Asia Pacific Management Review (2007) 12(1), 43-51
Tactical Supply Network Planning: An Example from Specialty
Chemicals Industry
Reinhard Hübner and Hans-Otto Günther*
Department of Production Management, Technical University of Berlin, Germany
Accepted in November 2006
Available online
Abstract
In this paper, we present a tactical supply network planning model focusing on applications in specialty chemicals industry. The
model incorporates both, industry-specific aspects such as product transfers, single-sourcing of intermediates or product mix effects
on capacity and elements of international trade such as duties, duty drawbacks and currency effects. The model is integrated into a
decision support system linking the optimization model developed using ILOG OPL 4.2/CPLX 10.0 to a visual user interface.
Keywords: Mixed-integer linear programming; Advanced planning systems; Tactical supply network planning; Specialty chemicals
1. Introduction
gregate production and inventory quantities planning.
Supply chain management has to address diverse
issues ranging from facility location to detailed production and procurement decisions (cf. Fleischmann,
Meyr and Wagner, 2005). To reduce the complexity of
planning processes, they can be hierarchically decomposed based on their time horizon and their importance
for the company. While some authors distinguish only
between strategic and operational planning, the
framework most commonly employed - originally
proposed by Anthony (1965) - includes tactical planning as an intermediate level. In the context of supply
chain management, the different planning levels can be
defined as follows (cf. Günther and Tempelmeier, 2005;
Chopra and Meindl, 2004; Simchi-Levi, Simchi-Levi
and Watson, 2003; Miller, 2002):
•
•
•
Operational planning ensures the optimum utilization of existing assets and efficient execution of the
decisions taken in strategic and tactical planning.
The time horizon covered is a maximum of one
year with daily or weekly intervals. Typical decisions include lot sizing and production scheduling.
While there are strong interdependencies between
strategic, tactical and operational planning, in practice,
planning processes take place in a hierarchical fashion
with strategic planning forming the basis of the different
tactical and operational plans. Following this logic,
separate models are typically being developed for strategic, tactical and operational supply chain planning.
Models integrating the different levels (e.g., Kallrath,
2002; Sabri and Beamon, 2000) are an exception.
Strategic planning focuses on creating and sustaining the conditions required for the successful
long term development of a company. The time
horizon usually covers a period of three to ten years
and decisions are of great importance for the entire
company. Typical decisions include among others
the product and services portfolio, configuration of
production and distribution networks and investments into new production technologies.
In this article, a tactical supply network planning
model for use in specialty chemicals industry is proposed. To this end, peculiarities of specialty chemicals
supply networks are discussed in Section 2. Section 3
introduces major elements of tactical supply network
planning in specialty chemicals industry such as product
transfers and product mix effects and provides references to the pertinent literature. The proposed optimization model is presented in Section 4. Finally, Section
5 summarizes the key findings and indicates directions
for future research.
Tactical planning implements strategic objectives
in a step by step approach with a time horizon of 1
to 3 years. Typical decisions include launch or
discontinuation of specific products, transfers of
products within the existing production network,
(limited) production capacity adjustments and ag
2. Specialty Chemicals Supply Networks
* E-mail: hans-otto.guenther@tu-berlin.de
43
Reinhard Hübner and Hans-Otto Günther/Asia Pacific Management Review (2007) 12(1), 43-51
The strategies can also be combined, e.g., by establishing product plants in each of the major economic
regions. Hayes and Wheelwright (1984) and Dornier,
Ernst et al. (1998) list some of the advantages and disadvantages associated with Schmenner's network
strategies. Kulkarni, Magazine and Raturi (2004) show
that a process plant strategy can have risk pooling advantages even in the absence of economies of scale. For
the United States, Schmenner (1982) found product and
to a lesser extent market area plants to be by far the most
common strategies. Comparing their findings 20 years
later with Schmenner's data, Vokurka and Flores (2002)
observe a strong trend away from market area plants
towards integrated production networks. This trend was
also observed by Flaherty (1986).
There are various basic options available to design
multi-site networks. One option is to split production
volumes so that all sites perform all activities. This
option duplicates activities at each new site. A second
option is to divide activities across several sites by
function, product or production process. In this case,
each site specializes on a specific segment of the overall
activities spectrum. Finally, the two options can also be
combined leading to a diversified site network.
Focusing on production network design, Schmenner (1979) provides a more specific classification of
four distinct multi-plant strategies. Based on a product,
market or process focus Schmenner defines four segmentation principles:
•
Product plants serve the company's entire market
for the products they produce, specializing on the
competitive priorities associated with their respective product portfolio.
•
Market area plants produce a majority of the company's products for distribution to their regional
market.
•
Process plants focus on certain process steps usually with some plants providing components for
other plants. The segmentation is based on manufacturing
requirements
of
the
components/products.
•
General purpose plants are designed for flexible
assignment of products, markets and process segments without a specific focus.
Specialty chemicals companies usually operate in
several business segments (value chains) with diverse
product and production process characteristics. Therefore, an analysis of the design principle underlying
specialty chemicals production networks has to be
performed separately for each business segment. Historically, specialty chemicals companies mainly established foreign plants to access regional markets (market
area plants). One underlying reason were trade barriers
such as tariffs. According to Ferdows (1997) these have
declined from an average of 40% of product value in
1940 to 7% in 1990). With the increasing integration of
the production networks, today many newly established
sites are set up to exploit cheap factor costs. A recent
example is the decision of the Germany-based Degussa
company to shift a large proportion of its pharmaceutical ingredient production from Europe to China (cf.
N.N., 2004).
Characteristics
Characteristics
• High value/volume products
• Significant economies of
World factory
World lead and regional
low cost followers
• Product portfolio with mix of
Intermediate hub and
regional spokes
• Large number of product
World slow movers and
regional fast movers
• Product portfolio consisting
scale in production
• Low degree of differentiation
• Stable products with low
transportation costs
Localized specialty
production
• Make to order products
• Low volumes, high degree of
differentiation
• Limited economies of scale
in production
• Limited product stability
and/or medium to high
transportation costs
Regional commodity
production
• Medium to low value
commodity products
• Stable products
• Medium to high transportation costs and/or
• Lead time requirements
new, innovative and
commoditized products
• Stable products with medium
to high transportation costs
• Only limited economies of
scale in production
variants made from
commodity intermediates
• Stable intermediates with low
transportation costs and
economies of scale in
production
of high volume and medium
to low volume variants
• Economies of scale in
production
• Stable product with low
transportation costs
Figure 1. Generic Production Network Design Alternatives in Specialty Chemicals
44
Asia Pacific Management Review (2007) 12(1), 43-51
of time chemical products cannot be transferred easily
from one site to another. Instead, recipes have to be
adjusted, personnel have to be trained and trial batches
have to be produced. Both, the costs associated with
such a scale-up and the production capacity required
should be considered explicitly. Only a few models in
literature do so. Lee (1991) includes fixed setup costs to
create the capability to handle a product at a facility. For
pharmaceutical industry Papageorgiou, Rostein and
Shah (2001) include product scale-up, further distinguishing between the actual scale-up and qualification
runs required to demonstrate the capability of meeting
specifications to regulatory agencies. The model proposed here considers both direct costs associated with a
scale-up and the costs/capacity consumption induced by
production trials.
Generally, the structure of specialty chemicals
production networks depends on value chain characteristics such as product stability, ratio of product value
to weight/volume or the level of vertical integration.
Figure 1 shows typical network designs to be found in
industry.
3. Optimization-based Tactical Supply Network
Planning in Specialty Chemicals
3.1 Major Elements of Tactical Supply Network Planning
According to Shapiro (2001) the objective of a
tactical supply network planning model is to determine
an integrated supply, manufacturing, distribution and
inventory plan that maximizes profits or minimizes
costs with a typical time horizon of 12 months. The
planning process is usually performed every month with
the time interval being months for the first quarter and
quarters for the remaining three quarters of the planning
horizon (cf. Shapiro, 2001).
3.1.3 Product mix effects
Product-plant allocation decisions in chemical industry are often associated with diseconomies of scope
due to changeover processes. Whether these effects
have to be modeled explicitly depends on the magnitude
of the economies existent with the type of products
considered. Since scope economies are especially hard
to model, a separate class of optimization models solely
dealing with plant loading decisions can be found. For
example Mazzola and Schantz (1997) propose a
non-linear mixed integer program that combines a fixed
cost charge for each product-plant allocation, a fixed
capacity consumption to reflect plant setup and a
non-linear capacity-consumption function of the total
product portfolio allocated to the plant. To develop the
capacity consumption function the authors build product families with similar processing requirements and
consider effects from intra- and inter-product family
interactions. Based on a linear relaxation the authors
explore
both
tabu-search
heuristics
and
branch-and-bound algorithms to obtain solutions.
In addition to the standard decisions such as product-plant-market allocations, which are at the interface
between tactical and operational planning, a number of
decisions affecting the entire planning horizon have to
be made in tactical planning. Of these, capacity planning and product transfers are explicitly discussed below.
3.1.1 Capacity planning
In tactical planning, changes to technical capacities
are typically not possible due to the long lead times
required to implement the corresponding investment
projects. Nevertheless, depending on the operating
mode of the different sites (e.g., five or seven day
workweek, plant holidays) overtime capacity may be
available at a subset of the plants. Additionally, inventory buildup can be used to deal with seasonal demand
patterns. In tactical planning, the trade-off between the
inventory carrying costs associated with stock buildup
and the additional costs associated with overtime production has to be resolved. While the decision to use
overtime production capacity can be made throughout
the entire planning horizon, the extent to which tactical
inventory buildup is to be used typically has to be determined at the beginning of each seasonal cycle.
Also, some production network design models
consider the problem. For example, Klincewicz and
Luss (1987) include a fixed cost charge for every
product allocated to a facility. Papageorgiou et al. (2001)
explicitly model capacity requirements for changeover
processes. They allocate products to individual production lines and implicitly assume that only one campaign
is produced per product and time period. Cohen and
Moon (1990) combine fixed cost effects with a variable
unit cost function that contains both additional scale and
scope effects to analyze their effects and the effects of
varying transportation costs on production network
design using a single-period, non-linear model. They
find that economies of scale and scope can have considerable effects on optimal production network design.
A feasible estimation approach can be developed
analogous to the major/minor changeover concept Bi-
3.1.2 Product transfers
In response to changes in comparative advantages
between sites and available capacities, product transfers
may be required to best satisfy demand. From a technical perspective, it is often possible to transfer products
between production sites in specialty chemicals without
having to invest into new equipments. However, even if
the receiving plant has been running the equipment
required to produce a certain product for a long period
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Reinhard Hübner and Hans-Otto Günther/Asia Pacific Management Review (2007) 12(1), 43-51
cases exceeding 30%. The applicable tariff rate for
importing a product depends not only on the product but
also on the country of origin. Within free trade zones no
duties have to be paid and for many trade relations
preferential rates apply either due to bilateral trade
agreements or because of exemptions to support less
developed countries. Several options exist to reduce
tariff costs. In some cases, duties can be avoided by
choice of production locations. In other cases, refunds
on duties paid (duty drawbacks) can be obtained. Figure
2 gives an overview of duty avoidance options and duty
drawbacks.
tran and Gilbert (1990) use to model sequence-dependent setup costs. Products are grouped
into changeover families with changeovers within a
family not significantly exceeding regular cleaning
requirements between two batches of the same product.
Assuming that comprehensive cleanings required independently of changeover family switches are already
deducted from technical capacity, a lower bound on the
number of comprehensive changeovers required can be
calculated by subtracting from the number of changeover families allocated to a plant the number of production lines available. If this approach is chosen it is
assumed that in each planning period the entire production volume of each changeover family is produced
in one campaign. If this assumption is not adequate,
additionally a maximum campaign size could be defined for each changeover family to account for the
tradeoff between changeover costs and inventory carrying costs.
Models from literature differ with respect to the
extent to which they cover the complexity of tariff
structures. Simplified modeling approaches only consider duties levied for supplying a certain market via
imports or simply integrate tariffs into transportation
costs (e.g., Kouvelis et al. 2004). For specialty chemicals, tariffs often constitute a higher share of total costs
than transportation costs, making obvious the need to
explicitly model tariff regimes. To model duty drawbacks, the lineage could theoretically be traced along
multiple production levels based on the bill of materials.
To reduce complexity in the case example only one
level of intermediates is considered.
3.2 Additional Complexities in Global Supply Networks
3.2.1 Exchange rate fluctuations
Exchange rate fluctuations affect companies in
different ways. Generally, one distinguishes between
three types of currency exposure. Translation or accounting exposure refers to the effects currency fluctuations can have on consolidated financial statements
whereas transactional exposure refers to the effects on
contractually defined cash flows and operational exposure on the way the viability and profitability of the
business are affected.
The effects of exchange rate fluctuations can be
significant. For example, Mohamed (1999) shows based
on a simple example that changes of the real exchange
rate (change of nominal exchange rate adjusted for
inflation levels in the countries involved) can lead to a
decrease of profits of almost 50% if capacity constraints
do not allow the company to re-allocate production
volumes within the network. Consequently, it may be
desirable to maintain excess capacity or utilize overtime
capacity to shift production in reaction to exchange rate
fluctuations (cf. Cohen and Huchzermeier 1999;
Rosenfield 1996). While supply network robustness to
currency fluctuations is primarily a strategic issue, significant exchange rate changes can also occur within
relatively short time periods. For example, the Euro
appreciated more than 20% against the US$ throughout
2002.
4. The tactical supply network planning model
4.1 Description of the Supply Network Considered
The basic structure of the supply network to be
considered is depicted in Figure 3. The production
network comprises echelons producing intermediate
products (which can be used internally and sold externally) and finished goods. Any intermediate facility can
supply any finished goods facility with intermediate
products. However, it is assumed that each facility receives each intermediate only from one source to ensure
homogenous product quality. For all products inventory
is assumed to be held only at the producing site (except
for intermediate safety stocks to ensure uninterrupted
production) to avoid transshipments between sites. Due
to the fact that the tactical planning model covers only a
single value chain, transportation costs were in the
range of 3-4% for the products considered and safety
stocks are in place, the structure of the distribution
network within the different markets is not considered
explicitly.
Based on existing technical capacities, in the tactical planning phase decisions such as product-plant-market allocations, product transfers from one
site to another site or the buildup of inventory to account
for seasonality of demand have to be taken. These decisions are primarily influenced by factors such as expectations on demand and price developments or exchange rates.
3.2.2 Duties and duty drawbacks
Duties are import taxes levied at the border for
importing a product into the respective country. Duties
are usually defined as a percentage of the value of imported goods including freight costs to border of destination country/trade area with product-specific rates
commonly varying between 0 and 10% and in extreme
46
Asia Pacific Management Review (2007) 12(1), 43-51
Focus in tactical
planning
Duty
avoidance
via
network
design
1 Direct routing
• Import of raw materials from China to Germany (tariff 4.5%)
• Production and sale of finished product in Europe
2 Indirect routing
• Import of raw materials from China to Switzerland (no tariff)
• Transformation and export of finished product to European Union
(no import duty charged due to Swiss origin)
1
2
Re-export in
different
condition
• Intermediates imported from China to Germany (tariff 3%)
• Finished product sold from Germany to Japan
• Duty drawback in Germany due to re-export in different condition
Re-export in
identical condition
• Import of finished product from China to Germany (tariff 6%)
• Re-export of finished product from Germany to Switzerland (tariff
Re-import in
different
condition
• Intermediate transported to China for processing (tariff 0%)
• Finished product exported from China to Germany (tariff 4%)
• Duty drawback of 4% on value of intermediate contained in
3% due to Chinese origin)
• Duty drawback in Germany due to re-export in identical condition
finished product due to re-import in different condition
Figure 2. Duty Avoidance and Duty Drawback Options
Intermediate
product sites
dint pff 't
trc ff 't
Finished
product sites
Demand regions
(countries)
dem pct Demand
Internal transport volume
Transportation costs
dext pfct Distribution volume
trc fct
Transport costs
x pft
y pft
z ft
Production volume
Inventory at period end
Use of overtime capacity
pcap ft Production capacity
pocap ft Overtime capacity
icap ft Inventory capacity
f ∈ FI
f ∈ FF
c ∈C
Figure 3. Supply Network Structure
4.2 Model Formulation
Products
p ∈ Pg
Products belonging to changeover family g
k ∈ PF
r∈R
t ∈T
Indices and index sets
c ∈C
c ∈ CNE f
f ∈F
f ∈ FF
f ∈ FI
f '∈ FNE f
g ∈G
i ∈ PI
p∈P
Demand regions (countries)
No export country relative to facility f
Production facilities (sites)
Finished products
Raw materials
Time periods
Parameters
Finished products facilities
Intermediate product facilities
capreq p
Capacity consumption factor of product p
No export facility relative to facility f
cfix ft
Fixed costs of facility f in period t
Changeover families
contvol p
Quantity of product p per full container load
Intermediate products
cv pft
Variable costs of product p at facility f in period t
47
Reinhard Hübner and Hans-Otto Günther/Asia Pacific Management Review (2007) 12(1), 43-51
cvo ft
Costs per unit of overtime capacity at facility f in
period t
dem pct
Demand of product p in country c in period t
duty pfc
Import duty rate for product p originating from
facility f into country c
fx ct
Exchange rate of country c in period t
fx ft
Exchange rate for facility f in period t
fx rft
Exchange rate for raw material r at facility f in
period t
h pft
Holding costs for product p at facility f in period t
icap ft
Inventory capacity of facility f in period t
ireqip
Quantity of intermediate i required per unit of
product p
pcap ft
Production capacity of facility f in period t
plines f
Production lines installed at facility f
pocap ft
Overtime capacity of facility f in period t
price pct
Sales price of product p in country c in period t
rprrft
Landed costs (excl. tariff) of raw material r at
facility f in period t
Quantity of raw material r required per unit of
product p
rreqrp
trrf
Import tariff rate for raw material r at facility f
trif ' f
Import tariff for intermediate i originating from
facility f' to facility f
Transport costs from facility f to facility f' in period
t
Transport cost from facility f to country c in period
t
trc ff' t
trc fct
trcost pt
Transfer costs for product p in period t
trpriceif' t
Transfer price of intermediate i originating from
facility f in period t
xmin pf
Minimum campaign size of product p at facility f
xocap f
Capacity consumption for major changeovers at
facility f
Costs for major changeovers at facility f in period
t
Large positive number
xocost ft
BigM
dext pfct
iduty if ' ft
iduty ft
rduty rt
u pft
viff '
w pft
x pft
xonum ft
xofamallgft
period t; 0 else
Inventory of product p at facility f at end of period
t
z ft
Use of overtime capacity at facility f in period t
Objective function
⎡
⎡ ⎡ price pct ⎤
⎤⎤
⎢
⎢⎢
⎥ ⋅ fxct ⎥ ⎥
(
)
−
duty
1
⎢
⎥
⎢⎢
⎥⎥
pfc ⎦
dext pfct ⋅ ⎢ ⎣
⎢
⎥⎥
trc
p
P
f
F
c
C
∈
∈
∈
fct
⎢
⎢⋅
⎥⎥
⎢
⎢ contvol p
⎥⎥
⎣
⎦⎥
⎢
⎢
⎥
⎡
⎤
⋅
x
cv
⎡ pft
pft ⎤
⎢
⎥
⎢
⎢
⎥ ⎥
⎢
⎥
⎢ p∈P ⎢⎣+ y pft ⋅ h pft ⎥⎦ ⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢+ z ft ⋅ cvo pft
⎥
⎢−
⎥
⎢+ xonum ⋅ xocost ⎥ ⋅ fx ft
ft
ft
⎢ f ∈F ⎢
⎥
⎥
⎢
⎥
⎢+ rduty ft
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢+ cfix ft
⎥
⎢
⎥
⎢+ iduty
⎥
ft
⎢
⎥
⎣
⎦
⎢
⎥
w
w
trcost
−
−
⋅
pft −1
pt
pft
⎢
⎥
p∈P f ∈F
⎢
⎥
⎢
⎥
trc ff 't
dint pff 'st ⋅
⎢−
⎥
contvol p
⎣⎢ p∈PI f ∈FI f '∈FF
⎦⎥
∑∑∑
∑
max
∑ ∑
t∈T
∑∑ [
(1)
]
∑∑ ∑
Subject to
Capacity constraints
∑
⎡
x pft ⋅ capreq p ⎤
⎢ p∈P
⎥ ≤ pcap + z
ft
ft
⎢
⎥
⎢⎣+ xonum ft ⋅ xocap f ⎥⎦
z ft ≤ pocap ft
∀ f ,t
(2)
∀ f ,t
(3)
∀ f ,t
(4)
⎡ p ∈ PF ,⎤
∀⎢
⎥
⎣ f ,t
⎦
(5)
∀ p, f , t
(6)
∀ p , c, t
(7)
∀ i, f ', t
(8)
x pft ≤ w pft ⋅ BigM
∀ p, f , t
(9)
w pft ≥ wpft −1
∀ p, f , t
(10)
∑y
pft
⋅ contvol p ≤ icap ft
p∈P
Flow constraints
Decision variables
dint pff' t
y pft
y pft = y pft −1 + x pft −
∑ dext
pfct
c∈C
Quantity of intermediate i shipped from facility f
to facility f' in period t
Quantity of product p shipped from facility f to
country c in period t
Import duties paid for import of intermediate i
from facility f' to facility f in period t
Import duties paid for import of intermediate i to
facility f in period t
⎡
⎢
yift = yift −1 + xift − ⎢
⎢+
⎣
∑ dext
∑ dint
∑ dext
∑ dint
ifct
c∈C
iff 't
f '∈FF
⎤
⎥
⎥
⎥
⎦
≤ dem pct
pfct
f ∈FF
Raw material duties paid at facility f in period t
1, if product p is produced at facility f in period t; 0
else
1, if intermediate i is supplied from facility f to
facility f'; 0 else
1, if product p can be produced at facility f in
period t; 0 else
Quantity of product p produced at facility f in
period t
Minimum number of major changeovers required
at facility f in period t
iff 't
≥
f ∈FI
∑
x pf 't ⋅ ireqip
p∈PF
Product transfers
Single sourcing of intermediates
1, if product family g is allocated to facility f in
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Reinhard Hübner and Hans-Otto Günther/Asia Pacific Management Review (2007) 12(1), 43-51
∑ dint ≤ v
v ≤ ∑ dint
∑v ≤ 1
∀ i, f , f '
(11)
∀ i, f , f '
(12)
∀ i, f '
(13)
x pft ≤ u pft ⋅ BigM
∀ p, f , t
(14)
u pft ⋅ xmin pf ≤ x pft
∀ p, f , t
(15)
∀ g, f ,t
(16)
∀ f ,t
(17)
⋅ BigM
iff '
iff't
port duties that might have to be paid and converted into
the home currency of the company. Subtracted are the
variable production costs, inventory holding costs, net
import duties, overtime costs, fixed facility costs and
transportation costs for both inter-site transports and
transports to final markets. All transport costs are assumed to be denominated in the home currency of the
company for simplification purposes.
The constraints (2) to (4) limit the production to
existing capacity and overcapacity and ensure inventory
constraints being observed. The constraints (5) to (8)
model the flow of goods between the stages in the supply chain. The first two link inventory levels to production and distribution quantities. The latter two ensure that distribution quantities do not exceed demand
and that sufficient intermediate quantities are supplied
to the consuming site. Again, it is assumed that all
stocks are held at the producing site.
The constraint (9) ensures that products are only
produced at sites the product has already been transferred to and (10) ensures the continuity of these decisions, i.e., if a product has been transferred it can also be
produced in later periods.
t∈T
iff '
iff't
t∈T
iff '
f ∈F
Product-mix effects
xofamall gft ⋅ BigM ≥
∑u
pft
p∈Pg
xonum ft ≥
∑ xofamall
gft
− plines f
g∈G
Import duties for raw materials and intermediates
⎡ ⎡ v if ' ft ⋅ BigM − BigM ⎤ ⎤
⎢⎢
⎥⎥
dext pfct ⋅ ireq ip ⎥ ⎥
⎢ ⎢+
iduty if'ft ≥ ⎢ ⎣⎢ p∈P c∈CNE f
⎦⎥ ⎥
⎥
⎢
fx f 't
⎥
⎢
⎥
⎢⋅ trpriceif 't ⋅ trif ' f ⋅ fx
ft
⎦
⎣
⎡i, f , ⎤
∀⎢
⎥
⎣ f ',t⎦
(18)
iduty ft =
∀ f ∈ FF , t
(19)
∑∑
∑∑ iduty
if ' ft
i∈PI f '∈FI
⎡
⎡dext pfct ⋅ rreqrp ⎤
⎢
⎢
⎥
fxrft
⎢
⎢
⎥
⎢ p∈PF c∈CNE f ⎢⋅ rprrft fx ⋅ trrf ⎥
ft
⎦
⎣
⎢
⎢
⎡dint iff 't ⋅ rreqri
⎢
⎢
fxrft
⎢+
⎢
⋅ trrf
⎢ i∈PI f '∈FNE f ⎢⋅ rprrft
fx ft
⎢⎣
⎣
∑∑
rduty ft =
∑
r∈R
∑∑
⎤
⎥
⎥
⎥
⎥
⎤⎥
⎥⎥
⎥⎥
⎥⎥
⎦ ⎥⎦
∀f , t
The single sourcing constraints (11) to (13) serve
two purposes. Firstly, supplying intermediates from
only one source has the advantage of reducing the
variability of material inputs. Secondly, the single-sourcing assumption is exploited in the duty drawback calculation for intermediates. It is assumed that
single-sourcing decisions are taken for the entire planning horizon.
(20)
The constraints (14) to (17) capture the effect of
product mix on capacity and production costs. As discussed above, products are grouped into changeover
families. It is assumed that all products from a product
family are produced within one campaign. The constraint (14) sets u to 1 for every product produced at a
facility in a time period and (15) enforces minimum
campaign sizes. The constraint (16) aggregates this to
the level of changeover families. Finally, the constraint
(17) determines the number of major changeovers as the
difference between the number of product families
allocated to a facility and the number of production lines
available. If the assumption of producing the entire
quantity allocated to a facility in one campaign is not
realistic, a maximum campaign size could be included
to further specify product mix effects.
Variable domains
dext pfct ≥ 0
∀ p , f , c, t
(21)
dint pff't ≥ 0
∀ p, f , t
(22)
iduty if ' ft ≥ 0
∀i, f , f ' , t
(23)
iduty ft ≥ 0
∀ f ,t
(24)
rduty ft ≥ 0
∀ f ,t
(25)
∀ p, f , t
viff ' ∈ [0,1]
(26)
∀ i, f , f '
wpft ∈ [0,1]
(27)
∀ p, f , t
(28)
x pft ≥ 0
∀ p, f , t
xofamall gft ∈ [0,1]
(29)
∀ g, f ,t
(30)
xonum ft ≥ 0
∀ f ,t
(31)
y pft ≥ 0
∀ p, f , t
(32)
z ft ≥ 0
∀ f ,t
(33)
u pft ∈ [0,1]
Finally, the constraints (18) to (20) determine the
net duties that have to be paid for intermediates and raw
materials. The constraint (18) uses the single-sourcing
assumption and non-negativity constraint (23) to determine duties payable for each intermediate. The
equation (19) determines the total import duties payable
for intermediates at a facility. For simplification purposes duties are not calculated on products kept in in-
The objective function (1) maximizes the pre-tax
profit of the production network considered. Revenues
realized in the different markets (it is assumed that no
storage takes place at the market) are adjusted for im-
49
Reinhard Hübner and Hans-Otto Günther/Asia Pacific Management Review (2007) 12(1), 43-51
Application-oriented examples based on such an approach have been proposed by Eppen et al. (1989) for
network design in automotive industry and Ahmed and
Sahinidis (1998) for process planning in chemical industry. The network design model proposed by Hübner
(2006), which was the basis for this tactical application,
contains an illustrative example of employing the robust
optimization framework to network design in specialty
chemicals.
ventory but only on those leaving the site in non-export
sales. The equation (20) performs a similar calculation
for raw materials. Again, supply from a single source
throughout the planning horizon is assumed.
4.3 Model implementation
The tactical planning model presented above is derived from the strategic production network design
model developed by Hübner (2006). It was implemented using ILOG OPL Development Studio 4.2 and
CLPEX 10.0 in conjunction with a visual user interface
based on an MS Access database. In addition to supporting data entry and result evaluation via standardized
reports the user interface also allows decision makers to
manage and evaluate alternative planning scenarios.
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