Introducing the problem
Suggested Approach
Results and Discussion
Aggregate Production Planning systems for
low-demand, remote manufacturing systems
C. Charalambous1
1 Frederick
2 Olayan
S. Pericleous1
K. Fleszar2
Research Center, Cyprus
School of Business, American University of Beirut, Lebanon
September 2, 2011
Charalambous C. et al.
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Preliminaries
I
I
This work presents results generated by the ’Novel
Technologies for Production Planning in Flexible Supply Chain
Systems’ project which was co-funded by the European
Regional Development Fund and the Cyprus Government
through the Research Promotion Foundation of Cyprus,
DESMI 2008
Partners
I
I
Sadolin Paints (Cyprus) Ltd
Olayan School of Business - American University of Beirut
Charalambous C. et al.
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Introducing the problem
Suggested Approach
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Results and Discussion
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Motivation
I
In Cyprus, manufacturing units are facing increasing
challenges over the last decade
I
The manufacturing sector has been steadily shrinking
I
Motivation stemmed from the investigation of a paints
production plant in Cyprus
I
The main research goal is to provide analytical tools and a
mechanism to evaluate whether the presence of manufacturing
facilities is justified
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Challenges
I
Low volume market, difficult to exploit economies of scale
I
Cyprus is an island - high transportation costs (in essence, sea
transportation is the only viable solution)
I
Difficult to justify R&D investment to allow competition on
quality
I
Exports are difficult (again transportation costs)
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Opportunities
I
Small competition (price premiums on non-standard products)
I
Highly responsive environment with flexible production
systems
I
Capacity to create strategic partnerships with EU producers
and act as distributor
I
Difficult to make make-or-buy decisions as raw material
quantities are affected
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Solution Approach
I
Construct a MILP model that captures the key characteristics
of the system
I
Evaluate model’s performance under different demand
scenarios and parameter values
I
Identify common patterns in obtained results.
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Model main elements
I
Represent manufacturing system as a single unit
I
Capture transportation and quantity discounts features
I
Allow make-or-buy decisions
I
Use ’big-bucket’ (months) time units for aggregate planning
decisions and ’small-bucket’ time units (weeks) to capture
production behavior
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Domains
N
M
U
Nj
T
Tb
L
—
—
—
—
—
—
—
set of products (SKUs) present in the system
set of core raw materials
set of key product families present in the system
set of products belonging to product family j ∈ U
set of ’small-bucket’ time units (weeks)
T b ⊂ T set of ’big-bucket’ time units (months or seasons)
number of ’small-bucket’ time units covered by one ’bigbucket’ time unit
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Parameters
dit
rim
RPm
hi
gm
ajk
BSj
— forecast demand for product i ∈ N for time period t ∈ T b
— quantity of raw material m ∈ M needed to produce one
unit of product i ∈ N
— price of raw material m ∈ M
— holding cost for product i per unit per time period (calculated based on the average selling price of product i)
— holding cost for material m per unit per time period (calculated based on the average buying price of material m)
— setup time incurred if products from both product families
j ∈ U and k ∈ U, (j 6= k), are produced in the same time
period
— minimum production quantity on a period for products of
family j
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Parameters (continued)
SCj
PRi
— setup time on a period for products of family j
— plant production usage for producing one unit of product
i
u
— maximum desired utilization level
PCi — production cost of product i at normal rate (excluding
material costs and fixed costs)
OC — additional production cost per unit incurred when the
plant operates above desired utilization level
PPC — plant production capacity for one time period
PIC — plant total storage capacity
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Variables
pit
oit
wmt
IPit
IMmt
xjt
— normal production of product i ∈ N for time period t ∈ T
— production of product i ∈ N for time period t ∈ T done
in excess of allocated utilization rate
— purchase of material m ∈ M for time period t ∈ T b
— inventory of product i ∈ N for time period t ∈ T b
— inventory of material m ∈ M for time period t ∈ T b
— binary variable indicating whether products of product
family j ∈ U are produced in time period t ∈ T
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Objective Function
min
P
i∈N
P
P
P t∈T
m∈M
P
Pt∈T
i∈N
P
m∈M
b
b
P t∈T
t∈T b
hi IPit +
(product holding costs)
gm IMmt + (raw material holding costs)
OCoit +
(production costs)
RPm wmt
(raw material purchase costs)(1)
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Inventory Capacity, Demand and Material Balancing
Constraints
X
IPit ≤ PIC
∀t ∈ T b
(2)
i∈N
IPi,t−L +
t
X
(piu + oiu ) = dit + IPit
∀i ∈ N, t ∈ T b (3)
u=t−L+1
IMmt +
X
IMm,t−L + wmt =
t
X
rim (piu + oiu )
∀m ∈ M, t ∈ T b(4)
i∈N u=t−L+1
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Additional Constraints
BSj xjt ≤
X
pit
∀j ∈ U, t ∈ T (min prod.)
(5)
i∈Nj
X
PRi pit ≤ PPCxjt
∀j ∈ U, t ∈ T (link p to x) (6)
i∈Nj
X
PRi pit ≤ u ∗ PPC
∀t ∈ T (norm. cap.)
(7)
PRi (pit + oit ) ≤ PPC
∀t ∈ T (overt. cap.)
(8)
i∈N
X
i∈N
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Variable Domains
pit , IPit , oit , ≥ 0
IMmt , wmt ≥ 0
xjt ∈ {0, 1}
C. Charalambous, S. Pericleous and K. Fleszar
∀i ∈ N, t ∈ T
(9)
∀m ∈ M, t ∈ T
(10)
∀j ∈ U, t ∈ T
(11)
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Transportation concerns: Additional Parameters and
Variables
I
Replace raw material purchase price RPm with the set bm (list
of (q, v ) pairs defining unit purchase price v given at least q
units of purchase
I
k represents the k quantity in the list; v k the k value
qm
th
th
m
I
k variable: purchase quantity of raw material m ∈ M for
BUmt
k
time period t ∈ T at price vm
I
k is a binary variable indicating whether raw material
ymt
k
m ∈ M was purchased for time period t ∈ T at price vm
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Transportation: Added Constraints
Update the material purchase cost term to
|bm |
XX
X
k
k
vm
BUmt
m∈M k=1 t∈T b
Update raw material balancing constraint
IMm,t−L +
|bm |
X
k
BUmt
=
k=1
IMmt +
X
t
X
rim (piu + oiu )
∀m ∈ M, t ∈ T b (12)
i∈N u=t−L+1
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Transportation: Added Constraints (cont.)
Link y variables to BU
k
k
k
qm
∗ ymt
≤ BUmt
∀k ∈ {1..|bm |}, m ∈ M, t ∈ T b (13)
k
k
BUmt
≤ bigM ∗ ymt
∀k ∈ {1..|bm |}, m ∈ M, t ∈ T b (14)
|bm |
X
k
ymt
=1
∀t ∈ T b , m ∈ M
(15)
k=1
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Setup considerations within a small-bucket period
I
Small bucket periods needed to express the system’s
operational characteristics
I
Straightforward way would be to introduce setup cost
whenever a product family is handled in a given time unit
I
Limitations: cost is mainly for changeovers not setup, does
not depict increased manufacturing complexity of multiple
family production
I
Solution: introduce a binary variable zjkt being 1 if both
families j and k are produced at t
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Setup representation: Added constraints
zjkt ≥ xjt + xkt − 1
∀t ∈ T ,
j = 1, 2, ..., |U| − 1
k = j + 1, j + 2, ..., |U|
X
i∈N
X
i∈N
PRi pit +
XX
ajk zjkt ≤ u ∗ PPC
∀t ∈ T
(16)
∀t ∈ T
(17)
j∈U k∈U
PRi (pit + oit ) +
XX
ajk zjkt ≤ PPC
j∈U k∈U
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Approach highlights
The model
Modeling Transportation
Representing Manufacturing Flexibility
Introduce make-or-buy option
Make-or-buy capacity
I
Introduce subcontracting option for certain products (sit
continuous variable)
I
Enforce minimum subcontract quantity
I
Update objective function and demand balancing constraints
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Implementation
I
Model implemented in C#.NET using a CPLEX 12.1 solver
I
The model is manageable in terms of execution timer
requirements if number of families is small (less than 10)
I
Initial experimentation with simulated demand scenarios and
subcontracting options
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Initial findings
I
Breadth of portfolio may hinder efficient operations
I
Hybrid operations are likely to yield maximum profit (drop
certain families, fully import other, manufacture only subset of
product portfolio based on same raw materials)
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Limitations
I
A lot of parameters are significantly stochastic and difficult to
model
I
MILP is too complex for continuous analysis
Only focuses on cost objective, other secondary but key
objectives are ignored - scalarization not adequate option
I
I
I
Responsiveness: ability to reach customers fast
System Flexibility: ability to modify/update product portfolio
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Future Work
I
Embed the model within a larger-scale simulation system
I
Extract common patterns
I
Develop simplified (non-MP) operation models for various
manufacturing modes (current state, downsized operations,
full import, etc) and evaluate system though a MOEA
platform.
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot
Introducing the problem
Suggested Approach
Results and Discussion
Thank you for your attention!
C. Charalambous, S. Pericleous and K. Fleszar
Aggregate Production Planning systems for low-demand, remot