\right)^N$$

$$\text{for } i = 1... N; j = 1,..., T \qquad (3.20)$$

The reliability of the system is measured at an instant. Case in point, the reliability of the system would be the reliability at the end of every period.

## 3.2. Formulation and Development of Optimization Model for an Optimal Maintenance Strategy Based on Cost and Reliability

The parameters, decision variables, cost functions and reliability equations have been defined, the optimization algorithm is presented as a multi-objective mixed integer non linear program optimization problem to minimize total maintenance cost and maximize system reliability:

### Minimize Total maintenance cost

$$= \sum_{i=1}^{N} \sum_{j=1}^{T} \left\{ F_i \times \lambda_i \left[ (xx_{i,j})^{\beta_i} - (x_{i,j})^{\beta_i} \right] + CLO_{ij} + CCW_{ij} + CRVP_{ij} + CLG_{ij} + CI_{ij} + CDA_{ij} + CT_{ij} + CL_{ij} + CDP_{ij} + CPOC_{ij} + CEMC_{ij} + CDA_{ij} + CRA_{ij} + CEH_{ij} + TEC_{ij} + LC_{ij} + AC_{ij} \right\} + \sum_{j=1}^{T} \left[ DC(1 - (PMC_{ij} + CMC_{ij})) \right]$$

### Maximize Reliability

Weibull distributed:
$$
\begin{align*}
&= \prod_{i=1}^{N} e^{-[\lambda_i [(xx_{i,j})^{\beta_i} - (x_{i,j})^{\beta_i}]]} \\
&= 1 - (1 - \prod_{i=1}^{N} e^{-[\lambda_i [(xx_{i,j})^{\beta_i} - (x_{i,j})^{\beta_i}]]})^N
\end{align*}
$$

Exponential distributed

$$
\begin{align*}
&= \prod_{i=1}^{N} e^{-[\lambda_i [(xx_{i,j}) - (x_{i,j})]]} \\
&= 1 - (1 - \prod_{i=1}^{N} e^{-[\lambda_i [(xx_{i,j}) - (x_{i,j})]]})^N
\end{align*}
$$

Normal distributed

$$
\begin{align*}
&= \int_{t}^{\infty} \frac{1}{\sigma} \sqrt{2\pi} e^{-\frac{1}{2} \left(\frac{t-\mu}{\sigma}\right)^2} dx \\
&= 1 - \left(1 - \left(\int_{t}^{\infty} \frac{1}{\sigma} \sqrt{2\pi} e^{-\frac{1}{2} \left(\frac{t-\mu}{\sigma}\right)^2} dx\right)\right)^N
\end{align*}
$$

Lognormal distributed

$$
\begin{align*}
&= \int_{\text{In}(t)}^{\infty} \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(t-\frac{\mu}{\sigma}\right)^2} dx \\
&= 1 - \left(1 - \left(\int_{\text{In}(t)}^{\infty} \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(t-\frac{\mu}{\sigma}\right)^2} dx\right)\right)^N
\end{align*}
$$

Subject to

$$
X_{i,j} = 0 \qquad \text{For } i = 1, \dots, N; j = 1, \dots, T
$$

$$
XX_{i,j} = X_{i,j} + \frac{T}{j} \qquad \text{For } i = 1, \dots, N; j = 1, \dots, T
$$

$$
PMC_{ij} + CMC_{ij} \le 1 \qquad \text{For } i = 1, \dots, N; j = 1, \dots, T
$$
$PMC_{ij}, CMC_{ij} = 0 \text{ or } 1$

For $i = 1, ..., N; j = 1, ..., T$

$$X_{ij} = (1 - PMC_{ij-1})(1-CMC_{ij-1})XX_{ij-1} + PMC_{ij-1}(\alpha_{pmi} \times XX_{ij-1})$$

For $i = 1, ..., N; j = 1, ..., T$

(3.21)

The first constraint indicated that the initial age of each component is zero,

The second constraint accounts for the changes in age thus representing the effective age of component $i$ at the end of period $j$.

The third to fifth constraint specifies that if a component is replaced with another new component then $X_{i,j} = 0$, $CRC_{ij} = 1$, $PMC_{ij} = 0$. If a component is maintained then $CRC_{ij} = 0$, $PMC_{ij} = 1$.

### 3.2.1 Optimization Algorithm Variables

A representation of the optimization algorithm variables is presented as follows:

* N: Number of Components

* T: Length of Planning Scope

* J: Number of Periodic Intervals

* λ: Scale Parameter

* β: Shape Parameter

* μ: Mean

* σ: Standard Deviation

* $X_{i,j}$: Effective age of component $i$ at the start of period $j$

* $XX_{i,j}$: Effective age of component $i$ at the end of period $j$

* $\alpha_{pmi}$: Age reduction factor of preventive maintenance on component $i$
*Fi*: Failure cost of component *i*

*PMCi*: Cost of preventive maintenance on component *i*

*CMCi*: Cost of Corrective maintenance on component *i*

*DC*: Downtime cost

### 3.2.2 Assumptions

In this section, a number of assumptions are presented and motivated in order to arrive at an optimal strategy formulation for the optimization problem in which the objective is to minimise the total cost of maintenance and to maximise the system-wide reliability. Some of these assumptions are aimed at decreasing the complexity of the problem, thereby making it possible to solve the algorithm efficiently. The optimization complexity is, however, decreased in such a manner so as not to generate maintenance schedules that are unrealistic or unfit for use in practice.

1. Number of Manufacturing Components: A number of components are required to produce an end product in a manufacturing system. Failure of any one of these components typically causes the manufacturing process to be interrupted until the component has been repaired or replaced. Therefore, a failure in one of the components of the manufacturing system typically leads to failure of the entire manufacturing system. For optimization purposes, all the components of a manufacturing system are considered as a whole in the sense that when the manufacturing system is shut down to carry out an appropriate maintenance action on one component, it may make sense to go ahead and perform preventive maintenance corrective maintenance of some other components, even if they are not at their individual optimum point where maintenance actions would have ordinarily been performed.

2. Frequency of Maintenance: A number of maintenance actions will be carried out on the manufacturing components, including complete overhaul due to corrective maintenance as opposed to just carrying out preventive maintenance. However, the duration of each maintenance activity, which will vary from one component to the other is outside the scope of this study.
3. Reliability after Maintenance: when maintenance is performed on any manufacturing components, the goal is to increase the reliability of the manufacturing component to as good as new or to the state it was operating before maintenance was performed on it. In this study it is assumed that after performing maintenance and the component is back into operation, the component's reliability will improve to as good as new or to a state it was operating before.

4. Effect of Maintenance on manufacturing component: in this study, it is assumed that any maintenance action or strategy has a positive effect on the manufacturing component. Thus based on Eygelaar (2018), any preventive maintenance actions carried out reduces the effective age of the manufacturing component by 30% while corrective maintenance results into the component to be as good as new.

5. Resources required for maintenance: in a realistic manufacturing environment, many resources are required to perform effective maintenance on manufacturing component. These resources include maintenance personnel, finance, spare parts inventory, logistics etc. An optimization algorithm containing all resources is expected to be very complex, hence for the purpose of this study, it is assumed that resources such as maintenance personnel and finance is the required resources to carry out maintenance activities. This is not an unrealistic assumption as the optimization algorithm in this study is expected to produce a schedule for maintenance strategies for the period of thirty six months, meaning that it will be known beforehand that the maintenance of any particular component will occur at a certain period within the scheduling window, thus provisions can be made well in advance of each maintenance active to ensure that the spare parts and maintenance equipment required are indeed available and that all logistics are appropriately taken care of.

6. Independence of component's failure: it is assumed in this study that failures that occur in a manufacturing system are independent of one another. Hence if a component is taken out of operation due to a failure it is assumed to have little or no effect on the timing of failures of the other components in the manufacturing system.

7. Failure rates of manufacturing components: it is assumed in this study that the failure rates of individual components follow a typical bathtub curve, hence the reliability model incorporated within the optimization algorithm if formulated for components through the different stages.

8. Nature of manufacturing components: within the realm of reliability theory, two main systems prevail, namely repairable systems and non-repairable systems. It is assumed
in this study that components in a manufacturing system are repairable system. In a
scenario where the manufacturing system has both repairable and non-repairable
systems, the optimization algorithm form this study is formulated for repairable
systems.

## 3.3 Validation of the developed Optimization Model with an Industrial Application

The optimization model presented in equation 4.21 is a mixed integer non-linear programming optimization problem. The optimization model was solved using Lingo software.

technique is used to find an optimum solution to the problem using the industrial applied
scenario. Data used for this analysis is presented in table 3.1:

The programming language codes written in lingo platform are developed for executing the
optimization algorithms in lingo and are as follows:
<table><caption>Table 3.1: Data for Optimization Analysis</caption><tr><td>T</td><td colspan="9">36 months (3 years)</td></tr><tr><td>DC</td><td colspan="9">₦ 197,561</td></tr><tr><td>N</td><td>Component</td><td>Shape (β)</td><td>Scale (λ)</td><td>Mean (μ)</td><td>Standard Deviation (σ)</td><td>α<sub>pmi</sub></td><td>Failure Cost</td><td>Preventive Maintenance Cost</td><td>Corrective Maintenance Cost</td></tr><tr><td>1</td><td>Conveyor System</td><td>1.5855</td><td>3396.50</td><td>2976.03</td><td>1920.25</td><td>0.7</td><td>₦ 884,210</td><td>₦ 387,450</td><td>₦ 496,760</td></tr><tr><td>2</td><td>Mixer system</td><td>1.7610</td><td>3375.42</td><td>3005.13</td><td>2741.21</td><td>0.7</td><td>₦ 366,415</td><td>₦ 93,855</td><td>₦ 272,560</td></tr><tr><td>3</td><td>Roller system</td><td>1.7397</td><td>3254.14</td><td>2899.20</td><td>1718.89</td><td>0.7</td><td>₦ 430,680</td><td>₦ 92,680</td><td>₦ 338,000</td></tr><tr><td>4</td><td>Slitter</td><td>1.7123</td><td>3252.65</td><td>2900.75</td><td>1744.82</td><td>0.7</td><td>₦ 513,322</td><td>₦ 99,500</td><td>₦ 413,822</td></tr><tr><td>5</td><td>Compounding Machine</td><td>1.6852</td><td>3170.13</td><td>2830.25</td><td>1727.30</td><td>0.7</td><td>₦ 618,685</td><td>₦ 231,685</td><td>₦ 387,000</td></tr></table>
## 3.4 Lingo Solver Computational Results

Data from the industrial case was applied to the optimization model developed was programmed into lingo 17.0 software and combined with excel solver for an optimal solution. It took approximately 8 hours 42mins on a 2.13 GHz processor to solve the optimization problem for each scenario within the planning scope with 710 variables of which 360 are integer variables and 532 constraints, of which 177 are non-linear. The objective function of the optimal solution is ₦7, 593,578 for which 50% reliability is achieved in the manufacturing system. The achieved reliability of 50% is a product of the reliability of the system at the end of each period and the result is shown in Table 3.2 and the Pareto optimal front is presented in Figure 3.1. The computational programing codes are presented in appendix b. The optimal maintenance strategy for the manufacturing components is as follows:
<table><caption>Table 3.2: Optimal Maintenance Method for Lingo (Cost = ₦7, 593,578, Reliability = 50%)</caption><thead><tr><th colspan="36">MONTHLY SCHEDULE</th></tr></thead><tbody><tr><td>N</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td>10</td><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16</td><td>17</td><td>18</td><td>19</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>25</td><td>26</td><td>27</td><td>28</td><td>29</td><td>30</td><td>31</td><td>32</td><td>33</td><td>34</td><td>35</td><td>36</td></tr><tr><td>1</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>P</td><td>C</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>C</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>C</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>P</td></tr><tr><td>2</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>C</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>C</td><td>-</td><td>-</td><td>-</td><td>-</td><td>C</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td></tr><tr><td>3</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>P</td><td>C</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>C</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>P</td></tr><tr><td>4</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>P</td><td>C</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>C</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>C</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>P</td></tr><tr><td>5</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>C</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>C</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>-</td><td>P</td><td>-</td><td>-</td><td>-</td><td>P</td></tr></tbody></table>

KEY: N = Number of Components; 1 = Conveyor System; 2 = Mixer System; 3 = Roller System; 4 = Slitter System; 5= Compounding Machine;

P: Preventive Maintenance; C: Corrective Maintenance
Table 3.2 presents the maintenance schedule generated by lingo 17, of which a combination of three maintenance strategies is presented for each component in the manufacturing system, 1) Preventive Maintenance, 2) Corrective Maintenance and 3) A period whereby nothing is done. The optimal strategy provides an optimal cost solution of ₦7, 593,578 for which 50% reliability is achieved.

Table 3.3 shows the reliability optimal solutions with associated cost. Each solution presents an optimal maintenance schedule and 50% was selected for example to show the optimal schedule as presented in table 4.4.2.

The system reliability for each period for the RR of 50% is shown in Figure 3.1

<table><caption>**Table 3.3: Lingo Reliability Optimal Solutions**</caption><thead><tr><td>Reliability</td><td>Cost</td></tr></thead><tbody><tr><td>10%</td><td>3,612,769</td></tr><tr><td>20%</td><td>4,839,280</td></tr><tr><td>30%</td><td>5,722,900</td></tr><tr><td>40%</td><td>6,900,431</td></tr><tr><td>50%</td><td>7,593,578</td></tr><tr><td>60%</td><td>8,832,608</td></tr><tr><td>70%</td><td>9,264,333</td></tr><tr><td>80%</td><td>10,480,991</td></tr><tr><td>90%</td><td>11,980,000</td></tr></tbody></table>
<figure><img src="image_8.png" /><figcaption>**Fig 3.1: System Reliability for Lingo/Excel Solver (Cost = ₦7, 593,578, Reliability = 50%)**</figcaption></figure>

The system reliability in figure 3.1 shows that the reliability of the system lies between 94% and 99.7% over the defined planning period of 36 months with average reliability over the planning period being 97.2%. The significant drop at period 6 and 28 is as a result of lack of adequate maintenance action in 4 and 3 consecutive periods.

<figure><img src="image_9.png" /><figcaption>**Fig 3.2: Lingo Optimal Fronts for Reliability**</figcaption></figure>
From the optimal maintenance strategy one can analyze the effective age of each component. This could be used to track the effective age of the components and then utilize the information to initiate additional monitoring activities. For example, after a component reaches a certain level of effective age, additional monitoring, tests or inspections might be warranted to assist in the detection of imminent failure. Figures 3.3, 3.4, 3.5, 3.6 and 3.7

<figure><img src="image_10.png" /><figcaption>Fig 3.3: Lingo Optimal Maintenance strategy effect on Conveyor System</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig 3.4: Lingo Optimal Maintenance strategy effect on Mixer System</figcaption></figure>

<figure><img src="image_12.png" /></figure>
<figure><img src="image_13.png" /><figcaption>Fig 3.6: Lingo Optimal Maintenance strategy effect on Slitter System</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig 3.7: Optimal Maintenance strategy effect on Compounding Machine</figcaption></figure>

From figures 3.3, 3.4, 3.5, 3.6 and 3.7, one can notice that the minimum age of each component at the beginning of the planning schedule is zero, and that most component undergoes corrective maintenance at a certain point in the planning schedule, thus making the average age of the component to be in the range of 0 months to 14 months as summarised in table 3.4.

<table><thead><tr><td>Components</td><td>Minimum Effective Age (Month)</td><td>Maximum Effective Age (Month)</td></tr></thead><tbody><tr><td>1</td><td>0</td><td>5</td></tr><tr><td>2</td><td>0</td><td>12</td></tr><tr><td>3</td><td>0</td><td>11.7</td></tr></tbody></table>
<table><caption>Table 3.4: Effective Age of Component with Lingo Solution Output</caption><tr><td>4</td><td>0</td><td>11.7</td></tr><tr><td>5</td><td>0</td><td>14</td></tr></table>

Another observation is the effect of failure rate on the number of scheduled maintenance, for example when one compares component 1 and 5, it can be observed that component 1 has more scheduled maintenance actions than component 5. This explains the variation in effective ages of the component as component one has higher failure rate than component 5. Thus it is necessary that component 1 receives more attention.

## 3.5 Development of a Decision Support Interface

The models proposed in equation 3.21 of this dissertation are implemented within a newly propose3d computerised user interface support tool aimed at facilitating maintenance strategy decisions. The design of this tool is described in detail as follows:

### 3.5.1 General Considerations in User Interface Support Systems

A user interface support system is a computerised information system that may be employed to support employees of companies with business and organisational decision making activities. Typically, such systems compiles useful information useful information, which is presented to the user, by analysing raw data and documents in order to identify or solve complex problems. The user interface support system developed in this study consists of three main components namely:

* The database: developed to allow input data to be stored in a structure manner.

* A graphical user interface: developed to ensure effective human-computer interaction, thus enabling the user the means of providing the required input and obtaining relevant output.
* A model base: the workhorse of the system, implementing one of the solution techniques developed in the study to provide the relevant output.

An illustration of the interaction between the three components is described in figure 3.6.1.

<figure><img src="image_15.png" /><figcaption>Fig 3.6.1: A Graphical Overview of the User Support System.</figcaption></figure>

### 3.5.2 System Development

The software environment within which the user interface support system was developed by this study is a framework supported by RStudio called Shiny. Shiny is an application framework used to construct elegant and powerful applications displaying interactive reports and data visualisations based in R. The framework Shiny was adopted in the development of the user interface support system in this study due to its ability to create elegant GUIs capable of changing dynamically, based on R script files.
### 3.5.3 Data Preparation

In order to standardise the procedures of the user interface support system, the required input data have to be prepared in a specific format before the user interface support system can be utilised. The system requires one user-specified input file, containing maintenance cost information, information on the age reduction factor and information of reliability parameters. The format required of the file for the system is a comma separated values (CSV) format. An example of the exact required input data required is shown in figure 3.6.2.

<figure><img src="image_16.png" /><figcaption>Fig 3.6.2: Required Input Format of the Specifications of a Manufacturing System</figcaption></figure>

### 3.5.4 System Walk Through

After having prepared the required input data in the specified format, as described in the previous section, the user interface support system can be utilised to recommend optimal maintenance strategies for the manufacturing system specified. Once the user interface support system is initialised, the user is presented with the "Home screen" shown in Figure 3.6.3. On this screen, a short introduction to the user interface support system is provided to the user, as well as the steps to be followed in order to utilise the user interface support system to its full potential. After the instructions have been read and understood, the user can navigate to the "System specifications" window on the left-hand side of the screen, which displays the window seen in Figure 3.6.4. The user may, however, navigate back to the "Instructions" window at any subsequent time if some of the instructions have to be reviewed. In the "System specifications" window, the user can input the input requirement specifications in the format specified above.
<figure><img src="image_17.png" /><figcaption>Fig 3.5.3: The “Home screen” presented to the user when the system is initialised</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig 3.5.4: GUI through which the user can upload the input specifications</figcaption></figure>

Once the user uploads the specified input data in the required format, the system generated an overview of the data uploaded, and if the user is satisfied with the data uploaded, he can click on the “save” button which will upload the specifications to the system database. This is illustrated in figures 3.5.5 and 3.5.6.
<figure><img src="image_19.png" /><figcaption>Fig 3.5.5: An Overview of the Specified System Specification</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig 3.5.6: An Overview of the Specified System Specification database upload</figcaption></figure>

After the input specifications have been uploaded successfully the next step is to indicate the
algorithm specifications for the model. In the algorithm specification window as shown in figure
3.5.7, the user is required to specify the objective functions and other requirements of the genetic
algorithm. This includes the desired maintenance objective functions (selected by clicking on the
radio buttons associated with the objective functions), the number of generations and population size (selected by moving the slider to the associated value), and other required parameters associated to the probability of selection, crossover and mutation (selected by choosing values from the dropdown list).

<figure><img src="image_21.png" /><figcaption>Fig 3.5.7: The Algorithm Specification Window</figcaption></figure>

Once the user is satisfied with the selected objective function, and the genetic algorithm parameter values, he/she can click on the solve button. Clicking this button will execute the genetic algorithm and the user interface support system will subsequently be occupied, solving the model. The duration for which the user interface support system may be occupied, depends on various factors such as Central Processing Unit rating, number of generation and population size.

Once the algorithm has found a solution (when the status window disappears), the solutions which includes an optimal schedule, optimal pareto fronts and system reliability will be saved in a comma separated values files through which the user can access the solutions in the user's personal computer.
## 4.0 Conclusions and Recommendations

Conclusions drawn with regard to this study are presented in this chapter. It begins with the summary of the findings, specific conclusions from the study, followed by a discussion on the contribution of this research to both theory and practice is presented. This is followed by an evaluation with the objectives. In the end recommendations for further research are made.

## 4.1 Summary of Findings

The findings from the present research are discussed in details in this chapter.

An optimal maintenance strategy for improved cost and machine reliability in food manufacturing was developed in this study. This strategy is expected to be useful as a decision support tool to obtain optimal cost and machine reliability through an efficient maintenance strategy in food manufacturing and any other manufacturing sectors.

The optimal strategy was obtained through the optimization of a mixed integer nonlinear multi-objective programming model presented in equation (3.21), to minimize total maintenance cost and maximize system reliability. The programming model was validated using an industrial case study at a food manufacturing company, Tummy Tummy Industries Limited.

## 4.2 Specific Conclusion

* Maintenance of manufacturing components can be improved using reliability parameters and cost of those components.

* For the strategy to be effective, input data needs to be as exact as possible. Therefore, there is a need for manufacturing companies to ensure that failure history and cost of maintenance/ replacement of every component are properly documented to ensure accurate reliability prediction and cost forecasting.

* The impact of various maintenance strategies determines the behaviour of the method. If the impact of the selected strategy on reliability is low, the algorithm allows more
replacements to occur to keep reliability high, and therefore this factor must be calculated
carefully.

4.3 Achievement of Research Aim

The purpose of this research was to develop an optimal maintenance strategy for improved cost and machine reliability. This aim has been achieved. In chapter 4, an optimization model that was based on improved cost and machine reliability was developed. The output of this model was a maintenance schedule that can be used to achieve a specific reliability at an optimum cost. An attempt was also made to illustrate the effect of the optimal maintenance strategy has on the age to the manufacturing components.

4.4 Contribution to Knowledge

* A multi-objective optimization model was developed, the optimization model was successfully validated with an industrial case study, can contribute to the field of maintenance management in food manufacturing. The model, although considered for the food manufacturing environment, can also be easily modified to suit any other multi-component system.

* The optimal maintenance schedule outputs from the multi-objective optimization model can be used to control cost and reliability of manufacturing components at an efficient level.

* Lingo and matlab codes for the execution of the multi-objective optimization model based on cost and reliability were also presented in this study.

* A Generic User Interface Support System was developed in this study and presented so that it can be employed to support employees of companies with business and organisational decision making activities.

**5.0 References**

Betts, H. (2018) *Equipment Maintenance : Food Manufacturing 's Secret Ingredient*.

Eygelaar, J. (2018) *Generator maintenance scheduling based on the expected capability of*
*satisfying energy demand*. Stellenbosch University.

Horenbeek, A. Van, Pintelon, L. and Muchiri, P. (2011) ‘Maintenance optimization models and criteria’, 1(3), pp. 189–200. Available at: https://doi.org/10.1007/s13198-011-0045-x.

Igbokwe, N. and Godwin, H. (2022) ‘Cost Effective Maintenance and Machine Reliability for Food Manufacturing Industries using Optimal Maintenance Strategy’, *Archives of Current Research International*, 22(8), pp. 27–34. Available at: https://doi.org/10.9734/ACRI/2022/v22i8543.

Igbokwe, N.C. and Godwin, H.C. (2021) ‘Maintenance Performance Evaluation and Downtime Analysis of Manufacturing Equipment in a Food Manufacturing Company’, *Journal of Engineering Research and Reports*, 20(11), pp. 100–107. Available at: https://doi.org/10.9734/jerr/2021/v20i1117413.

Pisacane, O. et al. (2021) ‘Data-driven predictive maintenance policy based on multi-objective optimization approaches for the component repairing problem’, *Engineering Optimization*, 53(10), pp. 1752–1771. Available at: https://doi.org/10.1080/0305215X.2020.1823381.

Regattieri, A. et al. (2015) ‘An innovative method to optimize the maintenance policies in an aircraft: General framework and case study’, *Journal of Air Transport Management*, 44–45, pp. 8–20. Available at: https://doi.org/10.1016/j.jairtraman.2015.02.001.

Savić, D.A., Bicik, J. and Morley, M.S. (2011) ‘A DSS generator for multiobjective optimization of spreadsheet based models’, *Environmental Modelling and Software*, 26(5), pp. 551–561.

Syan, C.S. and Ramsoobag, G. (2019) ‘Maintenance applications of multi-criteria optimization: A review’, *Reliability Engineering and System Safety*, 190(November 2018), p. 106520. Available at: https://doi.org/10.1016/j.ress.2019.106520.

Turuna Seecharan, Ashraf Labib, A.J. (2016) ‘Journal of Quality in Maintenance Engineering Maintenance Strategies: Decision Making Grid vs. Jack-Knife Diagram Abstract’, *Journal of Quality in Maintenance Engineering*, 23(6), pp. 1–31.