Optimization of Integrated Batch Mixing and Continuous Flow in

Glass Tube & Fluorescent Lamp

Mina Faragallah

1

and A. A. Elimam

2

1

Continuous Improvement Engineer, Mondeléz Egypt, 10

th

Ramadan, Egypt

2

Mechanical Engineering Department, The American University in Cairo, New Cairo, Egypt

Keywords: Production Planning, Continuous Production, Batch Mixing, Linear Programming.

Abstract: This paper deals with production planning of in-series continuous flow, and discrete production plants. The

work is applied to glass and fluorescent lamp industry, where raw materials are mixed in batches, charged to

a continuous furnace to produce glass tubes, and then assembled into discrete lamps. A non-linear

programming model was formulated from the raw material mixing stage till the production of fluorescent

lamps. Using the model, the amount of each raw material can be obtained at minimum cost, while satisfying

the desired properties of the produced glass. The model also provides the optimum lamp production

amounts, inventory levels, and the glass pull rate from the furnace, which determines the production

amounts of glass tubes. An important factor in the continuous flow process is the amount of broken glass

(cullet) added in the furnace, which has an impact of raw material cost and natural gas consumption. In

order to solve the model, separable programming methods and linear approximations were used to transform

the non-linear terms. Results are validated versus actual production data from local Glass & Lamp factories,

and the model proved to be an efficient tool of integrating the whole process at minimum cost.

1 INTRODUCTION

The sequence of manufacturing a fluorescent lamp

starts with the production of light bulb. Glass tube

production is considered a continuous process and it

is followed by a discrete assembling process. The

production of glass bulb starts with mixing of glass

basic material. Silica sand, dolomite, limestone,

potash feldspar, soda ash, borax, carbon, sodium

sulphate, magnesium, and alumina are the major raw

materials used to form the glass batch. The batch is

then charged to the furnace at 1475

o

C. In order to

shape glass into tubes, the molten glass flow over a

rotating hollow cylinder to take the shape and a flow

of air is blown inside the hollow cylinder. Then, the

formed tubes are pulled using conveyors, cooled

down at room temperature, and cut according to the

desired length. The edges are modified to facilitate

the assembly process. The tubes are then coated with

the phosphorous coating, and the tungsten filament

are assembled to the coated bulb. After that the bulb

goes through exhausting, in which the tubes are

vacuumed, the inert gas and the mercury drop are

inserted inside the bulb and then, the bulb is sealed.

End-Caps are then added to the edges of the sealed

bulb and finally the lamp is tested before packaging.

2 PROBLEM DEFINITION

In such an industry, the production processes are

dependent to one another. Any stoppages at one of

the processes due to breakdowns or material

shortages will affect the whole operation. For

example, when the assembly process stops, the

production of glass tubes should stop as well.

However, glass production is a continuous flow

operation where the production line runs 24 hours a

day over 7 days of the week. The furnace is the

crucial component at the whole production line

where any change in the production quantity for

example should be introduced gradually because of

the considerable setup cost. Therefore, furnace

shutdown can cause significant loss to the factory. In

case of low demand and in order to avoid shutting-

down the furnace, the production quantity is reduced

to the minimum, leading to lower utilization. In

addition, the unit cost of the glass tube increases due

Faragallah M. and A. Elimam A.

Optimization of Integrated Batch Mixing and Continuous Flow in Glass Tube Fluorescent Lamp.

DOI: 10.5220/0006192401190127

In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems (ICORES 2017), pages 119-127

ISBN: 978-989-758-218-9

Copyright

c

2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

119

to the reduction in production quantities. Therefore,

decisions should be taken with the objective to

minimize the total variable cost of the integrated

operations. The variable costs are raw material,

energy, inventory, and crushing cost. Several factors

should be considered in order to achieve such an

objective. The variables, representing these factors,

are the amount of each raw material inside the glass

batch, the Glass Pull Rate (P), the percentage of

glass culets added to the batch (MG), the thickness

of the glass tube, the inventory level in various

stages (straight tube, shaped tube, and fluorescent

lamp), and the scheduled scrap quantity. Given these

variables, the following variety of actions could be

pursued in order to minimize waste

• Given the chemical composition and the

cost of each raw material, the factory has to

decide upon the weight percentage of each

raw material inside the batch to minimize

the raw material cost without affecting the

basic characteristics of the final product,

such as the glass density, and the thermal

expansion coefficient.

• Increasing the glass cullet percentage in the

batch reduces the raw material, so the raw

material cost is reduced. On the other side,

the amount of glass cullet required

increases, so the amount of glass tubes

crushed increases.

• Also, reduction in P cause reduction in the

production quantity. However, this will

increase the residence time inside the

furnace causing changes in the chemical

composition of glass inside the furnace.

Therefore, change in P should be

minimized.

• The factory has to make a decision on the

inventory level and on the amount at each

stage, straight tube, end-formed tube,

fluorescent lamp based on the inventory

cost at each level and the storage limits.

• Moreover, the factory might decide upon

crashing some of the glass tubes if the

inventory level increases.

3 LITERATURE REVIEW

The problem mentioned above have been discussed

in the literature under two major research areas,

namely: raw material mixing to form the final

product and production planning.

Several scholars tackled the raw material glass

mixing to reach an efficient batch calculation.

Khaimovich and Subbotin (2005) have developed an

automated program for this batch calculation. The

aim of the program is to decide upon the amount of

each raw material to achieve a specified weight

percentage of each oxide by developing a system of

linear equations. In a follow up paper, Khaimovich

(2005) improved on the program to account for the

cullet composition.

Changchit and Terrell (1990) developed a linear

model to decide upon the amount of each raw

material in ceramic batch calculation. The model

objective function minimizes the batch cost. Linear

constraints were included to ensure satisfying the

desired ceramic properties.

Another two models were formulated to model

the mixing problem in two different industries. The

first is developed by Hayta, Mehmet, and Ünsal

Çakmakli (2001) to find the optimum mix of wheat

to produce break making flour. The other model,

which was developed by Steuer, Ralph E. (1984),

modeled the mixing process to form sausage.

In addition to raw material mixing contributions,

several articles discussed the production planning of

discrete processes. Díaz-Madroñero, Peidro, and

Mula (2015) presented a review of mathematical

models developed to tackle both production and

transportation routing problem. The paper have

presented how different models tackled various

aspects including production, inventory, and routing.

Although many papers tackled the production

planning problem in discrete production, small

attention is given to the production planning of

continuous processes.

Fabian, Tibor (1958) developed an integrated

production planning model for the continuous

process of iron and steel production. The model was

divided into three sections that were integrated at the

end of the paper. The first part dealt with the

production of iron. The second part of the model

was formulated to represent the steel production

operation. The final part dealt with the rolling

operations. Assumptions were made to facilitate the

solution and to guarantee linearity, such as constant

batch size and constant size of the output.

In another two scholars, Dutta, Sinha, and Roy

developed integrated production steel plant model.

In the first (1990), the aim was to optimize the

product mix taken into consideration allocation of

plant capacities to different products, capacity

expansion decisions, and the optimum route of a

product across available machines. The second paper

(1994) dealt with the allocation of energy in case of

shortage. The model developed with the objective of

maximizing profit, while considering energy as a

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

120

limiting constraint.

Almada-Lobo, Oliveira, and Carravilla (2008)

also tackled the production planning and scheduling

of continuous process problem in coloured glass

containers manufacturing. As a result of changing

the product colour, setup time is required to change

between colour and it's a sequence dependent

process based on the two colours. A multi objective

function was formulated to minimize the weighted

sum of sequence dependent setup times, average

inventory levels, and number of stock-outs.

In addition, Taşkın, and Ünal (2009) developed a

MIP model for the production and transportation

planning of a float glass manufacturing company

called Trakya Cam. The company produces various

product sizes in multi facilities. A model was built

with the objective of minimizing the total cost

including production, inventory, backorder, and

transportation cost.

In this paper, a mathematical model is developed

to integrate the production processes of fluorescent

lamp starting from mixing of raw material till the

storing of finished product. The model aimed at

minimizing the total operating cost including, raw

material, scheduled crushing, inventory at all levels,

and energy cost, while. In the developed model, the

optimum mix of raw materials is determined not

only based on input variation as developed by

Changchit and Terrell (1990), but also based on the

optimum cullet ratio. Also, the energy cost is

considered in the model to take into account the

relationship between using glass cullet and energy

saving as explained by Vishal, et. Al (2007) as well

as Štefanić and Pilipović (2011). In addition to the

mixing operation, the model takes into consideration

the balance between an in-series continuous-process

plant producing glass tubes followed by a discrete

plant assembling fluorescent lamps. Integration

between in sequence production stages is achieved,

so that the demand of the following stage is a

requirement from the previous stage. A major

distinction between the developed model and the

continuous models cited before is that the speed of

the continuous process is not constant and it changes

from one planning horizon to another depending on

demand. Therefore, the amount of raw materials

consumed and the output produced is dependent

upon that variable.

4 MATHEMATICAL MODELING

4.1 Symbol Definitions

In the following three sections, the model constant

parameter, sets, and decision variables are defined.

4.1.1 Constant Parameters

Symbol Definition

%E

m

Percentage of end-forming waste from the

weight of straight tube size m

%G

m

Percentage of cutting waste from the weight of

glass tube size m

A

t

Available hours per period t

CB

t

Raw material batch Cost at period t

CC

m

Cost of crushing one glass tube of size m

CI

E

m

Monthly cost to keep one unit of end-formed

tube of size m in inventory

CI

G

m

Cost of one glass tube in inventory of size m

CI

L

m

Cost to keep one lamp in inventory of size m

CN Cost per m

3

of natural gas used in furnace

CP

E

m

:

Cost to produce one unit of end-formed tube of

size m

CP

L

m

Cost to produce one unit of lamp of size m

CR

i

Cost per Kg of raw material i

D Outer diameter of glass tube

D

mt

Demand of fluorescent lamp of size m in period t

F(MG%)

Relation between cullet ratio percentage, and

natural gas consumption

F

jk

Chemical influence factor of oxide j on property

k

H Thickness of glass tubes

O

ij

Weight percentage of oxide j inside raw material

i

P

ij

Weight percentage of oxide j inside raw material

i

SI

B

Storage capacity of glass cullet

SI

E

Storage capacity of end-formed tubes

SI

G

Storage capacity of glass tubes

SI

L

Storage capacity of fluorescent lamps

SP

E

mt

Production capacity of end-formed tube of size

m in period t

SP

L

mt

Production capacity of fluorescent lamps of size

m in period t

SS

E

m

Safety stock of end-formed tubes of size m

SS

G

m

Safety stock of glass tubes of size m

SS

L

m

Safety stock of fluorescent lamps of size m

U

B

Lower limit for percentage of broken glass

U

j

Lower limit for percentage of oxide j

U

k

Lower limit of property k

U

P

Lower Limit of glass pull rate

V

B

Upper limit for percentage of broken glass (glass

cullet)

V

j

Upper limit for the percentage of oxide j

V

k

Upper limit of property k

V

P

Upper limit of glass pull rate

W Raw material batch Weight

X Standard aggregate tube length

X

m

Standard length of glass tube m

Y

m

Size factor of tube size m

ρ Density of glass

Optimization of Integrated Batch Mixing and Continuous Flow in Glass Tube Fluorescent Lamp

121

4.1.2 Sets

Symbol Definition

I

Set of raw materials used to form the glass

batch

J

Set of oxides forming the composition of

the output glass

K

Set of required properties of the output

glass, such as density and thermal

expansion

M Set of glass tubes sizes produced

T Set of planning periods

4.1.3 Decision Variables

Symbol Definition

B

t

Amount of broken glass (cullet) produced

in period t

C

mt

Amount crushed of glass tubes of size

m during period t

E

mt

Amount of end formed tubes m

produced in period t

G

mt

Number of glass tubes of size m produced

in period t

I

B

t

Inventory of broken glass at the end of

period t

I

E

mt

Inventory of end formed tubes of size

m at the end of period t

I

G

mt

Inventory of glass tubes of size m at

the end of period t

I

L

mt

Inventory of fluorescent lamp m at the

end of period t

L

mt

Amount of fluorescent lamps of size m

produced in period t

P

Glass pull rate of glass from the

furnace

Q

E

mt

Gross Requirements of end-formed tubes

of size m during period t

Q

G

mt

Gross Requirements of glass tubes of size

m during period t

R

it

Amount raw material i used in the

glass batch in period t

R

B

t

Amount broken glass used in the glass

batch in period t

4.2 Integrated Mathematical Model

4.2.1 Objective Function

The objective function is aimed at minimizing the

total cost which includes the cost of production,

inventory, scheduled crushed glass, raw material,

and natural gas.

Min.

∑∑

∈∈

.

+

.

+

∑∑

∈∈

.

+

.

+

.

+

∑∑

.

+(

)

⁄

∗

∈∈

∑∑

.

∗

∈∈

+∗

(

%

)

∗

(1)

4.2.2 Constraints

1. Production Capacity Constraints

A. Mass production processes (fluorescent lamp

assembly and end-formed tube production)

,∀∈&∈

(2)

,∀∈&∈

(3)

B. Continuous flow processes (glass tube

production)

(

/)∗

∈

−(

.)/(.∗∗

∗(−))=0,∀∈

(4)

Where the amount of glass tube produced in period t

is equal to amount of molten glass produced in t

(A

t

*P) over the mass of one lamp.

The glass pull rate has an operating range as follows

(5)

C. Glass Cullet Production

−..

∗∗

(

−

)

.

(

1−%

)

.

∈

+%

.

+%

.

=0,∀∈

(6)

The amount of cullet produced in t is equal to the

mass of one lamp multiplied by the cut loss amount

2. Inventory Safety Stock

,∀∈&∈

(7)

,∀∈&∈

(8)

,∀∈&∈

(9)

3. Storage Capacity

.

∈

,∀∈

(10)

.

∈

,∀∈

(11)

∑

.

∈

,∀∈

(12)

,∀∈

(13)

4. Linkage of In-Sequence Processes

−

= 0,∀∈&∈

(14)

−

=0,∀∈&∈

(15)

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

122

5. Production & Demand Balance

−

.

(

)

+

−

=0,

∀∈&∈

(16)

−

.

(

)

+

−

=0,

∀∈&∈

(17)

−

.

+

+

−

=0,

∀∈&∈

(18)

−

−

+/..

=0,∀∈

(19)

6. Oxide percentages upper limit & Lower Limits

∑

.

∑∑

.

,∀∈&

∈

(20)

The numerator is the amount in Kg of oxide j in all

raw materials and the broken glass divided by the

yielded glass batch weight.

The equations can be written in following linear

forms:

.

−

.

.

0,∀

∈&

∈

(21)

∑

.

−

.

∑∑

(

.

)

0,∀∈

&

∈

(22)

7. Broken glass percentage upper & lower limits

−

.

.

0,∀∈

(23)

−

.

.

0,∀∈

(24)

8. Properties upper & lower control limits

For each oxide, the weight percentage of that oxide

from the yielded batch weight is multiplied by a

chemical influence factor (F)

(

.

.

)−

∈

.

.

0,∀∈&∈

(25)

(

.

.

)−

∈

.

.

0,∀∈&∈

(26)

9. Batch Weight

,∀∈

∈

(27)

10. Non-negativity Constraint

All variables are higher than or equal to zero.

5 COMPUTATIONAL WORK

5.1 Computational Plan

In order to validate the model, it is tested against

base case data given by Al-Arabi Lamp and Glass

Factory. The model is used to generate the same

output variables, such as production and inventory

amounts. Input data includes actual demand forecast

for six months, cost figures for production,

inventory, and crushing, raw material chemical

composition, etc. Therefore, the plan goes as below:

• Linear approximation techniques are used

for the non-linear terms in the objective

function and constraints to transform the

integrated model into linear.

• The base case input parameters are fed to

the model and the results are compared vs.

the actual output variables to prove model

validity.

• Then, the integrated model is solved and

the optimum solution is compared with Al-

Arabi actuals.

• The last step is to test the sensitivity of the

integrated model to variability in the raw

material, energy, and crushing cost values.

Different scenarios are tested and the

model response is observed and analyzed.

All computational runs are solved using IBM-

ILOG CPLEX V.12.6.2 on an i7 HP ProBook4540s,

and the following assumptions are made:

• Raw material chemical compositions are

fixed over the planning horizon

• Glass pull rate are fixed over the planning

horizon, so once decided by the model, the

values are the same from one period to the

other.

5.2 Linear Approximations

5.2.1 Separable Programming Techniques

In order to solve the model as linear, the batch cost

term in the objective function (1), and the glass

cullet inventory balance constraints (19) needs to be

linearized. Moreover, a relationship between the

glass cullet percentage, and energy cost should be

figured out. First, the linearization of constraint (19)

and the batch cost term are done using separable

programming techniques, where the right hand side

of the equation can be expressed as the sum squared

of the two variables instead of multiplying both

variables. Faragallah (2016)

Optimization of Integrated Batch Mixing and Continuous Flow in Glass Tube Fluorescent Lamp

123

.

=(+

)/2 ,

.

=(−

)/2

(28)

.

−

.

=.

(29)

It is shown that for the given operating range of

glass pull rate (P) and the broken glass (

), Z

1

2

&

Z

2

2

can be expressed as linear functions as shown in

figure 1.

Figure 1: Linear Approximation for the Multiplication of P

&

.

Therefore, (19) can be expressed as

−

+

=

/∗(144.P

+708.

−101952)

(30)

The same methodology is used for the batch cost

term in the objective function, so the term can be

transformed into:

1.44.

∑

(

∈

245.216.−508.698.

+

73252.5)

(31)

5.2.2 Natural Gas Cost Formulation

According to Vishal, et. Al (2007) as well as

Štefanić and Pilipović (2011), the energy

consumption of melting glass is reduced by 2.5 – 3%

for every 10% of glass cullet addition to the batch.

The average natural gas consumption at 30% glass

cullet ratio is 742 m

3

/hr. (Abdelrahman 2015)

Therefore, a relationship can be derived between the

natural gas consumption and the cullet percentage as

shown below

F(MG%) = -86*MG% + 312.18 (32)

Therefore, the last term representing the natural

gas consumption cost in (Eq. 34) can be expressed

as:

720.

.

(

−86.

(

%

)

+312.18

)

(33)

Where

(

%

)

=(

)/(

∑∑

.

)

(34)

The term in (32) is a non-linear term, however,

from 2015 batch data from Al-Arabi factory, the

denominator for the operational range of cullet

percentage has an average value of 442.49 and a

standard deviation of 2.03. The model is tested with

the average value, and plus and minus 3 standard

deviations from the average, and the difference

between the three cases was neglected, so the

average value of 442.49 is used. Faragallah (2016)

5.3 Validation & Results

The developed model is used to generate the base

case data provided by Al-Arabi. Table 1 and table 2

show the demand data for 2014 and cost figures used

as an input. Table 3 shows the chemical composition

and oxide percentages of raw materials used. All the

input data was obtained from Al-Araby Glass

Factory. (Abdelrahman 2015)

Besides these data, the glass factory actual plan

was to set GPR at 750, cullet ratio of 30%, and to

run production for 19 hours a day, and 5 hours per

day of crushing. The plant total cost of production,

inventory, crushing, raw material, and energy was

LE 29,648,991.

These are the operating parameters fed to the

model and it proves efficiency by generate the same

production and inventory amounts of glass, end-

formed tubes, and lamps

Based on the input data, the number of decisions

variables are 188 and the number of constraints are

404 with 96 equalities constraints. The model is

solved in almost 240 seconds using CPLEX.

Then the model was solved to provide the

optimum solution, which is to run the glass factory

at 646 Kg/hr and a cullet ratio of 30%. Table 1, 2 &

3 provides the detailed optimum solution. The total

cost of the whole planning horizon, including

discrete process production cost, inventory cost,

crushing, raw material, and energy cost is equal to

22,488,970 + 739,000 + 1,194,102 + 1,408,674 +

1,634,000 = LE 27,464,746

With a total savings of LE 2,184,245 over that of Al-

Arabi lamp and glass factories actuals.

Z

1

2

= 852.Z

1

- 180076

R² = 0.998

0

50000

100000

150000

200000

250000

350 400 450 500

Z

1

2

vs. Z

1

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

124

Table 1: Optimum Result of End-Formed Tubes (EF) &

Lamps for 40 Watts.

Month

40 Watts lamp, 1000s units

Demand

Units Produced

Inventory

Level

EF Lamp EF Lamp

July 1,388.8 1,388.8 1,388.8 360 1,386

Aug 1,591.2 1,591.2 1,591.2 360 1,386

Sept 1,586 1,586 1,586 360 1,386

Oct 1,433.9 1,433.9 1,433.9 360 1,386

Nov 1,771.9 1,771.9 1,771.9 360 1,386

Dec 1,739.4 1,739.4 1,739.4 360 1,386

Table 2: Optimum Result of straight tubes for 40 Watts.

Month

40 Watts, 1000s units

Required Produced Inventory Crushed

July 1,388.8 1,764.3 1,386 375.47

Aug 1,591.2 1,721.5 1,386 130.3

Sept 1,586 1,721.5 1,386 135.5

Oct 1,433.9 1,878.7 1,386 444.77

Nov 1,771.9 1,814.5 1,386 425.91

Dec 1,739.4 1,752.9 1,386 135.32

Table 3: Optimum Glass Batch Mix.

Parameter Output

silica sand (Kg) 189.80

Soda Ash (Kg) 81.00

Dolomite (Kg) 45.20

Feldspar (Kg) 35.80

Borax (Kg) 4.90

Limestone (Kg) 7.82

Alumina (Kg) 0.00

Sulphate (Kg) 0.91

Carbon (Kg) 0.06

MG (Kg) 132.50

Density (gm/cm

3

) 2.488

Thermal Expansion (10

-7

*K

-1

) 100.60

Batch Cost, LE 271.61

5.4 Sensitivity Analysis

In this section, the impact of various cost figures on

the optimum solution is observed and analyzed. The

production cost is a major component of the total

cost structure, however, the production cost is driven

by the demand for lamps. Therefore, the focus is on

the effect of crushing, raw material, and energy cost

on the model results. A summary of the cost

structure for the optimum solution of the integrated

model is shown below:

Raw Material Cost = MLE 1.4086

Energy Cost = MLE 1.634

Crushing Cost = MLE 1.194

Inventory Cost = MLE 0.739

Production Cost = MLE 22.489

Total Cost = MLE 27.46

5.4.1 Impact of Raw Material & Natural

Gas Cost

Changes in Soda Ash, Silica Sand, and Borax cost

per ton are included in the sensitivity because they

represent more than 80% of the raw material cost

value. Based on historical data, changes in the cost

per ton for these materials are forecasted based on

the worst case scenario. Faragallah (2016) The same

was done for natural gas cost. However, the raw

material cost and the energy cost in the total cost

function increased without affecting the optimum

solution. Therefore, the model is insensitive to

changes in Silica Sand, Soda Ash, Borax, and

natural gas cost figures given that the remaining cost

figures of the objective function do not change.

5.4.2 Impact of Crushing Cost

The crushing cost at Al-Arabi factory is the

conversion cost to melt 1 Kg of glass cullet and

transform it to glass tubes again. (Elbendary 2015)

In order to reduce the crushing cost, the factory can

outsource percentage of the glass cullet. With close

chemical composition to that of the factory, the

outsourced cullet cost is 500 LE/ton. (Abdelrahman

2015)

Therefore, the effect of mixing the outsourced

cullet with the current batch mix is tested for

different percentages of outsourced cullet (5% -

20%).

Increasing the outsourced cullet percentage up to

5% causes the crushing cost and the glass pull rate to

decrease. Figure 2 summarizes the effect of

outsourced cullet over the crushing cost.

Figure 2: Total cost versus outsourced Cullet Percentage.

26

26,5

27

27,5

28

0% 5% 10% 15% 20% 25%

Cost (M LE)

Outsourced Cullet Percentage (%)

Effect of Outsourced Glass Cullet

Optimization of Integrated Batch Mixing and Continuous Flow in Glass Tube Fluorescent Lamp

125

From the above figures, increasing the

outsourced cullet percentage more than 15% doesn’t

have an impact on the optimum solution. Therefore,

the optimum solution of the integrated model is

achieved with 15% outsourced cullet ratio.

At this ratio, no crushing of straight tube is

needed. Therefore, the required cullet ratio in the

batch mix is achieved through the outsourced cullet

and the cut loss from operation. Accordingly, the

crushing cost is eliminated, the raw material and

energy cost is reduced because the optimum cullet

ratio in the batch mix changed from 30% to 35% due

to the introduction of outsourced cullet.

6 CONCLUDING REMARKS

Integration of batch, continuous, and discrete

manufacturing processes in florescent lamp

manufacturing was researched. In literature, glass

batch mixing, and continuous production planning

for glass furnaces were treated separately in the

literature found each by its own. Therefore, a

mathematical model was formulated to integrate the

optimum mixing of glass batch along with the

production planning of discrete glass tubes and

florescent lamps. The main factors affecting the

manufacturing process were considered. These

factors are the glass pull rate of molten glass from

the furnace which control the amount of glass tubes

produced, the percentage of glass cullet used in the

batch which affects the amount of crushed tubes to

meet the required cullet ratio, the optimum mix of

raw materials, and inventory levels of glass tubes

and lamps. The objective function was to reduce the

total manufacturing costs including crushing, raw

material, inventory, production cost, and energy cost

as a function in glass cullet percentage. The

objective function and some of the constraints

contained non-linear terms. Separable programming

methods were used to linearize the model. Then,

different Scenarios were tried to test the effect of

various parameters on the optimum solution. It was

found that changing in raw materials and energy cost

values changes the objective function value without

affecting the optimum solution. Moreover, trials

were made to reduce the crushing cost through using

glass cullet from outside sources. It was found that

with increasing the amount of outsourced cullet, the

glass pull rate along with the crushing cost

decreased dramatically till reaching zero. Also, the

glass cullet percentage increased causing the raw

material and energy costs to decrease. As a result,

the total cost decreases with the increase of

outsourced cullet ratio till reaching a constant value.

Therefore, using outsourced cullet ratio will help

reducing the amount of glass crushing, raw material

cost, and energy consumption.

The model proved to be a very helpful tool for

designing the optimum batch mix based on the raw

material chemical composition. In addition, the

model will facilitate the planning process of the two

factory as an integrated entity and will help

improving the total cost.

For future works, the model can be extended to

include diversification of customers of the glass

factory, which will reduce the unit cost. Deals from

other customers, such as other lamp producers,

laboratory glass ware companies, etc., should be

considered to increase the amount produced of glass

tubes. The following issues need to be taken into

account in selecting future customers:

• Quantities requested by the customer while

staying within the capacity of the glass

factory.

• Customization of each order, such as

different diameters and lengths which will

introduce set-up time to change from one

product to another. For example, changing

tube diameter may require to change the

GPR. This will cause production to stop for

some days based on the amount of change

and this may delay production to the main

customer which is the lamp factory, or to

other customers the factory decides to deal

with.

• Price discounts given to each customer

based on the quantity ordered and the level

of customization from the current situation.

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