The Factory Physics for the Scheduling: Application to

Footwear Industry

John Reyes

, Darwin Aldas

, Kevin Alvarez

, Mario García

and Mery Ruíz

Faculty of Engineering Systems, Electronics and Industrial, Universidad Técnica de Ambato,

Chasquis Avenue and Río Payamino Street, Huachi Campus, Ambato, Tungurahua, Ecuador

Faculty of Accounting and Auditing, Universidad Técnica de Ambato, Chasquis Avenue and Río Payamino Street,

Huachi Campus, Ambato, Tungurahua, Ecuador

Keywords: Productivity, Job Scheduling, Theory of Constraints, Work in Process, Cycle Time, Little Law, Promodel,

Process Simulation.

Abstract: In this paper, an analysis is made of variables such as inventory in process, cycle time and rate of production

of salable units proposed in the theory of constraints and applied in a case study in the manufacture of safety

footwear. The methodology used to evaluate these parameters is an experimental design with application of

Plant Physics laws in a simulation scenario with PROMODEL. The results reflect that the optimum quantities

of production for a cycle of work are achieved by adding 8.1% to the rate units that can be sold per unit of

time and reducing cycle time by 6.5%. It was determined that to produce a transfer batch the inventory in

process for each order hour is equivalent to 64% of the total of the units programmed for production based on

the maximum capacity of the manufacturing system.

1 INTRODUCTION

Effective production scheduling is essential for

successful operations that allocate resources over

time for specific tasks (Krajewski, et al., 2016), so an

unbalanced workload causes uncertainty in

organizations (Zhang & Wang, 2016).

In this context, optimal planning efficiency is

achieved by coordinating the production schedule

with Just in Time (JIT) distribution planning to

customers (Johar, et al., 2016), meeting deadlines,

optimizing resources, reducing time that does not add

value and increasing the production rate of the

system. By implementing operational planning,

scheduling, and production control strategies

organizations can make money today and in the future

(Goldratt & Cox, 2014).

Successful companies offer products and services

with optimal times of production and inventory

turnover, so three production management

approaches are important to achieve this goal:

Material requirements planning (MRPI, and MRPII),

Just in Time production and Theory of Constraints

(TOC).

TOC as a systematic management approach

focuses on eliminating the bottlenecks that prevent a

company's progress towards its goal of maximizing

profits and effectively utilizing the resources of the

production system (Mahapatra & Amit Sahu, 2006).

The productivity of a production system must

increase while its inventory and operating costs are

reduced, limited by the performance in the constraint

using TOC in the weakest link in the supply chain

(Günay, et al., 2014).

Factory physics provides a systematic description

expressed as laws of the underlying behavior of a

system. It helps to decide what performance measures

to collect and what alternatives to evaluate, as well as

in the interpretation of simulation results (Standridge,

2004).

To obtain a synchronized manufacturing process,

techniques are applied that analyze the constraints of

the production system, such as cycle time (CT),

which is the time a product spends since it enters the

system until it leaves, work in process (WIP) defined

by the inventory in process in the system and the

throughput (TH) referred to the rate units that can be

sold per unit of time. These techniques are based on

the approach proposed by Li, et al. (2005),

mentioning that the CT is an important indicator to

measure the performance of the factory. Sometimes it

is possible to lower the WIP level; however, excess

248

Reyes, J., Aldas, D., Alvarez, K., García, M. and Ruíz, M.

The Factory Physics for the Scheduling: Application to Footwear Industry.

DOI: 10.5220/0006403402480254

In Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2017), pages 248-254

ISBN: 978-989-758-265-3

WIP reduction can lead to decreased throughput.

Applying the Principles of Factory Physics, which

integrates Little's Law and the Operation Curve to

quantify the interdependence between operating

factors such as the Overall Equipment Efficiency

(OEE), CT, and WIP can be reduced the WIP level by

up to 10%.

Managing production scheduling has always been

a major challenge not only in the footwear industry

but in any field of production or service (Li, 2010).

Reyes, et al. (2016), when applying the TOC model,

proposes a management methodology for the

inventory of materials in the footwear industry, which

generates 18.7% of annual cost savings. However,

even today, footwear production processes continue

being totally artisan and the industries still follow the

conventional make to order production (Cocuzza, et

al., 2012).

Production planning and scheduling must evolve

and adopt new tools that help gain a deeper control of

what must be produced to efficiently meet customer

needs (Zangiacomi, et al., 2007). One of the tools

currently used to visualize the results that propose

strategies and methodologies of process

improvement, is the use of simulation software.

Simulation is a necessary tool to represent this

reality and make decisions that further reduce

manufacturing costs by validating the design or

redesign of any complex system such as footwear. In

this particular case the simulation is necessary for the

initial estimation of the throughput since a single

worker must perform multiple operations in several

workstations and the controls on the quantity of

inventory in process must be validated as well as the

costs of production (Grimard, et al., 2005).

The footwear industry presents WIP accumulation

caused by incorrect distribution of work areas,

inadequate production schedules and orders of

products not released on time (Marcelo, et al., 2016).

The accumulation of WIP generated by improper use

of job measurement techniques and erroneous sales

forecasts implies the execution of production orders

with long delivery times and orders that are not met.

The congestion of the productive system with the

presence of constraints finally reduces throughput

and business productivity.

This research proposes a study of the parameters

for shoe production through the detection of

manufacturing system constraints and their

evaluation with the laws of factory physics.

Using simulation with PROMODEL in a case

study, optimal results of TH, WIP and CT are

obtained with standard values of inventory in process

that an optimum shoe manufacturing system must

maintain to achieve the shortest cycle time and the

highest rate of production.

2 METHODOLOGY

The footwear industry in Ecuador has strengthened in

the last 6 years and generates in the country some

100,000 direct and indirect jobs, currently has about

5,000 Ecuadorian producers in the whole country,

being Tungurahua the province where concentrates

50% of the national production (Reyes Vasquez, et

al., 2016). From this sector of the country is taken as

case study an industry that produces safety footwear

because it is the product of greater demand.

For the study the corresponding manufacturing

processes are considered: punching, polishing,

trimming, fixing of eyelets, forming, assembly and

finished. The timing of the process is taken through

the chronometer technique with assessment of the

rhythm established in the leveling method proposed

in the Westinghouse system (Cevikcan & Kilic, 2016)

and calculation of supplements through a bi-objective

approach of assessment with fatigue standards

(Glock, et al., 2016). For the case study, the largest

overall time is taken for each of the processes to

encode in a Simulation model.

The timing and sequence of operations are entered

into the Promodel® process simulation software

version 7.0, which models the flow rate in the

manufacturing system, cycle times and the work in

process on a production line. Through simulated

experimentation it is proposes to validate the

hypothesis, which seeks to show that by keeping an

inventory in a constant process and reducing the cycle

time it is possible to increase the rate of production in

a situation in which the manufactured products go to

inventory. Reducing the size of process batches has a

much deeper effect than increasing the number of

transfer batches because the product mix is much

larger and generates reductions of WIP and waiting

times in production.

The parameters used in the simulation are

Throughput (TH) for machines, workstations,

production line and industrial installation per unit of

time, work in process (WIP) and cycle time (CT)

from the path between the beginning and end of

processes. One of the main restrictions of modeling is

to determine the bottleneck (Rb) which is the rate

(parts per unit time or jobs per unit time) of the

workstation that has the highest long-term utilization

(Hopp & Spearman, 2011).

In the Promodel simulation software, it is enter the

units that arrive to the system with a frequency

The Factory Physics for the Scheduling: Application to Footwear Industry

249

distribution of discrete random variable with

probability behavior of Poisson to obtain an

approximation to the reality of the manufacturing

system. This distribution is obtained with the

Promodel Stat Fit library comparing frequency

distributions. The experimentation is carried out

through simulation scenarios where the behavior of

the study variables is obtained.

For the evaluation of the relationship between the

productions parameters of plant physics, the Little

Law is used which establishes that there is a close

relationship between throughput (TH), cycle time

(CT) and work in process (WIP) defined by equation

(1). This equation shows that the longer the cycle time

will lower throughput with a constant level of

inventory. The research also seeks to obtain the

critical WIP of the line (Wo) which is the inventory

with the line produces the maximum throughput.

From this level, inventory only produces congestion

and storage costs. See equation (2) (Hopp &

Spearman, 2011)

TH = (WIP / CT) (1)

Wo = (rb) .To (2)

An adequate production program involves that

industries must adjust to the lower performance of the

rate of production. This is achieved by equations (3),

(4) and (5), where w is the WIP level.

TH best = w/To si w < Wo (3)

TH best = rb si w <Wo (4)

w= Wo (5)

The best performance law states that for a given

inventory level (w) and the highest throughput, are

obtained when the inventory level is equal to or

greater than the critical level (Wo). The result is equal

to the bottleneck rate (rb). The law of best

performance can also be formulated with equations

(6) and (7).

CT best= To si w <Wo o w= Wo (6)

CT best = w/rb, si w>Wo (7)

In order for companies to avoid developing their

manufacturing processes with the worst performance,

Plant Physics also evaluates this factor through

equations (8) and (9) for any level of inventory w.

TH worst= 1/To (8)

CT worst= w.To (9)

There is also the evaluation of the parameters

under a practical performance where an additional

time of CT by contingencies is considered. For this,

we use equations (10), (11), (12) and (13).

TH practical= (w/(Wo+w-1))rb (10)

CT practical= To+(w-1)/rb (11)

CT practical= ((w-1)/N) t + t (12)

CT practical = (1 + (w-1)/N) t (13)

The variable w represents the works in the

manufacturing system, N is the number of stations in

the production line, t refers to the process time in each

station, To = Nt is the system process time and rb = 1

/ T corresponds to the bottleneck. When a job arrives

at a station, the number of jobs waiting at this station

is (w-1) / N.

To the three cases proposed in Plant Physics, the

current case study is added, the equations for the CT,

TH and WIP of the four possible cases are modeled

in the Promodel® simulator: the best, the practical,

the worst and the current one. These results allow to

know the current state of the production system with

respect to the studied parameters in order to compare

through the generation of scenarios the variation of

the size of the order or the time of the simulation that

allows to obtain the greatest benefit for the

organization.

3 RESULTS

Figure 1: Distribution of probability of arrivals.

To program the attributes defined in the methodology

the Distributed Simulation (DS) method is used

(Anagnostou & Taylor, 2017). Locations are created

corresponding to each of the jobs where

manufacturing activities are developed and also 5

temporary storage areas that allow to know how many

units remain in process after a work shift.

The entity considered for the study is called

Model S15 which is the product in process. The

arrivals occur in defined trajectories from warehouse

of raw material to the production system with an

established frequency detailed in Figure 1. The

SIMULTECH 2017 - 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

250

number of occurrences or units that arrive to the

system is infinite since in the first instance it is

simulated as a function of the time that is of 8 hours.

In total, the basic model generates 47 variables to

measure the key performance indicators (KPIs) such

as bottleneck rates (rb), process times (tp), cycle

times (CT), system efficiency, work in process WIP)

and trougthput (TH) for the three cases analyzed with

Little's Law (Hopp & Spearman, 2011).

5 networks of movements are traced in which the

14 operators cross each of the locations with a node

of the network through interconnections or interfaces,

in the displacements the distance measured in the

plant between the different jobs is taken into account.

Attributes of type real numbers are used for the entity

defined as att_S15, a subroutine named id is

programmed in order to avoid a division between zero

in the process, because the cycle time is only

calculated after the first one Part, this programmed

code is shown below:

IF CT_ModelS15 <>0 THEN

TH_ModelS15=wip_ModelS15/CT_ModelS15

ELSE

TH_ModelS15=0

To program the processes, you enter data such as:

input entity, output entity, input and output location,

route, movement logic.

It creates a variable Real x that is internal where

an operation time will be stored. The id subroutine

checks if the cycle times of each entity are different

from zero.

Then the program places the time that the clock of

the simulation is marking the moment the entity

enters the production system in attribute att_S15, the

equation to obtain the production capacity and the

respective bottleneck is also determined. A logic is

also proposed in order to obtain an increase in the

zones of temporary storage and at the same time a

decrease while they go on to the next process of the

system. Finally the equations are codified for the

analysis of the constraints with Little's Law, as shown

below:

REAL x

att_S15=CLOCK()

tp_1=1.30x=(tp_1)

rb1=1/x

WAIT x

INC WIP_Zona1

tp_2=1.90x=(tp_2)

rb2=1/x

WAIT x

DEC WIP_Zona1

IF rb1<rb2 AND rb1<rb3 AND rb1<rb4

AND rb1<rb5 AND rb1<rb6 AND rb1<rb7

THEN

{

TH_General= rb1

}

ELSE

IF rb2<rb3 AND rb2<rb4 AND rb2<rb5

AND rb2<rb6 AND rb1<rb7 THEN

{

TH_General= rb2

}

ELSE

IF rb3<rb4 AND rb3<rb5 AND rb3<rb6

AND rb3<rb7 THEN

{

TH_General= rb3

}

ELSE

IF rb4<rb5 AND rb4<rb6 AND rb4<rb7

THEN

{

TH_General= rb4

}

ELSE

IF rb5<rb6 AND rb5<rb7 THEN

{

TH_General= rb5

}

ELSE

IF rb6<rb7 THEN

{

TH_General= rb6

}

ELSE

TH_General= rb7

WIP_critical_best=TH_General*CT_Mode

lS15

INC WIP_critical_best

CT_Worst=wip_ModelS15*CT_ModelS15

CT_Practical=(CT_ModelS15+((WIP_Mode

lS15-1)/TH_General))

CT_Best= (WIP_ModelS15/TH_General)

TH_Practical=((WIP_ModelS15/(WIP_cri

tical_best+WIP_ModelS15-

1))*TH_General)

Capacity_best=TH_General*60

Capacity_practica=TH_Practical*60

Capacity_actual=TH_ModelS15*60

Production_best=Capacity_best*(CT_Mo

delS15/60)

production_practica=Capacity_practic

a*(CT_ModelS15/60)

Capacity_worst=TH_Worst*60

production_worst=Capacity_worst*(CT_

ModelS15/60)

Efficiency=(TH_ModelS15/TH_General)*

100

The Factory Physics for the Scheduling: Application to Footwear Industry

251

For movements between jobs is coded according

to the following:

MOVE WITH Operario1 FOR 2.28 THEN

FREE

With the data entered in the Simulator it is obtain

the bottleneck rate (rb) of the system of 0.53 pairs per

minute, as seen in Figure 2.

Figure 2: Bottleneck rate.

Table 1 shows the production parameters in the first

column and in the first row are located the four cases

analyzed from the theory of Plant Physics.

Table 1: Results of the four possible cases.

Best

Case

Worst

Case

Practical

Case

Curren

t Case

Units

WIP

238

Pairs

449

11424

915,4

480

Minute

0,53

0,002

0,26

0,49

Pairs/min

The time (To) consider for the simulation is 480

minutes equivalent to a working day of 8 hours, in this

time 238 pairs of shoes are produced with a

production rate of 0.49 pairs per minute.

With equation (2) it is obtain the critical Wip (Wo)

whose value corresponds to 254 pairs per day.

As expressed in equation (4), the best TH is found if

the rate of production reaches the value of rb,

therefore the value of TH = 0.53 pairs per minute is

taken for the best possible case. Equation (7)

calculates the best CT, this time is less than the

planning of a working day. With these results, there

was an increase of the TH by 8.1% and a reduction of

the CT by 6.5%.

The worst case is determined that in a work cycle

a pair of shoes is produced, with a production rate of

0.002 pairs / min and a cycle time of 114,240 minutes.

There is also a practical case that is calculated

with the equations whose production rate is 0.26 pairs

per minute where the company requires 915.4

minutes to fulfill the production of an order of 238

pairs.

This case is considered when there are unforeseen

for which the company must reduce its rate by 50%

and increase the time by 100%.

In order to determine the inventory in process that

the company must maintain in each hour of work, the

simulation is performed for a production of 50 pairs

of shoes since the workers produce in each

workstation in function of those quantities before

passing the product to the following process.

The Little Law that relates the production

parameters analyzes the current case, the best case,

the worst possible case and a practical case of

production for different WIP values, in order to verify

the dynamics of the process with different

parameters.

To schedule the production it is necessary to know

how the production flow values change over time and

also to know the maximum value of WIP within the

system in a set time so that there is no excess

inventory in process. Finally know how many units

can be produced in a given time.

Controlling inventories in process WIP also helps

to fulfill the delivery of orders on time in addition to

achieving an increase in productivity. It is necessary

to know in which time the highest TH is obtained and

how many units must be produced, for this the results

of the TH vs the CT of Figure 4 are observed.

The "Best Possible" case generates the minimum

cycle time and the maximum throughput for each

WIP level.

The production dynamics of the case study are

plotted in Figure 3 with the relationship between the

TH and the WIP; And Figure 4 the TH and CT in the

one-hour time cycle for the batch of 50 pairs, in order

to know how many units should be kept each hour

occurring in the system to meet the established goal

and the sequence of income Of the units to the system.

Table 2: Comparison of the four cases.

Case

WIP

(pairs)

(min)

(pairs per min)

Worst

1920

0,002

Best

0,53

Practical

123

0,26

Current

0,49

Table 2 shows that when a WIP of 32 pairs is in the

system, it is possible to reach the maximum

production rate, therefore it is the amount that the

plant must maintain every hour as a minimum to

fulfill the delivery of orders to time using the

maximum capacity of the production line.

After this value of 32 pairs, the cycle time is

increased in the time that is invested in producing a

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252

0,000

0,100

0,200

0,300

0,400

0,500

0,600

0 20 40 60 80

WIP

TH VS. WI P

TH BEST TH WORST

TH PRACTICAL TH CURRENT

100

150

200

250

300

0 20 40 60 80

WIP

CT VS. WI P

CT BEST CT WORST

CT PRACTICAL CT CURRENT

pair with the best production rate. The results for the

other three cases are also presented.

Figure 3 shows that in the present case a

production rate of 0.49 pairs per minute with a CT of

60 min is achieved keeping an inventory in process of

29 pairs. According to the study, the company should

reach the best possible case by maintaining a

production rate of 0.53 pairs per minute with a CT of

60 minutes keeping an inventory in process of 32

pairs as shown in the green lines in Figure 3. From

these values the curve stops growing and the

inventory increases but not the production rate.

In the case study it is observed that in order to

maintain an inventory in process of 32 pairs the CT

must be increased to 123 min but the production rate

decreases to 0.26 pairs per minute.

Figure 3: Relation TH vs. WIP.

Figure 4: Comparison CT vs. WIP.

The results of Figure 4 indicate the variation of the

CT as a function of the WIP, in the best case possible

the time is kept constant in 60 minutes until an

inventory of 32 pairs. From this inventory the time

curve begins to grow which implies that to have more

units in the system the cycle time increases and

therefore the TH is reduced.

For every 50 pairs produced an inventory in

process of 32 pairs should be maintained every hour

within the system which implies that the inventory in

process should not exceed 64% of the total

production.

Figure 5 shows the behavior of the TH in the time

where the upper line shows the best possible case, it

is the only one that remains constant since it is the

case to which the system must tend optimally. The

second line indicates the current case with its

respective variability, this is due to different factors

that influence how the work rate of the workers or the

supply of raw materials, always must be taken care

that this line is between the best case and the practical

one to consider that the system of production is stable.

The third line is that of the practical case and the

fourth is the worst case possible.

Figure 5: Behaviour TH vs. CT.

4 CONCLUSIONS

A simulation model was programmed using the

Promodel software, considering the capacity

constraints and the production parameters where the

results were obtained for the four possible cases

stated in Plant Physics: best case, worst case, case

study and current case.

For a working day of 8 hours (480 minutes),

currently 238 pairs of shoes are produced with a

production rate of 0.49 pairs per minute.

Through the simulation it was determined that the

production rate that maximizes the capacity of the

line is 0.53 pairs per minute increasing from the

current one by 8.1%, also the reduction of the cycle

time For the best case to 449 minutes corresponding

this value to an improvement of 6.5% with respect to

the current one.

The Factory Physics for the Scheduling: Application to Footwear Industry

253

The inventory in process that must be maintained

at the maximum is 32 pairs per hour, which indicates

that if a greater value is conserved within the day, the

company begins to generate unnecessary

accumulation of the same one.

It is concluded that in order to maintain a

production rate that satisfies the maximum capacity

of the plant, every hour an inventory in process

equivalent to 64% of the total number of units

scheduled for production must be maintained.

For a manufacturing system to be optimal, the TH

production rate should not change over time but

remain constant, this is a clear indicator that resources

are coming to the system on time and supplying it is

efficient, where prevents waste generation.

The results of the model employed identify

companies with an efficient management of their

processes, and others that require support to analyze

and respond with data and facts scientifically proven

to eliminate the root causes of their problems.

ACKNOWLEDGEMENTS

The authors thank the National Footwear Chamber of

Ecuador and the Technical University of Ambato for

the support provided during the execution of this

work within the framework of the research project

called “Operational optimization based on a lean

dynamic system of alert of failures in the production

processes for the footwear industry”.

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