3.6 Numerical experience

To clarify how the proposed algorithm works, the following example is given. Consider an integrating problem with parameters as follows: number of parts q = 300 units, the setup time between batches s = 30 min, unit processing time of part t = 20 min, the length of the preventive maintenance time tPM = 60 min = 1/μ (constant), the shape parameter of Weibull distribution β = 1.69, and scale parameter α = 2857.14, constant repair rate μ = 1/60, common due date d = 10000.00, the unit inventory holding cost of finished parts c1 = US\$ 0.20 per unit per minute, the unit inventory holding cost of in-process parts c2 = US\$ 0.10 per unit per minute, the unit cost of PM cPM = US\$ 30.00, unit setup cost cs = US\$ 3.00, probability of defect part on in-control state p1 = 0.00, probability of defect part on out-of-control state p2 = 0.30, unit rework cost per unit part for nonconforming parts cw = US \$100.00, and unit corrective maintenance cost cr = US\$ 120.00.

The computational steps to solve the problem are the followings.

Step-1. Yields α = 2,857.14.

Step-2. Yields 30 + 20 x 300 = 6,030.00 ≤10,000.00 is met, then the problem is feasible.

Step-3.Yields g = 3 and Nk = 125, k = 1, 2, 3.

Step-4. Yields R = 1, 2, 3.

Step-5 to Step-21, for R = 1, yield the best solution TC[1]\* = 201,313.00.

1st looping

Step-5 to Step-21, for R = 2, yield the best solution TC[2]\* = 201,124.80. 2nd looping

Step-5 to Step-21, for R = 3, yield the best solution TC[3]\* = 201,158.80.

Step-23. Yields a set of the best solutions for R = 1, 2, 3 as a set of {TC[1]\*,TC[2]\*, TC[3]\*} = {201,313.00, 201,124.80, 201,158.80}.

Step-24. Yields a minimal TC = min {201,313.00, 201,124.80, 201,158.80} =

201,124.80 that occurs in two production runs with two PMs.

Step-25. Yield the complete solution as shown in Table 1 and Figure 6.

## 3.7 Conclusion

This chapter proposes a model of integrating batch scheduling and maintenance scheduling by criterion of minimization in holding cost, setup cost, PM cost, rework cost, and restoration cost (CM). The criterion of scheduling used is the minimization of the total actual flow time. The first preventive maintenance (PM) scheduling policy (from the direction of due date) is made precisely on due date. The second PM and so on would be done before the time of first deterioration according to Weibull ROCOF cumulative function.

production schedule, estimate the number of nonconforming parts and total restoration (CM). Next, compute estimated rework cost and estimated restoration cost, and then compute total cost. This step is done for two batches and so on until an increase on total cost is found. Write the best total cost for one production run and one PM. This process is carried out for two production runs with two PMs until the best total cost is found for two production runs with two PMs. Continue the process until g production runs with g PMs. The best solution of algorithm is a minimization

L½ � ikk Q½ � ikk B½ � ikk BPM[k] CPM[k] TC[2]\* L½ � 11 1 42.46 9150.77 BPM[1] = 10000.00 CPM[1] = 10060.00 201124.80

Integrated Batch Production and Maintenance Scheduling to Minimize Total Production…

L½ � 101 1 15.46 3937.69 BPM[2] = 3847.69 CPM[2] = 3907.69

L½ � 21 1 39.46 8331.54 L½ � 31 1 36.46 7572.31 L½ � 41 1 33.46 6873.08 L½ � 51 1 30.46 6233.85 L½ � 61 1 27.46 5654.62 L½ � 71 1 24.46 5135.39 L½ � 81 1 21.46 4676.15 L½ � 91 1 18.46 4276.92

DOI: http://dx.doi.org/10.5772/intechopen.85004

L½ � 12 2 6.46 3718.46 L½ � 22 2 3.46 3619.23 L½ � 32 2 0.46 3580.00

Best schedule for the example.

Table 1.

Figure 6.

41

The model makes a trade-off in the following two things. An increase in the number of batch (length of production run) up to a certain limit will minimize the

of all of the best total cost for k = 1, 2, …, g.

Gantt chart of the best solution for the example.

In the model developed, searching for a solution begins with problem resolving without involving restoration cost (CM) and rework cost for nonconforming part. It begins with one batch in one production run and one PM. After finding a

Integrated Batch Production and Maintenance Scheduling to Minimize Total Production… DOI: http://dx.doi.org/10.5772/intechopen.85004

Table 1. Best schedule for the example.

Min {TC[R], R = 1, 2, …, g}. Go to Step-25.

\$100.00, and unit corrective maintenance cost cr = US\$ 120.00.

Step-3.Yields g = 3 and Nk = 125, k = 1, 2, 3.

TC[3]\*} = {201,313.00, 201,124.80, 201,158.80}.

The computational steps to solve the problem are the followings.

Step-5 to Step-21, for R = 1, yield the best solution TC[1]\* = 201,313.00.

Step-5 to Step-21, for R = 2, yield the best solution TC[2]\* = 201,124.80.

Step-5 to Step-21, for R = 3, yield the best solution TC[3]\* = 201,158.80.

Step-25. Yield the complete solution as shown in Table 1 and Figure 6.

201,124.80 that occurs in two production runs with two PMs.

Step-2. Yields 30 + 20 x 300 = 6,030.00 ≤10,000.00 is met, then the problem is

Step-23. Yields a set of the best solutions for R = 1, 2, 3 as a set of {TC[1]\*,TC[2]\*,

This chapter proposes a model of integrating batch scheduling and maintenance scheduling by criterion of minimization in holding cost, setup cost, PM cost, rework cost, and restoration cost (CM). The criterion of scheduling used is the minimization of the total actual flow time. The first preventive maintenance (PM) scheduling policy (from the direction of due date) is made precisely on due date. The second PM and so on would be done before the time of first deterioration according to

In the model developed, searching for a solution begins with problem resolving without involving restoration cost (CM) and rework cost for nonconforming part. It

begins with one batch in one production run and one PM. After finding a

Step-24. Yields a minimal TC = min {201,313.00, 201,124.80, 201,158.80} =

To clarify how the proposed algorithm works, the following example is given. Consider an integrating problem with parameters as follows: number of parts q = 300 units, the setup time between batches s = 30 min, unit processing time of part t = 20 min, the length of the preventive maintenance time tPM = 60 min = 1/μ (constant), the shape parameter of Weibull distribution β = 1.69, and scale parameter α = 2857.14, constant repair rate μ = 1/60, common due date d = 10000.00, the unit inventory holding cost of finished parts c1 = US\$ 0.20 per unit per minute, the unit inventory holding cost of in-process parts c2 = US\$ 0.10 per unit per minute, the unit cost of PM cPM = US\$ 30.00, unit setup cost cs = US\$ 3.00, probability of defect part on in-control state p1 = 0.00, probability of defect part on out-of-control state p2 = 0.30, unit rework cost per unit part for nonconforming parts cw = US

Step 22. Observe whether R = g

3.6 Numerical experience

Industrial Engineering

Step-1. Yields α = 2,857.14.

Step-4. Yields R = 1, 2, 3.

Weibull ROCOF cumulative function.

feasible.

1st looping

2nd looping

3.7 Conclusion

40

Step-25. Write all values of decision variables.

Step 23. Write {TC[R], R = 1, 2, …, g}. Step-24. The minimal solution is

Figure 6. Gantt chart of the best solution for the example.

production schedule, estimate the number of nonconforming parts and total restoration (CM). Next, compute estimated rework cost and estimated restoration cost, and then compute total cost. This step is done for two batches and so on until an increase on total cost is found. Write the best total cost for one production run and one PM. This process is carried out for two production runs with two PMs until the best total cost is found for two production runs with two PMs. Continue the process until g production runs with g PMs. The best solution of algorithm is a minimization of all of the best total cost for k = 1, 2, …, g.

The model makes a trade-off in the following two things. An increase in the number of batch (length of production run) up to a certain limit will minimize the

### Industrial Engineering

total inventory holding cost. Meanwhile, an increase in the length of production run will imply on an increase in the number of nonconforming parts and in a number of restoration (CM).

References

33:185-195

[1] Dobson G, Karmarkar US, dan Rummel JL. Batching to minimize flow times on one machine. Management

DOI: http://dx.doi.org/10.5772/intechopen.85004

Integrated Batch Production and Maintenance Scheduling to Minimize Total Production…

[8] Jiang RY, Murthy DNP. Maintenance Decision Models for Management. Beijing: Science Press; 2008

[2] Dobson G, Karmarkar US, dan Rummel JL. Batching to minimize flow times on heterogeneous machines. Management Science. 1989;35:607-613

[4] Zahedi Z, Ari Samadhi TMA, Suprayogi S, Halim AH. Integrated batch production and maintenance scheduling for multiple items processed on a deteriorating machine to minimize total production and maintenance costs with due date constraint. International Journal of Industrial Engineering Computations. 2016;7(2):229-240

[5] Zahedi R, Yusriski R. Stepwise optimization for model of integrated batch production and maintenance scheduling for single item processed on flow shop with two machines in JIT environment. In: Presented in ICCSCI Bali, 13–15 Oct 2017. Procedia Computer

Science. 2017;116:408-420

ijiec.2018.7.001

43

[6] Zahedi Z, Salim A, Yusriski R, Haris H. Optimization of integrated batch production and maintenance scheduling on flow shop with two machines. International Journal of Industrial Engineering Computations (IJIEC). 2019;10(2):225-238. DOI: 10.5267/j.

[7] Daellenbach HG, McNickle DC. Management Science, Decision Making Through Systems Thinking. New York,

USA: Palgrave Macmillan; 2005

[3] Halim AH, Ohta H. Batch scheduling problems to minimize inventory cost in the shop with both receiving and delivery just in times. International Journal of Production Economics. 1994;

Science. 1987;33:784-799

For readers who want to learn more about the integration of batch production and machine maintenance scheduling, they can read Zahedi et al. [4–6].


**3.1** *Citrus exocortis viroid* **(CEVd)**

In 1948, this disease is showed with bark scaling on the rootstock of citrus trees grafted on trifoliate orange (*Poncirus trifoliata*) that is reported by Roistacher (1988) [5, 38, 51].

The agent of this disease is different. These are the smallest pathogen among the pathogenic agents of plants that are known. Usually, they have no coated protein and their body are circular. Their genome is single-stranded RNA [5, 7, 25] and they do not translate. Usually, they have between 246 and 399 or 400 nucleotides [6, 8, 9].

This viroid belongs to the *Pospiviroidae* family, the *Pospiviroid* genus. Members of this family have a rod-like or quasi-rod-like secondary structure with five structural domains (terminal left, pathogenic, central, variable, and terminal right) and a central conserved region (CCR) within the central domain (C). they do an asymmetric rolling-circle pathway for replication which occurs in the nucleus [5, 7, 8].

The significant symptoms that are caused by this viroid are bark scaling and cracking, general decline, decreased size and stunting, and leaf epinasty and cracks in the petiole (**Figure 4**) [10, 19]. This viroid can infect various kinds of citrus cultivars like *P. trifoliata* and its hybrids, rangpur lime (*Citrus limonia*), lemon (*C. limon*), and citron (*C. medica*) [10].

This agent of the disease is the same as viruses and is transmitted by grafting and infected trimming and cutting instruments [10].

### **3.2 Cachexia or xyloporosis (***Hop stunt viroid* **(HSVd))**

This disease was shown in 1950 on Parson's Special mandarin [19] and is reported by Roistacher (1983) [53]. This viroid the same as exocortis belongs to the *Pospiviroidae* family but in the classification, its genus is different and placed in the *Hostuviroid* genus. Because of a specific 6-nucleotide motif located in the Variable (V) domain of *Hop stunt viroid* that is responsible for the induction of cachexia symptoms in cachexia-sensitive hosts, this viroid was placed in the group [24, 38, 51]. In fact, those nucleotides express the symptom of *Citrus cachexia viroid* because the variable domain is responsible for pathogenicity [38]. The secondary structure of this viroid is a rod-like structure with five domains, a "central conserved region" (CCR) and a "terminal conserved hairpin" (TCH). The variable domain located at the Right of the central conserved region and basis on two strains is introduced. "pathogenic strains" that show cachexia symptoms in sensitive hosts, and "non-pathogenic strains" that infect the same sensitive hosts without inducing symptoms. Six nucleotides in this region show different symptoms. At the left of the central conserved domain is the pathogenicity domain that is responsible induce symptoms in sensitive hosts [24, 53].

The symptom of this disease includes discoloration, gumming, and browning of phloem tissue, wood pitting, and bark cracking [6, 19, 24, 38, 51, 53, 54]. If you remove the outer bark layers, you can see the discoloration of the bark. As a result, infected trees are stunted and chlorotic, and may decline and die [53]. The

#### **Figure 4.**

*Symptoms of* Citrus exocortis viroid *(a) decline of plant, (b) leaf epinasty as seen on grafting infected scion on Etrog citron rootstock, indicator host of CEVd, (c) bark scaling in the United States. Sources: Roy et al. [52].*

sensitive citrus cultivars are alemow (*Citrus macrophylla* Webster), clementines (*C. clementina* Hort. Ex. Tan), mandarins (*C. reticulata* Blanco), satsumas (*C. unshiu* (Macf.) Marc.), "Rangpur" lime (*C. limonia* Osb.), kumquats (*Fortunella* spp.), and hybrids like tangelos that if they can be infected, you will see the severe symptoms (**Figure 5**) [24].


*2.6. Water Productivity*

Two water productivity indices were calculated to compare the efficiency of irrigation water use and actual ET, using Equations (4) and (5):

$$\text{Irrigation water productivity (IWP)} = \frac{\text{Alf} \text{al } \text{dry matter}}{\text{Irrigation water applied}} \tag{4}$$

$$\text{Evaporation-Spin water productivity (ETWP)} = \frac{Afalfa \, dry \, matter}{ETa} \tag{5}$$

where the unit of alfalfa dry matter is kg ha−1, and the units of irrigation water applied and ETa are mm.


**3. Results and discussion**

*Trace Metals in the Environment - New Approaches and Recent Advances*

**Element Ppm** Au 45.93 Pd 1.92 Pt 0.005 Ce 81.79 Nd 56.97 La 51.89 Yb 33.35 Tb 25 Ge 9 Ga 2.5 Sm 1.75 Er 0.9 Eu 0.35

dilution factor. With this, all the elements fell in a range of concentration below 1 ppm for the case of Au, Ce, Nd, L, Tb, Ge, and Yb. For the rest of the elements, a direct sample was taken using standards between 1 and 5 ppm (without dilution).

*Chemical composition of the leaching liquors of the SEDEX mineral, done by ICP.*

The analytical methods used for the characterizations of the different mineral used to the ion exchange stage were characterized by dry granulometric analysis using a standard sieves (Tyler series); X-ray diffraction using an INEL equinox 2000 equipment was located at the Autonomous University of the State of Hidalgo (AUSH), and the spectra was obtained with a Cu Kα1 radiation of wave length of 1.50056 Å, a voltage of 30 kV, an intensity of 20 mA, and a sweep speed of 22 θ/ min, which were then treated with the software MATH to identify the mineral spe-

Then, to determine the chemical composition of standard solutions and leached liquors (before and after ion exchange), an inductively coupled plasma spectrophotometer (ICP-OES) Perkin Elmer brand/model 2100 located at the AUSH was used. In the same way, scanning electron microscopy (SEM) was used to determine morphology and particle type of minerals, using a JEOL brand microscope model JMS6300, having an Energy Dispersive Spectrometer of X-ray (EDS) for chemical microanalysis and also located at the AUSH. And finally, X-ray fluorescence (XRF) was executed to determine the chemical composition of minerals before and after the ion exchange procedure, and for this analysis, a portable spectrophotometer of X-ray brand BRUKER, model S1 TITAN was used, also using the GeoChem calibration software (equipment located at the National Autonomous University of Mexico).

**206**

**2.3 Analytical methods**

**Table 1.**

**ICP analysis**

*2.3.1 Characterization of minerals*

cies contained in each material.

*2.3.2 Chemical analysis*


**Author details**

Anyebe Onoja1 \* and Oluwaseyi Ajagbe2

1 Department of Virology, College of Medicine, University of Ibadan, Nigeria

2 Faculty of Veterinary Medicine, University of Abuja, Nigeria

\*Address all correspondence to<EMAIL_ADDRESS>
© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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Anze Djordjevic, Igor Knez, Fevzi Sarper Türker, Zeki Temiztürk, Davut Azboy, Habib Rehman Khan, Muhtashim Mian, Yasuhiro Shudo, Sameh M. Said

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3.3.1. Comparison A (Model 1–Model 2): Hedonic–Employee-Rated Performance (H-PE) vs. Eudaimonic–Employee-Rated Performance (E-PE).

If the whole sample is considered, 50.6% of the respondents belong to a homologous cluster in both the H-PE and E-PE models. This means that about half of the employees had comparable wellbeing and performance profiles in both models. They have similar profiles in terms of both kinds of wellbeing. Interestingly, the other half of the employees (49.4%) do not belong to homologous clusters, which means that they belong to a cluster that suggests that they are unhappy in a hedonic way and, simultaneously, to a cluster that suggests that they are happy in an eudaimonic way, or vice versa.