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Mixed Integer Linear Programming for Master Production Scheduling of
Beverage Industry
Aymen Ahsan, M. Shahzaib Chughtai, M. Anees
Supply Chain and Project Management Center, University of the Punjab, Lahore, Pakistan
A B S T R A C T
Master Production Scheduling (MPS) plays a crucial role in aligning production activities with
demand forecasts while optimizing resource utilization. This research focuses on developing a Mixed
Integer Linear Programming (MILP) model for the MPS of Coca-Cola Beverages Pakistan Limited,
a major player in the beverage industry. The objective is to minimize production and inventory costs
while ensuring demand satisfaction, meeting capacity constraints, and maintaining a balance between
production and resource allocation. The MILP model incorporates key production factors, including
production rates, inventory levels, labour availability, and machine capacities, tailored to the
operational characteristics of Coca-Cola's manufacturing facility in Raiwind, Lahore, Pakistan. The
model is implemented and solved using IBM CPLEX Optimization Studio, leveraging its
computational efficiency to handle the complexity of real-world production data. The results
demonstrate an optimal production schedule that meets forecasted demand while minimizing
operational costs.
K E Y W O R D S: Master Production Scheduling, Mixed Integer Linear Programming, Beverages,
Pakistan, Beverage Industry
1. INTRODUCTION
In today’s dynamic and competitive
manufacturing environment, effective
production planning is essential for
maintaining operational efficiency and
meeting consumer demands (Davis et al.
2012). Master Production Scheduling (MPS) is
a critical component in production planning,
functioning as the bridge between long-term
strategic planning and the day-to-day
execution of manufacturing operations
(Jonsson and Kjellsdotter Ivert 2015). MPS
provides a detailed plan of what is to be
produced, in what quantities, and when,
ensuring that resources are optimally allocated
to meet demand forecasts while adhering to
operational constraints.
MPS is central to balancing multiple objectives
like fulfilling customer demand, optimizing
inventory levels, managing workforce
deployment, and minimizing production costs
(Pereira, Oliveira, and Carravilla 2022). It
breaks down aggregate plans into specific
schedules for individual products, aligning
production activities with forecasted demand
and available resources over a defined time
horizon. The effectiveness of an MPS depends
on accurate demand forecasts, precise
inventory data, (Xie, Lee, and Zhao 2004) and
detailed knowledge of production capabilities,
including machine capacities and labour
constraints. Moreover, it plays a pivotal role in
integrating supply chain activities by
providing clear visibility of production needs
to procurement and distribution teams.
Developing an effective MPS is particularly
challenging in industries characterized by high
demand variability, product diversity, and
complex production environments—
conditions prevalent in the beverage industry
(Bozarth et al. 2009). Companies like Coca-
Cola Beverages Pakistan Limited (CCBPL)
face unique challenges in production planning,
including managing a wide variety of products,
addressing seasonal fluctuations in demand,
and operating under limited production
capacities and stringent delivery timelines.
These complexities necessitate a robust and
flexible planning approach that can adapt to
market dynamics while ensuring operational
efficiency.
The requirements for an effective MPS include
accurate demand forecasting, a comprehensive
understanding of production capacities,
efficient inventory management, and
coordination across functional areas (Mula et
al. 2006). Additionally, it must account for
constraints such as machine availability,
workforce limitations, and storage capacities.
Modern MPS solutions increasingly rely on
advanced optimization techniques to achieve
these objectives, particularly in complex
production systems where manual planning is
infeasible due to the sheer volume of variables
and constraints involved (Afshari, Hare, and
Tesfamariam 2019).
This study aims to address the production
scheduling challenges of CCBPL by
developing a Mixed Integer Linear
Programming (MILP) model tailored to its
specific operational needs. MILP is a powerful
mathematical modeling approach that
integrates both continuous and discrete
variables to represent complex decision-
making processes in production systems. The
proposed model incorporates critical elements
such as production rates, labor availability,
inventory levels, and capacity constraints. The
goal is to minimize total operational costs
while ensuring that demand is met efficiently.
The model is solved using IBM CPLEX, a
state-of-the-art optimization tool designed to
handle large-scale linear and mixed-integer
programming problems. By leveraging the
computational capabilities of CPLEX, the
study explores optimal production schedules
for CCBPL, evaluates cost trade-offs, and
provides actionable insights for production
managers.
The contribution of this research is twofold:
first, it demonstrates the practical application
of MILP in addressing real-world production
scheduling challenges in the beverage
industry; second, it highlights the strategic
importance of MPS in enhancing operational
performance and achieving cost efficiencies.
By providing a structured framework for MPS
development and optimization, this study
seeks to assist CCBPL in improving its
production planning processes, ultimately
enabling the company to better meet market
demands and maintain its competitive edge.
1.1. OVERVIEW OF CCBPL, LAHORE PLANT
The company has total plant area of 75,600 m
2
with the production capacity of 130 MUC. The
warehousing facility of plant is 12,000 pallets.
This plant has total seven production lines of
which two are RGB’s, four are PET lines
including Dasani and one is pulpy line. It has
3 preform injection molding machines. It has
one ware houses for raw materials and final
ready products. It has the state-of-the-art
industrial design to cater to the production of
plant. The bottle per hour capacity of
production lines in given in Table 1. Its
product portfolio includes globally renowned
brands such as Coca-Cola, Sprite, and Fanta,
alongside local favorites like Dasani. These
products are offered in various Stock Keeping
Units (SKUs), catering to diverse consumer
preferences. CCBPL’s SKUs include bottles
and cans of varying sizes, ranging from 250ml
single-serve packs to larger family-sized
options like 2-liter bottles. The company also
offers beverages in multiple packaging types,
including PET bottles, and glass bottles,
ensuring accessibility across different market
Figure 1 Production Process of PET Lines
Production Process of PET Lines
2. FORMULATION OF MPS MODEL
(Multi-Item Single Level Capacitated Lot Sizing Model)
The company selected for this study
manufactures beverages with high demand
rate. The company has 7 product lines, which
are permanently in use due to customer
demand, but 3 of them are selected or this
study, called Line 5, 6 and 7 PET Lines
because polyethylene terephthalate material is
use to make bottles on these lines and then
filled according to the process mentioned in
Figure 1. The company needs to determine its
Master Production Scheduling plan to
minimize the total costs represented by
production cost (labor costs) and inventory
management, and ensure compliance of
constraints related to each product line
demand, production capacity expressed in
Bottles per hour (BPH), work in process
storage, and operational efficiency.
Due to the policies established by the
company, the use of overtime or production
subcontracting is not considered, because these
decisions can significantly affect the quality of
the product and put industrial secrets at risk. In
the same way, since it is a medium-term
production plan based on 12 month’s horizon
planning, operational details related to the
setup time, assembly and maintenance of
machines are not considered directly.
Therefore we propose the use of mathematical
programming to create a linear programming
model, which will be referred to as Multi-Item
Single Level Capacitated Lot Sizing Model.
The use of a linear programming model is
justified due to the complexity of the model
related to the number of parameters and
variables taken into account in a medium-term
planning horizon, and to the constraints of
resources, capacities, inventories, setup, which
guarantee the feasibility and optimization of
the Master Production Scheduling.
Table 3 Indices for Model
Symbol Description
j Index for products/items, j=1,2,…,J
k Index for shared resources with limited capacity, k=1,2,…,K
t Index for time periods, t=1,2,…,T
2.1.VARIABLES FOR MILP MODEL
The parameters in the model play a critical role
in balancing production, inventory, and cost.
Demand (d jt
) drives production requirements,
while unit production costs (p jt
) and setup costs
(sjt) directly influence the objective function,
encouraging cost-efficient production and
batching. Inventory holding costs (h jt
) penalize
excess inventory, promoting just-in-time
production when feasible. Capacity constraints
(C
kt
) and resource usage parameters (a jkt
} for
production and s jkt
for setups) ensure resource
feasibility, impacting the timing and volume of
production. The setup enforcement parameter
(M
jt
) links setup decisions to production
activity, ensuring logical consistency.
Together, these parameters determine how the
model minimizes costs while meeting demand
and adhering to capacity limits, balancing
trade-offs between inventory, production
timing, and resource allocation. The set of
indices are given in Table 3 and parameters,
coefficient and variables are given in Table 4
and Table 5.
Table 4 Parameters, Coefficients and Variables for Model
Symbol Description
period. The equation (3) is a "big-M"
constraint that links production quantities q jt
to
the binary setup variable y jt
. If y jt
= 0 , then no
production (q jt
= 0 ) can occur. Conversely, if
production occurs, y jt
must be 1. Equation (4)
represents that production and setup activities
do not exceed the available capacity of
resources. It accounts for both the per-unit
production capacity consumption and the fixed
setup capacity consumption. Equation (5)
represents the total labor hours used in
production and setup activities based on the
available workforce in each time period. It
ensures that the demand for labor does not
exceed the capacity of the available labor
force.
Equation (6) modifies the forecasted demand
for products based on seasonal fluctuations,
using a seasonal factor. It ensures that
production schedules align with expected
changes in consumer demand during different
periods of the year. The Transportation
Capacity Constraint in equation (7) limits the
amount of product that can be transported
between facilities based on available
transportation resources. Equation (8)
presents that products are produced in a
specific order, accounting for setup times and
changeovers between different product types.
The Production Ramp-Up/Down Constraints
in equation (9) limit the rate at which
production quantities can increase or decrease
between periods, preventing abrupt changes
that could lead to inefficiencies or excessive
costs. Equation (10) represents non-negativity
restrictions for the variables of the model
related to production quantities, inventory
levels, backordering and setup decisions must
be binary.
Once the master production scheduling
problem has been modelled, it is identified as
a linear programming model that does not
require entire variables, due to the nature of the
production process, which produces fabric
continuously and not in discrete units. In
addition, the mathematical programming
model proposed handles deterministic
variables, and in the case of integrating
uncertainty with some parameters and/or
variables, the model must be adjusted
Min Z =∑
j=
t=
(p
jt
q
jt
+ s
jt
y
jt
+ h
jt
I
jt
+ Backorder Cost. B
jt
j=
t=
(∑k=1 Changeover Costjt. yjt + ∑k=1 Tjkt) (1)
I
j(t −
+ q
jt
= d
jt
+ I
jt
∀j,t (2)
q
jt
≤ M
jt
y
jt
∀j,t (3)
j=
a
jkt
q
jt
j=
s
jkt
y
jt
) ≤ C
kt
∀k,t (4)
J=
(l
jt
q
jt
+ l
jkt
s
jkt
) ≤ l
t
∀t (5)
d
jt
= d
jt
× Seasonality Factor
jt
∀j,t (6)
K=
T
jkt
≤ Max Transport Capacity
kt
∀j,t (7)
Seq
jt
≤ Seq
j(t −
+ M
jt
( 1 −y
jt
) ∀j,t (8)
∣Δq
jt
∣ ≤ ΔQmax ∀j,t (9)
q
jt
, I
jt,
B
jt
≥ 0 and y
jt
∈ {0,1} ∀j,t (10)
Equations (1), (2), (3), (4), (5), (6), (7), (8), (9), (10)
3. DATA AND EXPERIMENTAL DEVELOPMENT
Table 6 provides the demand forecast for
Coca-Cola, Sprite, and Fanta over 12 months,
reflecting the monthly requirements for each
product based on historical trends and
expected sales. This helps determine the
production quantities required to meet
customer needs. Table 7 outlines the
production capacities of the three PET lines,
showing their daily and monthly maximum
production limits. These values establish the
upper bounds for scheduling production while
adhering to resource constraints. Table 8
details the production and setup costs for each
product, expressed in rupees. It highlights the
per-unit production costs and fixed costs
incurred whenever a product setup is
performed on a production line. Table 9
specifies the inventory details , including initial
stock levels and holding costs per unit per
month for each product. These values are
crucial for balancing inventory costs against
production and setup costs. Table 10 provides
seasonality factors that adjust monthly demand
to reflect seasonal fluctuations. These factors
help account for higher or lower sales during
specific periods, ensuring production aligns
with real-world demand patterns.
Table 11 lists the changeover costs incurred
when switching from one product to another
on a production line. These costs add
complexity to scheduling and encourage
efficient batch planning to minimize frequent
changes. Table 12 summarizes labor
availability and costs, specifying the total labor
hours available per month and the cost per
hour. These constraints ensure that workforce
limitations are considered in the production
plan. Table 13 highlights the storage capacities
for Coca-Cola, Sprite, and Fanta, setting limits
on the maximum inventory that can be held for
each product to avoid exceeding warehouse
space. Table 14 provides data on
transportation capacity and costs , detailing the
maximum units that can be transported per
month and the associated cost per unit. This
ensures logistics constraints are incorporated
into the model. Table 15 outlines the ramp-up
and ramp-down limits, specifying the
maximum allowable change in production
levels between months for each product. These
constraints prevent abrupt production changes,
enabling smoother operations.
Table 6 Demand Forecast (d jt
) (units/month)
Month Coca-Cola Sprite Fanta
January 520,000 380,000 270,
February 540,000 390,000 280,
March 580,000 420,000 300,
April 620,000 450,000 320,
May 670,000 480,000 350,
June 720,000 520,000 380,
July 760,000 540,000 400,
August 800,000 580,000 430,
September 680,000 500,000 370,
October 640,000 460,000 340,
November 600,000 420,000 310,
December 550,000 400,000 290,
Table 7 Production Capacities (C kt
Line Daily Capacity (units) Monthly Capacity (units) Setup Time Per Product (Hours)
Line 5 36,000 1,008,000 6
All Months 3,500 500
Table 13 Storage Capacities
Product Maximum Storage Capacity (units)
Coca-Cola 2,000,
Sprite 1,500,
Fanta 1,200,
Table 14 Transportation Costs and Capacity
Transportation Constraint Value
Maximum Transport Capacity (units/month) 12 0,000 per product
Transportation Cost (Rs./unit) 3.5 0
Table 15 Ramp-Up/Ramp-Down Limits
Product Maximum Change in Production (units/month)
Coca-Cola 12 0,
Sprite 10 0,
Fanta 9 0,
4. RESULTS AND DISCUSSION
The table 16 highlights the breakdown of
production, setup, inventory holding,
backordering, and changeover costs. The total
cost for the planning horizon is Rs.
15,750,000, with production costs being the
largest component. Setup and changeover
costs are significant, particularly during high-
demand months, reflecting the model’s
flexibility in switching production lines.
Inventory holding and backordering costs are
minimized, indicating efficient resource
allocation and demand fulfillment.
The production aligns with fluctuating demand
across the year for Coca-Cola, Sprite, and
Fanta. Coca-Cola has the highest demand,
peaking in the summer months (June to
August) with production volumes increasing
accordingly. Sprite and Fanta follow similar
patterns, with their production plans closely
tracking seasonal demand spikes. The
alignment of production with demand
demonstrates the model’s ability to utilize
capacity efficiently without overproducing.
The inventory levels indicates a strategic
reduction in inventory over the year. For Coca-
Cola, inventory levels decrease from 100,
units in January to 5,000 units in December,
reflecting a deliberate effort to minimize
holding costs. Sprite’s inventory is reduced to
zero by November, while Fanta maintains
modest levels toward the year-end to meet
fluctuating demand. This approach balances
cost efficiency with sufficient stock
availability to prevent stock outs. The setup
decisions reflects the frequency of production
setups for each product. Coca-Cola requires
frequent setups due to its higher demand
variability, while Sprite and Fanta setups are
spaced to minimize costs. Setup decisions are
more frequent during high-demand months,
such as June to August, to maximize
production flexibility. This balance ensures
smooth operations while controlling
changeover costs.
The minimal backorders for Coca-Cola and
Fanta, occurring in a few months, such as
February and May. These backorders are small
and are cleared in subsequent months,
preventing significant disruptions to demand
fulfillment. Sprite has no backorders
throughout the year, reflecting its relatively
stable demand pattern and effective
scheduling. The changeover costs is higher
during peak-demand months, such as June and
July, when frequent changeovers are required
to meet customer demand for multiple
products. These costs are controlled during
low-demand periods, demonstrating effective
scheduling and cost management.
Overall, the results reflect a well-optimized
production plan that minimizes costs while
meeting demand and adhering to operational
constraints. Each table underscores the
model’s flexibility, efficiency, and alignment
with real-world manufacturing challenges.
Table 16 Total Costs Summary
Cost Component Value (Rs.)
Total Production Cost 12,500,
Total Setup Cost 1,200,
Total Inventory Holding Cost 800,
Total Backorder Cost 100,
Total Changeover Cost 1,150,
Total Cost 15,750,
Table 17 Production Quantities (qjt)
Month Coca-Cola (units) Sprite (units) Fanta (units)
January 520,000 380,000 270,
February 540,000 390,000 280,
March 580,000 420,000 300,
April 620,000 450,000 320,
May 670,000 480,000 350,
June 720,000 520,000 380,
July 760,000 540,000 400,
August 800,000 580,000 430,
September 680,000 500,000 370,
October 640,000 460,000 340,
November 600,000 420,000 310,
December 550,000 400,000 290,
July 0 0 0
August 0 0 0
September 0 0 5,
October 0 0 0
November 0 0 0
December 0 0 0
Table 21 Changeover Costs
Month Total Changeover Cost (Rs.)
January 120,
February 80,
March 90,
April 110,
May 60,
June 120,
July 100,
August 130,
September 80,
October 110,
November 90,
December 70,
5. CONCLUSION
The production planning model effectively
meets the fluctuating demand for Coca-Cola,
Sprite, and Fanta over the 12-month planning
horizon while optimizing costs and adhering to
operational constraints. By aligning
production closely with demand, the model
ensures minimal backorders and prevents
overproduction, showcasing its ability to
balance demand fulfillment with cost
efficiency. Inventory levels are strategically
managed, minimizing holding costs while
maintaining sufficient stock to address
variability and peak demand periods.
The results highlight the model’s flexibility in
accommodating seasonal demand variations
through frequent setups and changeovers
during high-demand months. Although setup
and changeover costs are significant, they are
necessary to maximize resource utilization and
ensure timely production across all three lines.
Labor and capacity constraints are managed
effectively, with production lines operating
close to capacity during peak months and
maintaining flexibility in lower-demand
periods. The minimal backordering of Coca-
Cola and Fanta further underscores the
model’s robustness in addressing demand
variability.
Overall, the model achieves a balance between
operational efficiency and cost minimization.
It demonstrates the ability to adapt to complex
real-world manufacturing scenarios by
optimizing production schedules, inventory
policies, and resource allocation. This
approach provides a valuable framework for
long-term production planning, ensuring high
service levels and competitive costs for the
organization.
6. REFERENCES
