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1. AN ADVANCED PRODUCTION PLANNING AND SCHEDULING SYSTEM FOR
BATCH PROCESS INDUSTRY
Nagham El-Berishy Amr Eltawil M. Nashaat Fors M. Hamdy Elwany
Production Engineering Department, Faculty of Engineering
Alexandria University
Egypt
naghamelbreshy@alex.edu.eg
ABSTRACT
The need for effective planning and management
techniques motivates the integration between
different operations management areas. These areas
include the production planning and operations
scheduling which is one of the most challenging tasks
facing managers today. Researchers have produced
extensive literature in this field in the batch process
industry. The importance of this integration forces by
it's directly effect on the overall performance of the
system in terms of quality of services to the customer
and cost to the organization.
In this paper an Advanced Production Planning and
Scheduling (APPS) model is constructed via the
mathematical programming. The objective of
minimizing the total costs, including the production
costs, inventory holding costs, idle time costs and
lateness costs is presented. The model addresses
related production characteristics as well as
scheduling characteristics by taking into
consideration the minimum order quantity from each
batch at each period, the inventory accumulation in
each period, and setup time and processing time for
each batch. The proposed model is solved using
LINGO®
optimization package and verified using test
models that use empirical data adjusted so that the
output can be expected in advance. The APPS model
successfully passed all verification tests. The detailed
assumptions, formulation, advantages and
contributions of the APPS model are presented,
together with the testing methodology. Finally, it was
implemented to a real world industrial case study.
KEYWORDS
An Advanced Production Planning and Scheduling,
Batch Process Industry, Mixed integer linear
programming, Optimization, Integrated planning
1. INTRODUCTION AND BACKGROUND
The globalization of business is driving many
manufacturers to try optimizing the total systems
(Min, H. and Zhou, G., 2003). This trend brings the
idea of supply chain, which is to optimize not only
the plant operations but also the whole activities from
suppliers to customers. As a result, manufacturing
companies are migrating from separated planning
processes toward more integrated planning processes
to provide high quality products, on time and at
lower costs.
Although numerous integration schemes have been
developed, the decisions taken among tactical and
operational levels play a vital role towards
optimization of the overall manufacturing
performance (Alvarez, E. 2007). These decisions are
related to determining the optimal quantity to be
produced from each type of products, when it should
be produced, how much to store in at each time
period, and in which order the jobs should be loaded
on the production stage(s) to get the optimal
production schedule.
Integration of production planning and scheduling is
one of these schemes that support the total
optimization (Silver, E. et al. 1998). Production
planning and scheduling are interrelated in the
assignment of factory resources to production tasks.
Hence, they should be solved concurrently. From
mathematical modeling view point, the problem has
more complexities due to the alternative machines
and alternative operations sequences.
After reviewing the production planning and
scheduling models characteristics, conclusions could
be drawn concerning each of these important
characteristics. These characteristics will be reviewed
in brief.

2. 1.1. Type of Production Processes
There are four broad classes of production processes:
job shop, batch flow, assembly line, and continuous
process. The differences among them have important
implications on the choice of the production planning
and scheduling system (Silver, E. et al. 1998). For
long years, continuous operations have been the most
prevalent mode of processing. In recent years,
however, there has been a renewed interest in batch
process for a variety of reasons. The most appealing
feature of batch process is their flexibility in
producing multiple products in a single plant through
sharing of process equipment (Burkard, R., et al.
2002). The batch operations are economically
desirable, especially when small amounts of complex
or even when a large number of products is made
using similar production paths (Stankovic, B., and
Bakic, V., 2006).
Batching is the process of transforming some product
or mix of products on a machine into different
products, and the amount of the products processed
as a single operation/job by that machine is called the
batch size. To satisfy each short term customized
demand, production lines of the facility can vary
substantially over time, and batches need to be
scheduled (batch scheduling) on equipments or
machines with various batch sizes (batch sizing)
during a short time period.
In a batch manufacturing environment, products are
released to the production system in batches of one
or more parts. For each batch, the production
sequence and processing times at each workstation in
the sequence are known. The batch is regarded as one
unit, which is each operation at each stage completes
the entire batch parts before any of the material is
moved to the next stage.
A batch process is frequently found in consumer
goods manufacturing processes, food processing,
chemical manufacturing, oil refining and
pharmaceutical industries. It is one of the complex
and important problems faced by a wide variety of
processing industries. In batch process industries it is
difficult to predict the completion time or makespan,
of a set of jobs. It is intermittent process that consists
of a collection of processing. Batches of the various
products are produced by scheduling a set of
processing tasks or operations like reaction, mixing
or distillation on multiple equipments/machines.
Batch scheduling is mostly concerned with the
optimal allocation of resources to tasks and optimal
scheduling of tasks to meet a given demand schedule
(Damodaran, P., and Srihari, K., 2004).
Planning and scheduling of batch process problems
have been considered a very long time ago and still
under research. Scheduling groups of jobs as a batch
is a subject that has received growing interest, due to
the desire for exploiting economies of scale (Mazdeh,
M., et al. 2007). These features motivated this work
to address the batch process industries as an
important type of production process.
1.2. Setup/Changeover Time
Considerations
The main time components through production
environments are processing or serving time, setup
time and changeover time. Setup includes work to
prepare the machine, process, or bench for product
parts or the cycle. Changeover is the process of
converting a line or machine from running one
product to another. Changeover times can last from a
few minutes. The terms setup and changeover are
sometimes used interchangeably however this usage
is incorrect. Setup is only one component of
changeover.
Jobs are activities to be done. A job may depend on
another job. One type of dependency occurs when
one job must precede another. Another type of
dependency occurs when the time needed for a job
depends on the previous job processed. This is
typically called a sequence dependent setup time. If
setup times are not sequence-dependent they can be
included in the processing time. Jobs are assumed to
be independent unless otherwise stated. If a job must
be processed by more than one machine, the job can
only be processed by one machine at any given time;
it cannot be done simultaneously with another job.
Machines process jobs. The machine environment is
broken into several classes:
 Single machine, there is only one machine
and all jobs must be processed on it. The
machine can be processed at any time. Once
a job has been processed by the machine, it is
completed. Mazdeh et al. (2007) formulated
their model to schedule groups of jobs on a
single machine with a batch delivery output.
 Several machines that can do the same
process on jobs are called parallel machines.
A job can be processed on any of the
machines, and once processed by one
machine, it is completed. All parallel

3. machines are identical (Souayah, N., et al.
2007). The time to process a job on one of
several identical machines is independent of
which machine does the work. The shop
floor is arranged in parallel lines to produce
efficiently high volumes (Cunha, A., and
Souza, M., 2008). Omar and Teo (2006)
considered at their problem the scheduling of
jobs on a set of identical parallel machines.
The jobs produced as product families which
make it sequence dependent setup every time
a job is switched from one family to another.
 A flow shop consists of different machines.
Each job must be processed by each machine
exactly once. All jobs have the same routing.
They must visit the machines in the same
order. A flexible flow line consists of several
processing stages in series. These stages may
be separated by finite inter stage buffers,
where each stage has one or more identical
parallel machines (Sawik, T., 2000). The
flow shops are flexible in the sense that a job
can be processed once by any of the identical
machines at each stage (Babayan, A., and
He, D., 2004).
 A job shop is more general than a flow shop,
each job may have a unique routing, and
each job has its own individual flow pattern
through the machines which is independent
of the other jobs. Each machine can process
only one job and each job can be processed
by only one machine at a time (Jain, A., and
Meeran, S., 1999). Number of jobs and
machines influence the complexity of the job
shop scheduling problem.
 Open shops are job shops in which jobs have
no specified routing.
A review of scheduling models which take setup into
considerations was provided by Allahverdi et al.
(1999). They noticed that the majority of scheduling
research assumes setup as negligible or part of the
processing time. This assumption simplifies the
analysis and/or reflects certain applications. Some
approaches consider that setup time exists, but the
average of the setup time is added to the processing
time. They classified scheduling problems into batch
and non-batch, and sequence-independent and
sequence-dependent setup.
They highlighted that when setup cost is directly
proportional to setup time, a sequence that is optimal
with respect to setup cost is also optimal with respect
to setup time. Their survey on setup considerations
furthermore considered sequencing problems
regarding the following characteristics:
 Batch setup where jobs are grouped into
batches and a major setup is incurred when
switching between jobs belonging to
different batches, whereas a minor setup is
incurred for switching between jobs within
the batches.
 Sequence dependent setup: Including setup
cost/time that depends on the succeeding job
gives the possibility to further improve the
sequence.
 Setup time separable from processing time:
The case in which setup time is separable
from processing time leads to the possibility
of further reducing the total processing time.
James et al. (2003) stated that revising the MPS to
improve plant performance is critical in process
industries with sequence dependent changeovers.
Plant performance is defined in terms of process
changeover time, total shortages, and finished goods
inventory.
The design of APPS models will be more accurate
when involving setup time. Supithak et al. (2007)
studied the setup time effect through the scheduling
models. They presented an algorithm, based on the
use of the assignment problem, to optimally solve the
problem with zero setup cost and another one for the
problem with setup cost. They noticed that the
scheduling models will be more efficient when the
setup time is considered. Also, Fakhrzad and Heydari
(2008) developed a mathematical model with the
objective of minimize the sum of the earliness and
tardiness costs. They used three heuristic algorithms
to solve their problem. They considered the setup
times for each job which was defined by the
manufacturer in their model. They concluded that the
setup time consideration leads to more realistic
results.
1.3. Schedule Output
A schedule provides the order in which jobs are to be
done. It allocates time intervals on one or more
machines to each of one or more jobs. A sequence
only lists the order in which jobs are to be done. In
other words, a sequence can include jobs that are yet
to arrive at a work center.
Some schedules consider assignment only without
sequencing depending on the type of production
process. In product layout for example, the sequence
of operations or tasks which jobs or products should

4. route is an input to the schedule not an output. The
sequencing problem appears when variations of the
same basic product are produced in the same
production line. The sequence here is an output
where the sequencing problem determines an
appropriate order for the jobs to be processed and the
shortest possible time to accomplish these jobs is
called the makespan.
The sequencing problems directly affect the due date
limits of the jobs which is an important performance
measure used to evaluate the efficiency of the
schedule output. Johnson, 1954, one of the pioneers,
proposed a solution that solves the case of
sequencing jobs with optimality, known as the
Johnson-rule. Johnson first proposed an efficient
algorithm which guaranteed optimality in a two-
machine flow-shop problem (Hong, T. et al. 2007).
1.4. Schedule Type
There are two main types of generated schedules.
They are static and dynamic schedules. In static
scheduling all the scheduled orders are available for
processing immediately at the current time. Once the
production sequences are defined, no change during
operations is assumed. In this type of problems the
main objective of the production schedule is to
achieve the due dates of the orders. Otherwise, in
dynamic scheduling new orders will arrive over time
and scheduled after arrival. In this type of problems
the main objective of the production schedule is to
minimize the slack of orders i.e. the difference
between the times until the orders due dates and their
remaining processing times.
According to this classification, two types of
production planning problems are identified:
incremental planning which aims to design a
schedule for the incoming orders without affecting
the schedules for the existing orders in static
scheduling problems and regenerative planning
which aims to regenerate a schedule for the existing
orders as well as for the new orders in dynamic
scheduling problem (Silver, E. et al. 1998).
1.5. Scheduling Performance Measures
There are many performance measures used to
evaluate the efficiency of the operations schedule.
Some of these measures are directly related to the
time that jobs spend in the shop such as the Work in
Process (WIP) inventory level, the flow time and the
makespan. The flow time is the amount of time a job
spends from the moment it is ready to processing
until its completion including waiting time prior to
processing. The duration in which all operations for
all jobs are completed is referred to as the makespan
(Jain, A., and Meeran, S., 1999).
Other performance measures are relative to each job
due date. These include lateness the amount of time a
job is past its due date, and earliness; the amount of
time a job is previous its due date.
Gordon et al. (2002) noticed that the facilities
managers must select an appropriate scheduling
approach that will provide cost-efficient running of
the factory, and meet the due dates of customers
order by consider jobs earliness and lateness
penalties which is motivated by the just-in-time
concept (JIT), which had been developed in the
1980s, where the globalization impacts began to take
place.
Due to the growing interests in JIT production
strategy in industry, planning and scheduling with
earliness–lateness penalties has received increasing
attention (Chen, K., and Ji, P., 2007). In JIT,
inventory is minimized and scheduling problems
began to diminish, as the cooperation with the
suppliers increased. This approach requires only the
necessary units to be provided with the necessary
quantities, at the necessary times. Producing one
extra unit is as bad as being one unit short (Cunha,
A., and Souza, M., 2008). The scheduling problems
involving due dates are of permanent interest
(Supithak et al., 2007). Many researches considered
the jobs due date as a performance measure through
their research.
Moon et al. (2002) presented an integrated process
planning and scheduling framework approach with
objective of minimizing total lateness in multi-plants
supply chain. They carried out the numerical
experiments and demonstrate the efficiency of the
proposed approach.
2. THE PROPOSED MODEL
In order to consider the characteristics of the
planning decisions for batch process, the APPS
problem is divided into two sub-problems: the
Master Production Schedule (MPS) and the
Operations Schedule (OS). Once the MPS is
determined, it triggers all other activities related to
the OS. The proposed APPS model aims to design a
schedule for the incoming orders without affecting
the schedules for the existing one. The batch process
is based on a short scheduling time period (typically

5. one week), so the static scheduling has an advantage
of MPS stability during the planning period.
The proposed APPS model has been developed to be
used as an automated Decision Support System
(DSS). It helps determining the optimal MPS and the
optimal OS for the production facility. The model
addresses a deterministic demand environment for
production systems with multiple production stages
and batch processing restrictions.
The determination of the MPS is a complex
operation. The MPS is the aggregate planning tool
that determines what item to be produced, when, and
in which quantities. The MPS gives initially the
material, capacity, and demand constraints and with
objectives of minimizing cost or maximizing profits.
The proposed DSS will make the MPS generation
task much faster. Also, the optimal schedule is a
complicated issue that takes the outputs of the MPS
and determines those decisions. All this should be
determined in an automated manner using the DSS
tool that was developed. The APPS model provides a
systematic approach to production planning and
scheduling problems solving. It emphasizes
qualitative information that enables managers to
answer "what-if" questions which are related to the
tactical and operational decisions.
2.1. The APPS Model Problem Definition
Batch processing is a multi stage industry. There is a
known set of products produced in batches. Each
batch consists of a predetermined quantity of similar
products. Another set is for the production stages.
Each batch should pass through each stage to be
accomplished with a well known sequence and
targeted due date. The sequence of stages that a batch
should follow, the route, is provided by a process
plan. Also, the capacity of each stage for each batch
is known. Some production related issues are
determined in advance, such as the processing times,
setup times for each batch at each stage and ready
time for each production stage. Figure 1 illustrates
the APPS model configurations.
The main objective of the proposed APPS model is
to minimize the total cost associated with a process
plan. Minimizing the overall costs include
manufacturing costs, idle time costs for nonworking
time periods, holding costs for a quantities which are
produced to be stored as a safety stock, and penalty
costs for a tardy batches which are accomplished
after its due date.
Figure 1 The proposed APPS model configuration
The required output is the optimal quantities from
each product to be produced, in order to fulfill the
customers' needs within a certain service level and in
time. Also, the optimal amounts of inventory, to be
sorted at each time period, are to be determined.
Other than that, the optimal schedule; loading and
sequencing of the different products in form of
batches at the different stages, is a complicated issue
that takes the outputs of the MPS as an input to
determine these decisions. The OS, with batches start
and finish times, is the main output from the
proposed model.
2.2. The APPS Model Assumptions
In the design of the model, the following
assumptions are made:
 The customer demand from each product is
deterministic and well known beforehand for
each period.
 Backlogging and outsourcing are not
allowed.
 The required quantity from each batch is
considered as a job.
 Although batch splitting may be possible,
this model assumes that this is not allowed.
This due to the nature of the batch processing
systems used mainly for food processing.
 The setup time of each batch is sequence
independent.
 All the parameters are deterministic and
known in advance.
 There is a predetermined amount of
beginning inventory for each product given
in terms of batches.
 All required materials are assumed to be
available when needed.
Batch flow
Stage
1
Stage
2
Stage
K
Product 1
Product 2
Product I

6.  The generated schedule for an existing order
is not affected by the incoming orders.
 The process route for each product is
provided.
2.3. The APPS Model Formulation
The MPS model is formulated as follows:
Notation
I set of products, i = {1………I}
K set of stages, k = {1……….K}
T set of periods, t = {1……….T}
 customer service level
i
 production cost per product i
(L.E./batch)
i
 holding cost per product i, when stored
for one period (L.E./batch)
Uk ready time of stage k equipments
(minute)
Bi beginning inventory from product i at
period one (batch)
Eit safety stock inventory from product i
in time period t (batch)
Gik setup time for product i in stage k
(minute)
Rik processing time for product i in stage k
(minute)
Nkt total available time for stage k at time
period t (minute)
Dit demand of product i at time period t
(batch)
Decision variables
Ait average inventory of product i in time
period t (batch)
Pit total ending inventory of product i in
time period t (batch)
Qit quantity of product i produced in time
period t (batch)
Objective function

 


I
i
T
t
it
i
it
i A
Q
Z
Min
1 1
)
( 

Subject to
it
it D
Q 
 t
i,
 (1)
it
it
t
i
it
it E
P
P
Q
D 


  )
1
(
}
.......,
,
3
,
2
{
, T
t
i 
 (2)
it
it
i
it
it E
P
B
Q
D 


 1
, 
 t
i (3)
2
)
1
( it
t
i
it
P
P
A



}
.......,
,
3
,
2
{
, T
t
i 
 (4)
2
it
i
it
P
B
A

 1
, 
 t
i (5)
it
it E
P  t
i,
 (6)





I
i
ik
ik
it
k
kt R
G
Q
U
N
1
)
( t
k
i ,
,
 (7)
it
it P
Q , are integers t
i,
 (8)
0
, 
it
it P
Q t
i,
 (9)
The objective function of the MPS model is to
minimize the total cost along the planning horizon.
The different cost elements are the total production
costs and the total inventory holding costs. The
holding cost is calculated based on the average
inventory units in each period. This is justified by
using small time periods, typically one week. The
introduction of this cost element and all other
elements ensures the generality of the model.
The demand constraint set (1) ensures meeting the
customers' demand to a certain level. The customer
service level here refers to the minimum demand
percentage to satisfy. This service level can easily be
changed according to customer requirements, the
company policy or the required amount of customer
satisfaction. In addition, this service level makes the
model mathematically more likely to obtain a
feasible solution, instead of the rigid demand
constraints, and makes the model a flexible decision
support tool.
Constraint sets (2) and (3) are used to balance the
total amounts produced from the products at any time
period to satisfy the required demand. For each
product, these sets of constraints ensure that the
required demand at a time period is equal to the
amounts produced through the production stages in
addition to the inventory quantities left from the
previous period subtracted from these currently
required and the safety stock amount. Constraint set
(3) deals with the demand of the first period,
indicating that it can be only fulfilled from the initial
inventory already exist at the beginning of the
planning horizon. The balance for the rest of periods
is presented by constraint set (2).
Constraint sets (4), (5) and (6) introduce the issue of
inventory which acts as balance constraints. In this
case, the amount of average inventory at any period

7. from a certain product is equal to the average of the
amount of inventory from that product present in the
previous period, in addition to the amount of that
product held as a stock through the same period.
Constraint set (4) deals with the average inventory
stored in any period starting from the second period.
Constraint set (5) deals with that inventory stored
from each product type at the first period, indicating
that it is equal to the average of inventory already
present at the beginning of the planning horizon from
each product, in addition to the amounts which will
be stored from that product in the first period of
production. Constraint set (6) ensures that the total
amount of inventory at any period from any product
should be greater than or equal to the economic
production quantity. The average inventory holding
amount is based on the holding time cost. Figure 2
illustrates the case of three periods.
Figure 2 Illustration of inventory in three periods
Because most of batch process industries are fast
moving consumer goods, the holding cost was
negligible due to its small value through the most
reviewed models. In the proposed APPS model the
holding cost is considered. As the holding cost is not
only related to the holding quantity, but also is
related to the storage space or volume, which is
critical in the fast moving consumer products.
Constraint set (7) ensures that the total available
production time at each stage at any time period
should cover the total required time for production at
each stage. The total required time at any time period
is a combination of three components: the ready time
of each stage, the setup time of each batch at each
stage, and the processing time at each stage of each
product. It presents the capacity constraint for
production. The availability of the overall capacity of
all production stages is guaranteed by checking the
availability of each stage individually.
Constraint sets (8) and (9) are the integer and non
negativity constraints respectively. As for the integer
variable Ait, it is already ensured to be non negative
from constraint sets (4) and (5).
The output from the MPS model is the optimal plan
which determines the optimal quantities to be
produced and held from each product as a form of
batches at each stage in all periods. The output is
disaggregated in order to develop the operations
schedule. It presents the optimal loading sequence of
production that should be followed. The objective of
the operations schedule is to maximize the resources
utilization.
The OS model is formulated as follows:
Notation
I ,J set of products, i = {1………I}, j =
{1………JI}
K set of stages, k = {1……….K}
M a very large number
 idle cost per unit time (L.E./batch)
 lateness cost per unit time (L.E./batch)
Fi required quantity of product i (batch)
DDi due date of product i (minute)
Uk ready time of stage k equipments
(minute)
Nk total available time for stage k
equipments (minute)
Gik setup time for product i in stage k
(minute)
Rik processing time for product i in stage k
(minute)
Decision variables
Ci completion time of product i (minutes)
Ei earliness time of product i (minutes)
Li lateness time of product i (minutes)
Sik start time of product i in stage k
(minute)






otherwise
k
stage
in
sequance
in
j
product
preceeds
i
product
if
xijk
0
1
Objective function






 






I
i
i
K
k
k
ik
ik
I
i
K
k
i
K
k
k
L
U
R
G
F
N
Z
Min
1
1
1 1
1
.
}
)
(
{
.


Subject to
k
ik U
S  k
i,
 (1)
)
1
(
)
( ijk
ik
ik
i
ik
jk x
M
R
G
F
S
S 




k
j
i ,
,
 (2)
Q11 Q12 Q13
B1 P11 P12 P13
E11 E12 E13
First
Period
Second
Period
Third
Period

8. ijk
jk
jk
j
jk
ik x
M
R
G
F
S
S 


 )
(
k
j
i ,
,
 (3)
1

 jik
ijk x
x k
j
i ,

 (4)
0

ijk
x k
j
i ,

 (5)
)
( )
1
(
)
1
(
)
1
( 

 

 k
i
k
i
i
k
i
ik R
G
F
S
S
}
,
.......
,
3
,
2
{
;
, K
k
k
i 
 (6)





K
k
ik
ik
ikt
ik
i R
G
F
S
C
1
)
(
K
k
i 
 , (7)
i
i
i
i DD
L
E
C 

 i
 (8)
i
i
i L
E
C ,
, are integers i
 (9)
0
,
, 
i
i
i L
E
C i
 (10)
ijk
x
is binary k
j
i ,
,
 (11)
0

ik
S k
i,
 (12)
The objective function of the OS model is to
minimize the total cost along the scheduling horizon;
typically one week. These costs include the total idle
time costs, and product lateness costs. Since the sum
of setup times, processing times from all batches at
all stages, and the sum of ready times required to
prepare all stages are constant, minimizing the idle
time cost is equivalent to minimizing the flow time
cost or maximizing production stage utilization.
Also, the penalty costs associated to lateness of each
batch will be minimized to ensure on time delivery of
batches. At any time period t, the produced quantity
of the product Fi equal the optimal quantity produced
at that time period Qit which was obtained at the MPS
stage.
Constraint set (1) provides that the product can only
start to be produced at each stage after the stage will
be ready to load. So, the start time of any product
should be at least equal to the stage ready time.
Constraint sets (2), (3), and (4) guarantee that no
products can be processed simultaneously in the
same stage. The start time of any product at a stage
must be later the completion time of any other
product that preceding it. This condition is ensured
by constraint set (4) which introduces the binary
constraints for the binary variables. In constraint set
(2), if product j succeeds the product i in sequence,
then the start time for product j should be greater
than or equal to the start time for product i. The
difference between the two start times is related to
the setup and production time for the product i. In
this case the value of the binary decision variable xijk
equals one. Otherwise, the product j precedes the
product i in sequence and the start times are ensured
by constraint set (3). Constraint set (4) ensures that
product i can only precede or succeed product j in
sequence and not both of them; if a product has been
chosen in one stage of the sequence, it can not appear
again in any other stages. A product has to be
processed by only one stage at a time.
Constraint set (5) controls the start time for the same
product. It is not logic to switch from a product type
to the same product type. Switching is only between
different product types.
Constraint set (6) ensures that the stage can only
process one product at any given time; it cannot be
done simultaneously with another product. The route
of products through the production stages is fixed.
The product can start the new stage only when it
completes the current one. The total starting time of
each product at a stage exceeds, at least, its starting
time in the previous stage plus setup time and
processing time in this stage.
The main output from the OS model is the Gantt
chart which is a graphical presentation for the
operations schedule using the previous outputs.
Figure 3 illustrates a schema of the OS output in the
APPS model. In this chart, the start times of all
products with their optimal sequence and the
completion time of each of them are presented.
Constraint set (7) presents the production makespan
of each product by calculating the completion time.
The completion time of any product is given by the
summation of product start times at all stages, total
setup times and processing times.
Constraint set (8) defines the earliness and lateness of
each product, respectively with respect to the defined
due date. While constraint set (9) is the non
negativity constraint for completion time, earliness
and lateness respectively.
Constraint set (10) is the binary constraint for the
binary variables; xijk is a decision variable equal one
if product i precede product j at stage k and zero
otherwise. As for constraint set (11), it is the non
negativity constraint for the continuous decision
variables.

9. Figure 3 A schema of the OS output in the proposed
APPS model
3. THE APPS MODEL ADVANTAGES
From the previous explanation, the following
advantages and contributions of the proposed APPS
model over the existing models in the literature are:
1. The APPS model is general in its
characteristics. It can be applied at any
industry with the batch process features. The
batch process industry are present in a wide
range of industries such food industries,
chemical manufacturing, oil refining and
pharmaceutical industries. It prevents the
flexibility through the production system.
2. It is suitable for the companies that apply JIT
philosophy. It can handle the case of a
company that considers satisfying customers'
need on time with a minimum associated
cost. The APPS model considers both of the
earliness and the lateness cost.
3. It addresses most production aspects, which
are the production time, the setup time, the
preparation time, and the idle time. This is
very important in many industries, especially
in batch production where setup costs are
critical. Furthermore, it considers the
production capacity limitations.
4. The proposed DSS will make the MPS
generation task much faster and will
guarantee an optimal MPS and optimal OS
which is not possible in traditional methods.
5. It provides both tactical and operational
decision support. The tactical decisions
include the optimal production quantities and
inventory amount at each period, while the
operational ones include the optimal
scheduling and loading decisions for the
optimal batch sizes.
6. The proposed model optimizes the total
system, not only the plant operations but also
the whole activities from a supplier to a
customer by integrating the MPS and OS
decisions to provide high quality and in time
products at lower cost.
4. INDUSTRIAL CASE STUDY
The verified model was implemented in a real world
case study. The case study was conducted in the
Egyptian subsidiary of one of the world's leading
companies in the field of fast moving consumer
goods. This company has a strong and well
differentiated portfolio of global and regional brands
of foods as well as Home and Personal Care (HPC)
brands, which are positioned to meet the needs and
aspirations of their consumers across a variety of
price points, segments and channels. Twelve of their
brands have global turnover in excess of €1 billion.
According to the company's statistics, they are one of
the largest suppliers to the food, home care and
personal care service industry. They have operations
in around 100 countries, and their products are sold
in about 80 more and have more than 250,000
employees. This company has a turnover in 2007 of €
40 billion, by product area as percent of turnover.
The food goods present 54% from this total turnover
value in 2007.
4.1. Current Situation and Description of
the Company's Problem
Currently, in Egypt, the company has two plants, one
for HPC goods located in 6th of October industrial
city and another for food goods located in Borg
Elarab industrial city and two warehouses. The
warehouses are located at 6th of October industrial
city to be near plant in 6th of October industrial city
for HPC goods and Alexandria, so as to be near plant
in Borg Elarab industrial city to store the food goods.
Twenty product batches are produced at the plants,
shipped to the warehouses as intermediate points and
then shipped again to store in one of a three large
stores: Cairo, Alexandria, and Assuit.

10. Borg Elarab industrial city plant contains three
factories. One of these factories is a culinary factory
where this case was studied. This factory is the
company's number one brand. It is a limitless global
brand with passion for food and its heart. It is the
world's leading culinary brand, the biggest food
brand with a strong presence in over 80 countries and
a product range including soups, sauces, bouillons,
noodles and complete meals with sales of around €
3.5 billions annually.
The company wants to develop a DSS tool to help in
determining optimal MPS and optimal OS in their
food plant. In addition, the company wants to
determine the optimal quantities from each batch to
be shipped from each plant to each warehouse and
then to each store to satisfy the demand over the
planning horizon, the optimal quantities from each
batch to be stored as a safety stock to avoid the
uncertainty in customers demand, and the best
sequence so that to minimize the total costs,
including the total production cost, the total
inventory holding cost, the total lateness cost, and the
total required production time cost which includes
the processing time, the setup time, which is batch
sequence independent, and the ready time which is
stage dependent. All required date inputs were
provided by the company.
The proposed APPS model has been implemented on
the powder department which only 12 SKUs
produces on it. The route of each batch is: mixing,
filling, and packaging. In the mixing stage, the main
components of each batch are mixed together to get
the final product composition.
The company uses six weeks time period and a week
as time bucket. The required Master Production
Schedule (MPS) is generated every month while the
Operations Schedule (OS) is generated weekly. The
MPS is then translated into specific planned start and
due dates for all products and a detailed OS. This
study was conducted for 6 time periods (T=6) in the
MPS and the OS was generated only for the first
week. The MPS should be revised weekly to
compare between the planned and actual produced
batches.
4.2. Case Study Results and Discussion
The APPS model was used to solve this case study.
Using LINGO®
optimization package, this industrial
case study was solved in 8 hours on a hardware
having a Pentium IV processor with 3.2 GHz, 2 MB
cache memory and 1 GB physical RAM. The
problem includes 915 variables, out of which 540 are
integer ones and 1,316 constraints. The obtained
optimal solution for the first week is L.E 2,176,475
as a sum of ZMPS = L.E 2,161,575 and ZOS = L.E
14,900. Dividing this value to its cost elements yields
the pie chart in figure 4. It is obvious that the
holding, idle times and lateness costs constitute a
considerable portion of 22% from the total cost. The
cost structure for this case study is the production
costs, holding costs which present 10%. This
percentage is a total of 5% from the value of
production costs and the rest as a result of renting
cost.
78%
1%
7%
14%
Production Costs
Holding Costs
Lateness Costs
Idle Time Costs
Figure 4 Percentages of cost elements for the optimum
objective function value
The optimum solution involves the production
related decisions. Figure 5 represents the quantities
produced in all of the six periods from the 12
batches.
In addition, the customers' needs are satisfied for all
batches in all periods. This was ensured by the
balance constraints. The balance constraints were
also satisfied for all periods. The results of the model
involved determining the quantities hold from each
batch at each time period.
The solution also yields the scheduling decisions.
The model describes the product sequence at each
production stage. This sequence is determined as a
result of the binary decision variable xijk. Table 1
show these values. It is obvious that there is no
switching between of the similar types of batches.
The Gantt chart is illustrated in figure 6. The optimal
makespan for these batches is 7,666 minute (around
127 hour). The Gantt chart presents the start time of
each batch at each stage.
5. CONCLUSION
The APPS model is designed for the case of batch
process industry. The APPS model attempts to cover
important characteristics identified from the

11. comprehensive review of literature. The model has
been tested, verified, and then applied in a large scale
case study.
 The proposed APPS model provides a
systematic approach to production planning
problems in batch process industries by
emphasizing qualitative information related
to the production planning and scheduling
issues.
 The model is considered as a decision
support tool for production planning and
operations scheduling by helping the
decision maker in the production, inventory,
loading and sequencing decisions.
 It captures most of the batch process industry
characteristics, such as: setup time, multiple
stages, one time processing, customers'
service level and due dates for the required
batches.
 Most of the cost elements through the
production planning and scheduling activities
were taken into consideration, such as:
production cost, holding cost, idle time cost,
and lateness cost. All of these elements are
directly related to the total efficiency and
utilization of the studied system.
 The model generates the master production
schedule and operations schedule.
 It is flexible enough to deal with problems of
different sizes. Because the batch process
industry has not a wide range of variety of
products or even production stages, the
model was tested till the 30 product type and
10 production stages.
 The problem instances were solved
successfully using LINGO®
till dimensions
of 30×30×10 in a sensible time. It was solved
in about 33 minutes using a Pentium IV, 3.2
GHz, 2 MB cache memory and 1 GB
physical RAM computer.
 Exact algorithms are more convenient as
solution tools for the addressed problem;
therefore they were used successfully via the
optimization package LINGO®
to solve the
proposed model.
 There is a significant increase in the total
cost by 12.5% weekly compared with the
optimal value.
ACKNOWLEDGMENT
Acknowledgements are due to Unilever Mashreq
Egypt for providing the required data for the case
study.
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13. Table 1 Batches' sequencing decision variable value xijk for the first week
Batch j
1 2 3 4 5 6 7 8 9 10 11 12
Stage k 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
Batch
i
1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
3 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0
4 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0
6 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0
7 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
9 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0
10 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0
12 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0

14. Batch
0
50
100
150
200
250
300
350
400
Period (Weeks)
Produced
Quantitied
(Batches)
12
11
10
9
8
7
6
5
4
3
2
1
Figure 5 Quantities produced from each batch in the all time periods (batch/week)
Figure 6 Gantt chart for the first planning period
Time (* 103
minutes)
Batch 2
Batch 4
Batch 8
Batch 12
Batch 9
Batch 3
Batch 11
Batch 10
Batch 6
Batch 1
Batch 5
Batch 7
Stage
Mixing
Filling
Packaging
0 1 2 3 4 5 6 7 8
1 2 3 4 5 6