Ecole Centrale Paris
Laboratoire Génie Industriel
Cahier d’Études et de Recherche / Research Report Capacity planning in textile/apparel supply chain
Imen Safra, Asma Ghaffari, Aida Jebali, Zied Jemai, Hanen Bouchriha CER 12– 03 Mai 2012
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Capacity planning in textile/apparel supply chain Imen Safra 1,2, Asma Ghaffari1, Aida Jebali2,3, Zied Jemai1, Hanen Bouchriha2
1Laboratoire Génie Industriel, Ecole Centrale Paris, Chatenay Malabry, France 2Analyse et commande des systèmes, Ecole 3Business Administration Department, Prince Sultan University, Riyadh, Kingdom of Saudi Arabia
This paper deals with an integrated approach for production and distribution planning at the tactical and operational decision levels. Applied to a textile industry context, the proposed approach aims to offer more flexibility to the production system, by planning a safety production capacity at the tactical planning level. This safety capacity is released at the operational planning level to satisfy reduced-lead time orders. Our approach aims at minimizing the total production, storage and distribution cost of a 3-echelon supply chain so as to satisfy the customer demand on time. In addition to these classical costs, this paper considers an under-utilization cost of production capacity. At the tactical level, decisions related to production and distribution over a six-month planning horizon are made while taking into account outsourcing options, safety production capacity, transportation modes and products lead times. At the operational level, a rolling horizon planning is proposed to better place the unplanned and urgent newly arrived demands. The operational planning involves available full production capacity in addition to overtime production capacity and takes into account the ongoing production. Tactical and operational planning problems are formulated as integer programs. Our approach has been validated on a real case study of a Tunisian textile/apparel company. The obtained results show that considerable supply chain cost savings (reaching 10%) are achieved if a safety production capacity is considered at the tactical planning.
Keywords: integer linear programming; production; distribution; outsourcing; tactical and operational planning; textile apparel industry.
Introduction
A supply chain includes companies which intervene to offer the adequate product to retailers.
Its structure is getting more and more complex as it involves a number of actors who provide
a supply of raw materials and components; production of finished products; transportation;
warehousing and logistics operations. It is well understood that, to enhance supply chain
performance and to improve customer service level, there is a need to reduce inventory levels.
In the literature review of integrated production and distribution models presented in
Sarmiento and Nagi (1999), the authors pointed out that this trend led to a closer link between
the different stages of the supply chain and, at the same time, they highlighted the need for
better coordination in decision making. In this paper, we focus on the coordination of
production and distribution operations. This problem has received a great deal of attention
from many researchers (e.g. Erengüç et al. (1999), Mula et al. (2010)). Most of the works
developed integrated production/distribution models at strategic and tactical planning levels
(Chen (2010)). At the strategic level, decisions were related to plant capacity and network
design (e.g. Kim et al. (2007), Vidal and Goetschalckx (1997)). However, the vast majority of
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the published papers have dealt with the tactical level and have investigated problems
regarding the size of production, inventory and delivery lots and their assignment. Various
approaches have been proposed: Lee et al. (2002) and Lee and Kim (2002) developed a
hybrid approach combining analytic and simulation methods; Aliev et al. (2007) and Selim et
al. (2008) opted for fuzzy programming to incorporate uncertainty; Eksioglu et al. (2007)
applied Lagrangean relaxation and decomposition techniques to solve this problem treated as
a multi-product flow problem; Armentano et al. (2011) proposed tabu search and path
relinking heuristic solutions. Operational aspects of supply chain planning, as it has been
pointed out by Erengüç et al. (1999), are still topical and challenging research subjects. In this
paper, our aim is to expose the interest of considering integrated production and distribution
planning including the coordination between tactical and operational levels.
For some applications involving perishable and/or seasonal products such as textile, apparel
and fashion industries creating an intimate link between production and distribution
decisions is even crucial in order to achieve a desired on time delivery performance at a
minimum total cost (Chen (2010)). This work falls within this issue. We propose an integrated
production and distribution planning approach that addresses both tactical and operational
decisions for the textile/apparel industry. The objective is to minimize the overall production
and distribution cost.
The considered textile/apparel supply chain model is based on a real case study which is
representative of the vast majority of current worldwide textile, apparel and fashion supply
chains. The supply network includes a set of manufacturers and subcontractors located in
different countries. The products are manufactured in a make-to-order policy. Some of the
ordering retailers are local but the majority of them are located overseas, mainly in Europe.
Manufacturers receive two kinds of orders: pre-season orders and replenishment orders. Pre-
season orders are due within some months since the ordered products have to be sold during
the next season. However, replenishment orders have shorter due dates compared to pre-
season orders as they have to fill stockouts of products to be sold over the same season.
Our study focuses on a manufacturing company involved in the supply chain described below
(see figure 1). The company owns several manufacturing units and warehouses which are
located in Tunisia. It also has the option of outsourcing some orders to local or overseas
subcontractors. The company is adopting a commit-to-delivery business mode. It commits a
delivery due date for any received order and it is responsible for the shipping cost. The
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finished products are batched and shipped immediately towards the warehouses where they
are gathered and stored till their delivery time. Different transportation modes may be used for
delivery operations: trucks, ships or aircrafts. Each transportation mode is characterized by a
fixed cost and a variable cost (the latter is accounted for each shipped unit). Each product
incurs a production set-up cost and a variable cost (the latter is accounted for each produced
unit).
Mostard et al. (2011) pointed out that, for the textile/apparel industry, 95% of SKUs (Stock
Keeping Units) change in every selling season. The paper stressed on the unavailability of
historical demand data that could be used by retailers to establish demand forecasts because of
short life-cycle products due to fashion changes. For this reason, retailers usually opt for in-
season replenishments and product updates after observing the demand. However, this
solution remains risky for the retailer and its success hinges to a large extent on the flexibility
and the reactivity of their suppliers: the manufacturers. Henceforth, production flexibility to
time deliveries becomes essential and a competing
key issue for any textile/apparel company.
Various approaches have been proposed in the literature to handle the lack of advance
information on future demands for textile/apparel products. They were based on statistical
methods (Suh et al., 2000) or on safety stock concepts (Gebennini et al., (2009), Tuzkaya and
Önüt, (2009)). We can note that they are more appropriate when demand historical data are
available and products are with no risk of obsolescence. Other papers, like Thomassey et al.
(2002) and Mostard et al. (2011), developed specific forecasting systems for textile/apparel
industry. But it has been shown that these methods become more efficient when they are used
by the retailers while observing and following up demand behaviour.
The proposed approach in this paper aims at providing the textile/apparel company optimal
production and distribution planning both at the tactical and operational decision levels. A
safety production capacity is considered at the tactical level and then released at the
operational level in order to better satisfy replenishment orders with short due dates. The
-season and replenishment orders on time, while
minimizing supply chain cost.
The remainder of this paper is organized as follows: Section 2 presents the textile/apparel
supply chain under consideration; Section 3 describes the proposed approach for an integrated
production/distribution planning both at the tactical and operational levels; Section 4 details
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the tactical and operational planning models used by the proposed approach. In order to
validate the proposed approach, experiments were conducted on real data extracted from the
considered textile/apparel company. Section 5 exposes the experimentations and some
analyses of the obtained results. Finally, section 6 presents the conclusions and some insights
for further research.
Textile/apparel supply chain
In this paper, we investigate a 3-echelon textile/apparel supply chain involving: (1)
manufacturing units, (2) warehouses and (3) retailers. Manufacturing units belong either to
the textile/apparel company (internal manufacturing units) or to subcontractors. Internal
manufacturing units are located in Tunisia, but those of subcontractors are either located in
Tunisia (local subcontractors) or overseas.
Figure 1: 3-echelon textile/apparel supply chain
The textile/apparel company owns several manufacturing units where only knitting operations
-to-delivery business
mode by promising to deliver orders to retailers on or before committed delivery dates. This
can reduce lead time variability and then improve customer satisfaction. Finished products are
stored in intermediate warehouses before being shipped to retailers. Orders received over one
season contain a large number of product references. In general, the number of product
families (a product family does not consider colours and sizes) is larger than one hundred.
The company receives two types of orders from local and overseas retailers: pre-season and
replenishment orders. Pre-season orders with due dates higher than some months are
predictable, planned and ordered in advance to meet next season collections. However,
replenishment orders with shorter due dates are generally unexpected and even urgent, and
Internal m
anufacturing units Subcontractors
manufacturing units
Warehouses
Retailers Manufacturers
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products. In fact, because of the short life cycles of textile/apparel products due to fashion
why, retailers usually have recourse to in-season replenishment opportunities after observing
current demands. This solution remains risky for the retailer and its success depends closely
these unpredictable production orders with
short due dates while meeting the ongoing production, the company may use expensive
solutions either by outsourcing production or by scheduling overtime. Nevertheless,
outsourcing must not lead to an under-utilization of the internal production capacity.
The subcontractors are of two kinds: (1) local subcontractors, providing flexibility in
production capacity but at prices higher than internal production costs; and (2) overseas
subcontractors, having the capacity to provide large quantities of basic products at relatively
low prices but with long delivery lead time. However, for non basic products, overseas
subcontractors do not necessarily offer lower prices by comparison with local competitors.
Finished products are shipped from warehouses to retailers using different transportation
modes. As a matter of fact, transportation lead times, as well as fixed and variable
transportation costs, depend closely on the chosen transportation mode.
Given the frequent arrival of replenishment orders, it is important for the company to provide
the ordered quantities on time and with low cost in order to preserve a sustainable position in
the current international market. Therefore, we propose, in this paper, for the manufacturer to
consider an internal safety production capacity at the tactical level. Thus, in the tactical
planning, only a given percentage of the production capacity can be used. The rest of the
capacity is indeed the safety capacity and can be used only at the operational level to meet the
demand with short due dates efficiently and without disrupting the ongoing production. The
internal safety production capacity is considered in order to provide protection from
replenishment orders that must be scheduled shortly at the operational level. The objective is
to satisfy the demand on laid on cost
minimization and due date respect.
On the other hand, as the company is adopting a commit-to-delivery business mode, it has to
tackle the production and distribution planning problems jointly. Henceforth, we propose an
integrated approach for production/distribution planning at tactical and operational levels.
At the tactical level, a safety production capacity is introduced to offer more flexibility to the
operational production/distribution planning where lots of replenishment orders have to be
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placed. Our goal is first to test the adequacy of this approach in the considered real case study.
Then, insights concerning the textile/apparel industry in general will be drawn. The
experimentations conducted in this approach show that cost savings are achieved when a
safety production capacity is adequately chosen and introduced at the tactical planning.
Production-distribution planning approach
The integrated approach for production and distribution planning, as presented at figure 2, is
based on two mathematical models. The main objective is to minimize the overall cost
incurred by internal production, outsourcing, internal capacity under-utilization, storage and
distribution operations.
A first model is developed to address the tactical planning problem. It considers a planning
horizon of six one-month periods. Each period of the tactical planning horizon consists of 4
weeks. This assumption ensures the respect of the monthly production decided by the tactical
model. The tactical planning model takes into account received pre-season orders and safety
production capacity and permits to plan the quantity of products to outsource, to produce in
internal manufacturing units, to store and to distribute, so as to minimize costs incurred at the
tactical level.
A second model is besides developed to address the operational planning problem. It
considers initially a two-month planning horizon with the week as period. The planning
horizon is then considered variable and will be detailed later in paragraph 3.2. A weekly
rolling horizon is also considered to integrate newly arrived orders over weeks.
Model objectives are twofold: (1) split the monthly planned quantities to produce internally
according to the tactical planning over weeks; and (2) place newly arrived replenishment
orders while respecting their short lead time. Obviously the replenishment orders have
reduced lead times and must be processed and delivered over the operational planning
horizon; they are considered in the operational planning with respect to their arrival date over
the weekly rolling horizon. The internal safety production capacity considered at the tactical
level is released and the entire internal capacity can be used in addition to overtime. This will
give more flexibility to accommodate unforeseen and urgent replenishment orders that arrive.
New replenishment orders are planned and assigned to different internal manufacturing sites
or/and to local subcontractors.
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When a new pre-season order, with a delivery lead time larger than the number of periods of
the operational level, arrives, it is introduced to the tactical planning model, at the following
month, to decide on production assignment while taking into consideration subcontractors
(both local and overseas). The operational planning model may afterwards takes into account
these demands if the tactical model proposes to place them in internal manufacturing units.
This procedure is repeated accordingly to orders delivery lead times as mentioned above. It
permits to plan production and distribution in global textile/apparel supply chain.
Initially, the first two months are considered and produced quantities decided at the tactical
level are detailed over weeks. Quantities produced, stored and distributed at the first week are
retained and related costs are recorded. However, decisions concerning the other periods
(weeks) are released and reconsidered while running the operational planning model. Finally,
we obtain a weekly detailed production, storage and distribution scheduling plan, considering
tactical assignments and newly urgent and unforeseen demands arrivals.
Figure 2: Hierarchical planning approach
In this study, the proposed approach is tested over a six-month horizon. However, the
approach can be applied on a longer horizon, covering more months. The aim, here, is to
evaluate the proposed approach and to point out the cost savings that could be achieved if
internal production capacity is adequately and efficiently planned.
Detailed tactical and operational planning models are introduced in the following.
Tactical model Horizon=6months Period=1month
Operational model Variable rolling horizon
Overtime
Replenishment orders
Weekly planning decisions
Safety capacity
Monthly planning decisions to detail
Outsourcing decisions
Pre-season orders
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Mathematical formulation
Tactical planning model
The tactical planning model considers a six-month planning horizon with monthly periods,
and aims at minimizing the total production, inventory holding and distribution costs. Tactical
planning model decides on: the monthly production quantities over internal and
subcontractors manufacturing units, the monthly stored quantities in warehouses and the
monthly delivered quantities to retailers. Different transportation modes and production
/distribution lead times are taken into account.
In model formulation, we consider the following sets and indices:
K: set of manufacturing units k K ; K = U V
U: set of internal manufacturing units, k U
V: set of subcontractors V
I: set of retailers, i I
J: set of warehouses, j J
P: set of products, p P
L: set of transportation modes, L= {trucks, ships, aircrafts}, l L
T: number of periods included in the planning horizon, t [1 .. T]
For this tactical model, each retailer i expresses a need for product p as demand to be
delivered at period t (Dpit); orders are assigned to manufacturing units characterized by a
monthly limited production capacity (Ukt) where they are produced, incurring variable and
fixed monthly production costs (Spkt,, Cpkt) or monthly outsourcing costs (Gpkt). A monthly
under-utilization cost of internal production capacity (CSUkt) is also considered to penalize
the unused available resources. Each product is characterized by a production lead time (Tpp)
Vp). Manufactured quantities are then transported to warehouses
where monthly inventory holding costs (KPpjt
(Wj) is limited. Transportation modes are characterized by a limited transportation capacity
(Capl) and a transportation lead time (el). Variable and fixed distribution costs from
manufacturing units to warehouses (CFkjplt, CTkjplt) and from warehouses to retailers
(CFSjiplt, CSjiplt) are also considered. We denote by kt (k U), the percentage of internal
production capacity that can be used to fulfill pre-season orders. Obviously, for k V (V is
, kt=0.
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Decision variables are as follows:
Z1kjplt: transported quantity of product p from manufacturing unit k to warehouse j over period
t by use of transportation mode l.
Z2jiplt: transported quantity of product p from the warehouse j to retailer i over period t via
transportation mode l.
Xpkt: quantity of product p produced in manufacturing unit k over period t.
SUkt: unused production capacity at internal manufacturing unit k over period t.
Jpjt: stock level of product p in warehouse j at the end of period t.
Ypkt =1 if product p is produced in manufacturing unit k over period t, 0 otherwise.
N1kjlt: number of transportation modes used to transport products from manufacturing unit k
to warehouse j over period t by use of transportation mode l.
N2jilt: number of transportation modes used to transport products from warehouse j to retailer
i over period t by use of transportation mode l.
Model formulation (M1)
The problem of integrated production-distribution is formulated as an integer program which
aims to minimize the overall cost in the considered logistic network.
)2*
1*2**
1**2/)(
(
1
tjiTt Pp Ii L Jj
tjip
tkjTt Pp Kk L Jj
tkjptjippTt Pp Ii L Jj
tjip
tkjppTt Pp Kk L Jj
tkjppjtpjtJj Tt Pp
pjt
ktUk Tt
ktTt Pp
pktVk
pktTt Pp Uk
pktpktpktTt Pp Uk
pkt
NCFS
NCFZVCS
ZVCTJJKP
SUCSUXGYSXCMin
Subject to:
Kketkjp
Lpjtpjt ZJJ 11
-Ii
tjipL
Z2 j J ; p P ; t T ; (1.1)
jPp
pjt WJ j J ; t T (1.2)
ktktpktPp
p UXTp ** k K ; t T (1.3)
pktpkt YMX *
k K ; p P ; t T (1.4)
pktpkt XY
k V ; p P ; t T (1.5)
pktPp
pktktkt XTpUSU **
k U ;t T (1.6)
10
Jjtkjp
Lpkt ZX 1 k K; p P ; t T (1.7)
Jj
etjipL
pit ZD 2 i I; p P ; t T; (1.8)
ptjipp ZV 2* CapN tji *2
j J ; i I; l L ; t T (1.9)
tkjpp
p ZV 1* CapN tkj *1 j J ; k K; l L ; t T (1.10)
pktY 0,1 k K ; p P ; t T (1.11)
tkjpZ1 ; tjipZ2 ; pktX ; pjtJ ; tkjpN1 ;tjipN2 ; ktSU (1.12)
k K ; j J ; p P ; t T ; l L ; i I
The objective function minimizes the tactical planning cost, composed of: variable production
cost, set up cost, outsourcing cost, internal capacity underutilization cost, average inventory
holding cost, variable transportation cost from manufacturing units to warehouses, variable
transportation cost from warehouses to retailers, fixed transportation cost from manufacturing
units to warehouses and finally the fixed transportation cost from warehouses to retailers. The
transportation cost is composed of a variable cost, depending on the quantity transported, and
a fixed cost depending on the selected transportation mode; the latter is proportional to the
number of trucks, aircrafts or ships used.
Constraints (1.1) calculate the inventory level of product p in warehouse j at the end of period
t. Constraints (1.2) guarantee that over each time period, the total stored quantity does not
exceed the storage warehouse capacity. Constraints (1.3) state that produced quantities respect
available internal production capacities while considering production lead times and a safety
production capacity to be used at the operational level. Constraints (1.4) and (1.5) ensure the
relationship between binary and integer variables. Constraints (1.6) with the objective
function define the under-utilized internal production capacity. Constraints (1.7) guarantee
that all produced quantities are transported to warehouses. Constraints (1.8) state that products
transported from warehouses to retailers satisfy the demand with respect to delivery lead
times. Constraints (1.9) and (1.10) guarantee that over each time period, the transported
quantities do not exceed capacities. Constraints (1.11) and (1.12) are
the integrality constraints.
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Operational planning model
Below, we first describe the proposed operational planning horizon and then we define model
parameters and notations. Variable operational planning horizon
As mentioned above, the operational planning model considers initially (at the beginning of
each month) a two-month planning horizon with a weekly periodicity where each month
contains 4 weeks. This choice is necessary to detail decisions taken at tactical level over
weeks, and guarantee concordance between tactical and operational levels. A weekly rolling
horizon is used to integrate replenishment orders. Besides, once the operational planning
horizon starts a month, we must collect all tactical planned decisions for this month. Thus, the
rolling operational horizon must reach the end of the month to detail decisions related to
tactical planning per weeks. In fact, by introducing replenishment orders, tactical decisions
must be met until the end of months considered at the operational horizon as shown in figure
3. Henceforth, a variable operational planning horizon is used. The number of weeks included
Figure 3: Variable operational planning horizon
Hereafter, weeks in the operational planning model are denoted by a couple (t, s), where s is
the position of the week in the month, t.
To cons , a set TS of
periods is to be considered (see table 1). For example, to construct an operational planning at
, the concerned periods are , ,
Operational horizon = 9 weeks
Operational horizon = 10 weeks
Operational horizon= 11 weeks
Operational horizon = 8 weeks
New orders
Tactical model
Operational model
New orders
New orders
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, , , , , , ), , and are given
by the second column of table 1 (TS 2).
Table 1: Operational planning model periods at week of month
Model description
In the operational planning model, we consider the same sets and parameters as in the tactical
model by adding a tilt (~) to distinguish between
parameters are also considered for any (t,s) TS .
This model decides on weekly quantities to produce, store and deliver taking into account
different transportation modes and transportation lead times. Only local subcontractors are
considered here and overtime may be planned to allow greater flexibility to our system.
In the operational planning model, tactical planned quantities for first, second and third
months (Xpk , Xpk +1 , Xpk +2) are considered as inputs and have to be detailed per week. In
addition, newly arrived demands ( pitsD~ ) have to be planned. Orders are assigned to
manufacturing units characterized by a weekly limited production capacity ( ktsU~ ) where they
are produced incurring variable and fixed weekly production costs ( pktsS~ , pktsC~ ) or weekly
outsourcing costs ( pktsG~ ). A weekly under-utilization cost of the internal production capacity
( ktsSUC~ ) is also considered to penalize the unused available resources. Each product is
characterized by a production lead time (Tpp Vp). Capacity
production flexibility is provided by a weekly overtime production capacity ( ktsHU~ ) incurring
an overtime production cost ( pktsHC~ ). All produced quantities are transported to warehouses
where weekly inventory holding costs are incurred ( pjtsPK~ ). Warehouses are characterized by
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a limited storage capacity ( jW~ ). Transportation modes are characterized by a weekly limited
transportation capacity (Capl) and a delivery lead time (dl). Variable and fixed weekly
distribution costs from manufacturing units to warehouses ( tskjpFC~ , tskjpTC~ ) and from
warehouses to retailers ( tsjipFSC~ , tsjipSC~ ) are also considered. For better approximation of
the inventory holding cost; it is calculated by considering the average stock level between the
beginning and the end of period. The underutilization capacity cost is estimated by means of
hourly labor/machine cost. Obviously, here, the underutilization cost is determined relatively
to the entire internal production capacity.
Decision variables are as follows:
tskjpZ1~ : transported quantity of product p at week s of the month t from manufacturing unit k
to warehouse j using transportation mode l.
tsjipZ 2~ : transported quantity of product p at week s of the month t from warehouse j to
retailer i in period t using transportation mode l.
pktsX~ : quantity of product p produced in manufacturing unit k at week s of month t.
pktsHX~ : produced quantity of product p during overtime in manufacturing unit k U at week s
of month t.
ktsUS~ : under-utilized production capacity at internal manufacturing unit k at week s of month
t.
pjtsJ~ : inventory level of product p in warehouse j at the end of week s of month t.
pktsY~ =1 if product p is produced in manufacturing unit k at week s of month t, 0 otherwise.
pktsHY~ =1 if product p is produced during overtime in manufacturing unit k at week s of
month t, 0 otherwise.
tskjpN1~ : number of transportation modes l used to transport products from manufacturing unit
k to warehouse j at week s of month t.
tsjipN2~ : number of transportation modes l used to transport products from warehouse j to
retailer i at week s of month t.
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Model formulation (M2)
)2~*~1~*~
2~**~1~**~
2/)~~(~~~~~
~~)~~(~~~(
),(),(
),(),(
),(1
),(),(
),(),(TS),(
jipltsTSst L Pp Ii Jj
tsjiptskjpTSst Pp L Kk Jj
tskjp
tsjippTSst Pp Ii L Jj
tsjiptskjppTSst Pp Kk L Jj
tskjp
Jj TSst Pppjtspjtspjtskts
TSst Ukktspkts
TSst Pp Ukpkts
pktsTSst Pp Vk
pktspktsTSst Pp Uk
pktspktspktsst Pp Uk
pkts
NFSCNFC
ZVSCZVTC
JJPKUSSUCHXHC
XGHYYSXCMin
Subject to:
L Iitsjip
Kk Ltskjpspjtpjts ZZJJ 2~1~~~
1 j J ; p P ;(t,s) TS (2.1)
jPp
pjts WJ~ j J ;(t,s) TS (2.2)
1~~pktspkts YHY k U ; p P ; (t,s) TS (2.3)
)~~(*~pktspktspkts YHYMHX k U ; p P ; (t,s) TS (2.4)
pktspkts HXHY ~~ k U ; p P ; (t,s) TS (2.5)
ktspktsPp
p UHHXTp ~* k U ; (t,s) TS (2.6)
ktspktsPp
p UXTp ~* k K ; (t,s) TS (2.7)
)~~(*~pktspktspkts YHYMX k K ; p P ; (t,s) TS (2.8)
pktspkts XY ~~ k K ; p P ; (t,s) TS (2.9)
1
11/),(
~~s
spkpkTSst
pkts XXX
k K ; p P (2.10)
11/),(
~pk
TSstpkts XX
k K ; p P ; t= (2.11)
21/),(
~pk
TSstpkts XX
k K ; p P ; t= (2.12)
Pppktspktskts XTpUUS ~*~ k U ; (t,s) TS (2.13)
Jjtskjp
Lpktspkts ZXHX 1~~~ k K; p P ; (t,s) TS (2.14)
Jjsetjip
Lpits ZD 2~~ i I; p P ; (t,s) TS e (2.15)
CapNZV tsjitsjipPp
p *2~2~* j J ;i I; (t,s) TS ; l L (2.16)
15
CapNZV tskjtskjpPp
p *1~1~* j J ; k K; (t,s) TS ; l L (2.17)
pktsY~ 0,1 ; pktsHY~ 0,1 k K ; p P ; (t,s) TS (2.18)
tskjpZ1~ ; tsjipZ 2~ ; pktsX~ ; pktsHX~ ; pjtsJ~ ; tskjN1~ ; tsjiN2~
; ktsUS~
k K ; p P ; (t,s) TS ; j J ; i I ; l L (2.19)
The objective function minimizes operational planning costs. The first term represents the
variable production cost, the second represents the set up cost and the overtime set up cost.
The third term is related to production outsourcing and the fourth is related to production
during overtime. The fifth term is the production capacity underutilization cost. The average
inventory holding cost between successive weeks s-1 and s is represented by the sixth
term. Finally, the last four terms are related to variable and fixed transportation costs from
manufacturing units to warehouses and then to retailers.
The constraints (2.1) are production flow balance constraints. Constraints (2.2) enable the
respect of storage capacities. Constraints family (2.3), (2.4) and (2.5) are to ensure the
consideration of overtime set-up production cost only in case there was no production of the
same products previously. Constraints (2.6) and (2.7) ensure compliance with production
capacity during both regular working time and overtime, considering production lead
times. Constraints (2.8) and (2.9) ensure relationship between binary and integer variables.
Families of constraints (2.10), (2.11) and (2.12) ensure accordance with decisions made by the
tactical planning model (M1). Constraints (2.13) with the objective function define the under-
utilized internal production capacity. The distribution of all produced quantities to warehouses
is guaranteed by constraints (2.14). The family of constraints (2.15) ensures the satisfaction of
demands on time respecting transportation lead times. The respect of transportation
modes is ensured by constraints (2.16) and (2.17). Finally, constraints (2.18) and
(2.19) impose the integrality of some decision variables.
Experimentation and results
Experimental data
The considered company has three knitting manufacturing plants located in Tunisia. About
200 different knit product references are produced per year. Two warehouses located in
Tunisia are used to store finished products: one is used to store products ordered by local
retailers, the other is used to store products ordered by overseas ones. Apparel items are then
16
transported to retailers with respect to their delivery due dates. The company deals with about
30 retailers per year.
Transportation is provided through three modes. Local transportations are made by trucks,
while overseas ones are provided by ships or aircrafts. The trucks transportation cost is a fixed
cost for each delivery. The choice between ships and aircrafts for overseas deliveries takes
into account the related lead times. Indeed, for the ship, a period of about five weeks is
needed. However, for the plane, delivery is made in the same week. The overseas distribution
costs are composed of variable costs, depending on transported quantities, and fixed costs of
freight, depending on the number of conveyance done in the same period. The fixed aircraft
transportation cost is three times bigger than the fixed ship transportation cost.
The objective is to orders which have to be delivered in time and with lower
costs. In order to reinforce its production capacity and flexibility, the company works with ten
local subcontractors and a Chinese one. Working with subcontractors allows increasing
production capacity when it is necessary and so provides flexibility. The Chinese
subcontractor offers very competitive prices: a unit price for a basic product is almost half of
its internal production cost. It has the capacity of producing large volumes of basic products
but only orders having a lead time larger than two months could be assigned to it. Local
subcontractors provide products with prices higher than internal production costs; in general
they are 20% higher than internal production costs. Production capacities of internal
manufacturing units are limited. However, subcontractors capacities are high enough to
satisfy ordered quantities.
A capacity underutilization cost is incurred by labour and machine hourly fixed costs. Internal
manufacturing units can be used after regular working hours. This additional capacity is
limited to 25% of the production capacity in regular working hours, while production during
overtime costs 40% higher. Finished products are gathered and stored in appropriate
warehouses. These warehouses are characterized by their limited storage capacity and an
inventory holding cost of around 5% of unit production cost.
Safety production capacity determination
We propose to evaluate the impact of a safety production capacity at the tactical planning. In
our experimentation, we are considering the same value of safety production capacity for all
internal manufacturing units.
17
First, we consider for each month of the six-month planning horizon the same fixed value for
the safety production capacity. The percentage of internal production capacity that can be
used to fulfill pre-season orders is thus a fixed value and is denoted by .
Second, we consider a value of safety production capacity varying from month to month of
the six-month planning horizon. The percentage of internal production capacity that can be
used to fulfill pre-season orders is thus a monthly-varying value and is denoted by t, where t
indexes the month.
In practice, safety production capacity has to be estimated a priori
based on historical demand data. In our work, we have two-year historical data from which
we have to determine an adequate safety production capacity to use at the tactical planning
level.
The safety capacity is estimated by computing the ratio: replenishment production / total
production. The used internal production capacity rates are reported below:
Table 2. Observed used internal production capacity rates based on 2-year historical demand data
Month M1 M2 M3 M4 M5 M6 Average
rate N-2 (%) 62 90 89 71 61 76 75
rate N-1 (%) 75 91 72 91 87 95 85
Average rate 69 91 81 81 74 85 80
Numerical results and analyses
We simulate the proposed approach over six months (M1, M2, M3, M4, M5 and M6) of the
year N. In our experimentation, the tactical planning model is run 48 times. However, the
operational planning model is run 192 times. After running the different models according to
the proposed approach, a production planning is obtained for each week of the considered six
months. Storage details and distribution schedules are also determined.
All ILP models used by the proposed approach are solved using the package ILOG OPL
Studio V6.3/ Cplex 11. The code is run on a PC Intel Core i5 with a 2.3-GHz processor and
512-MB memory. A near-optimal solution to 10-4 is obtained for all run models with no more
than five minutes. For the tactical planning model the number of constraints is about 122000
and the number of variables is about 66000 including more than 5000 binary variables. The
operational model contains about 55000 constraints and 25000 variables including more than
18
3000 binary ones. For all the experimentations presented below, the supply chain cost over six
months is composed of two parts. The first part is deduced from the tactical planning solution
and is incurred by subcontracting costs. The second part is obtained from operational planning
solutions by summing up the costs corresponding to the first periods of the rolling horizon.
A Full production capacity
Considering full production capacity at the tactical planning means that no safety production
capacity is taken into account. This case represents the situation of the textile/apparel
company under study, as the latter does not consider any safety production capacity in tactical
planning. When a full production capacity is used at the tactical planning level, the supply
chain cost obtained for the considered six months is equal to 2 864
In what follows, we test other values of safety production capacity. The objective is twofold:
(1) showing the importance of integrating a safety production capacity in the tactical planning
to earn flexibility, (2) pointing out the necessity to develop adequate methods based on
demand historical data that can provide accurate estimation of safety production capacity.
A fixed safety production capacity
In the following, first ranging between 70% and 100% with a 5%
gap between two successive values (see table 3 we record the related
supply chain cost as mentioned above.
Table 3. Cost variation according to
70% 75% 80% 85% 90% 95% 100%
3 896 2 990 2 746 2 667 2 716 2 723 2 864
Figure 4 shows the curve representing the variation of the supply chain cost according to .
We can see that the obtained curve has almost a convex shape. Higher costs are noticed for
70%, 75% and 100% values.
A reserve of 30%-25% of production capacity leads to assigning a lot of orders to
subcontractors at the tactical level. Subsequently, a high capacity underutilization is noticed at
the operational planning level. When no safety capacity is considered at the tactical planning
(which is currently practiced in the company), at the operational planning level a lot of
replenishment orders are assigned to subcontractors or produced during overtime as internal
production capacity is used during regular working hours to satisfy pre-season orders.
19
Figure 4. Supply chain cost variation according to
We can notice that in the considered real case study the best supply chain cost is obtained for
around 85%. Therefore, a safety production capacity around 15% guarantees a production
flexibility that minimizes the supply chain cost.
We note that =80% is the average value obtained from the historical data base (presented in
table 2). The obtained supply chain cost for the considered six months of the year N is 2 746
equal to 100%. However, the
benefit may be greater if the safety production capacity could be better estimated by using
more accurate historical demand data and developing more efficient estimation methods. In
ction capacity
use (as shown in table 3).
A Monthly-varying safety production capacity
In this part, we propose to test a monthly-varying safety production capacity. For each month
t of year N, we consider as value of t, the average of the percentage of internal production
capacity used for the years N-1and N-2 (as indicated in table 2).
After introducing t values in tactical planning models and applying sequentially tactical and
operational models, we obtain a supply chain cost equal to 2 575 . This cost is lower than
the supply chain cost obtained when a fixed safety production capacity equal to 20% is
considered. The used method leads to 6.2% cost cutting comparing to the previous one.
Besides, it allows a 10.1% cost cutting in comparison with the case of tactical planning
considering full production capacity (as shown in figure 5). However, the profit may be
bigger if more accurate historical demand data are available and more efficient estimation
methods are developed.
2500000
2700000
2900000
3100000
3300000
3500000
3700000
3900000
4100000
70% 75% 80% 85% 90% 95% 100%
20
Figure 5. Supply chain cost comparison
This cost saving is due to the six-month production assignment to internal manufacturing
units and subcontractors as shown in figure 6.
Figure 6: Production assignment On the one hand, over the considered six months, we notice a better use of the internal
production capacity when a safety capacity is taken into account at the tactical level. Internal
production capacity is better used in the case of a monthly-varying safety production capacity.
On the other hand, we denote that some production is performed during overtime, even
though internal production capacity during regular hours is not fully utilized. This is mainly a
2 864 k
2 746 k
2 575 k
2400000
2450000
2500000
2550000
2600000
2650000
2700000
2750000
2800000
2850000
2900000
Full production capacity
Fixed safety production
monthly-varying safety production capacity
259359 259654 259727
1833 1401 2303
25507 35373
16793
0
50000
100000
150000
200000
250000
300000
350000
full production capacity,
Fixed safety production
Monthly-varying safety production capacity
Internal manufacturers' production Overtime internal production
subcontractors' production available-internal capacity
6%
10%
4%
21
result of the position of due dates of pre-season orders over the month. Since products
planned in internal manufacturing units over one month are detailed at the operational level
per week, it seems compulsory in some cases to produce massively over the first weeks of the
month in order to respect delivery due dates. Thus, it is needed to produce during overtime as
production during regular hours cannot satisfy the required quantities. Meanwhile, internal
production capacity over the remaining weeks of the month is under-utilized.
We also point out that produced quantities in
monthly-varying safety production capacity is considered are less than those proposed when a
fixed safety production capacity is used (for both 80% and 100%). Henceforth,
production assignment to subcontractors is better optimized for monthly-varying production
safety. This result highlights the benefit of considering a monthly-varying safety production
capacity adjusted to replenishment orders: production assignment to subcontractors is decided
at the tactical level while adequately and accurately preserving some internal production
capacity to insert replenishment orders.
Nevertheless, p
s considered at the tactical level. At the same time, total
quantities produced over the considered six months are larger than those produced when we
100%, or a monthly-varying safety production capacity. This is due to
demand variations from month to month. In fact, when a fixed safety production capacity with
80% is considered, two situations can occur: (1) replenishment orders to be
satisfied during the month require more than the available capacity (so require more than the
safety production capacity). In this case production assignment to subcontractors is the main
solution ; (2) replenishment orders to be satisfied during the month require less than the
available capacity (so require less than safety production capacity) ; in this case and in order
to minimize underutilization, replenishment orders to be satisfied for the next months are
processed in advance. When a fixed 100% is considered, replenishment orders are
assigned to subcontractors as full production capacity is used for pre-season orders at the
tactical level.
Finally, using a monthly-varying safety production capacity at the tactical level allows
efficient use of internal production capacities and optimizes production assignment to
subcontractors. The performance of capacity planning can however be improved, if more
accurate historical demand data are used and monthly-safety production capacity estimation
methods are developed.
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Conclusion and further researches
In this paper, we propose a sequential approach integrating tactical and operational decision
levels for textile/apparel supply chain planning.
In this field of industry, there is an imminent need for developing planning approaches that
take into account demand specificities: variability, fashion dependency and short life-cycle
products. In this context, production and distribution planning are closely linked and have to
be performed so that the schedules flexibility is maximized. The deal here is to emphasize
flexibility we opt for the implementation of a safety production capacity at the
tactical level to provide more flexibility at the operational level so that weekly new orders
with short due dates can be planned through the rolling horizon. The objective is to minimize
the supply chain cost while ensuring on time deliveries.
First, we evaluated the supply chain cost when a full production capacity is used at the tactical
planning. Second, we tested our approach with different percentage values for safety
production capacity and we pointed out that the best supply chain cost could be obtained
when about 15% of production capacity was not allowed at the tactical planning level.
Third, considering historical demand data, we tested other percentage values for safety
capacity: (1) we considered a fixed value for all periods of the planning horizon (an average
estimate of the historical data); (2) we proposed to consider a percentage value for safety
capacity for each period of the planning horizon. We proved then that a good estimated
monthly-varying safety production capacity at the tactical level led to a better placement of
new replenishment orders which arrived urgently. Cost saving attained 10% compared with
production capacity fully used at the tactical level. This significant gain reflected the
effectiveness of the approach developed to face unpredictable textile/apparel demands.
For this present work, the producer had no advanced information on current sales and
therefore no advanced information on replenishment orders that could happen. However, in
our future work, we propose to consider a supply chain coordinating informational flows,
where the retailer shares the information they have on future replenishment orders of outlets
with the producer. This advanced information will allow the producer to anticipate planning
a safety production capacity at the operational level. The latter will be adjusted over weeks,
based on forecasts of future replenishment orders and considering a weekly variable
adjustment rate. A comparison will be then established between the different cases to study
the approach performance on the textile/apparel supply chain.
23
References Aliev R A, Fazlolllahi B, Guirimov B G and Aliev R R (2007). Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management. Information Sciences 177 (20): 4241-4255. Armentano V A, Shiguemoto A L and Løkketangen A (2011). Tabu search with path relinking for an integrated production distribution problem. Computers & Operations Research 38: 1199-1209 Chen Z L (2010). Integrated Production and Outbound Distribution Scheduling: Review and Extensions. Operations Research 58 (1): 130-148. Dhaenens Flipo C and Finke G (2001). An integrated model for an industrial production-distribution problem. IIE Transactions 33: 705-715. Erengüç S S, Simpson N C and Vakharia A J (1999). Integrated production/distribution planning in supply chains: An invited review. European Journal of Operational Research 115 (2): 219-236. Eskioglu S D, Eskioglu B and Romeijn H E (2007). A Lagrangean heuristic for integrated production and transportation planning problems in a dynamic, multi-item, two-layer supply chain. IIE Transactions 39(2): 191-201. Gebennini E, Gamberini R and Manzini R (2009). An integrated production distribution model for the dynamic location and allocation problem with safety stock optimization. International Journal of Production Economics 122: 286-304. Kim Y, Yun C, Park S B, Park S and Fan L T (2008). An integrated model of supply Network and production planning for multiple fuel products of multi-site refineries. Computers and Chemical Engineering 32: 2529-2535. Mostard J, Teunter R and Koster M B M de (2011). Forecasting demand for single-period products: A case study in the apparel industry. European Journal of Operational Research 211: 139-147. Lee Y H and Kim S H (2002). Production-distribution planning in supply chain considering capacity constraints. Computers & Industrial Engineering 43: 169-190. Mula J, Peidro D, Díaz-Madroñero M and Vicens E (2010). Mathematical programming models for supply chain production and transport planning. European Journal of Operational Research 204: 377-390. Sarmiento A M and Nagi R (1999). A review of integrated analysis of production-distribution systems. IIE Transactions 31: 1061-1074. Selim H, Araz C and Ozkarahan I (2008). Collaborative production-distribution planning in supply chain: fuzzy goal programming approach. Transportation Research Part E: Logistics and Transportation Review, 44(3): 396-419. Suh M W, Lee E K and Holt M (2000). Estimation of consumer demands : an application to U.S apparel expenditures. Journal of textile and apparel, 1(1). Thomassey S, Happiette M and Castelain J M (2002). An automatic textile sales forecast using fuzzy treatment of explanatory variables. Journal of Textile and Apparel, Technology and Management 3(1).
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Tuzkaya U R and Önüt S (2009). A Holonic Approach Based Integration Methodology for Transportation and Warehousing Functions of The Supply Network. Computers & Industrial Engineering 2(56): 708-723. Vidal C J and Goetschalckx M (1997). Strategic Production-Distribution Models: A Critical review with Emphasis on Global Supply Chain Models. European Journal of Operational Research 98: 1-18.
