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Int. J. Production Economics 128 (2010) 3–10
Contents lists available at ScienceDirect
Int. J. Production Economics
0925-52
doi:10.1
� Corr
E-m
(B. Avit
journal homepage: www.elsevier.com/locate/ijpe
Supply chain strategies based on recourse model for very shortlife cycle products
Rahul Patil a, Balram Avittathur b, Janat Shah c,�
a SJMSOM, IIT Bombay, Mumbai 400 076, Indiab IIM Calcutta, D.H. Road, Joka P.O., Kolkata 700 104, Indiac IIM Bangalore, Bannerghatta Road, Bangalore 560 076, India
a r t i c l e i n f o
Article history:
Received 9 December 2008
Accepted 26 January 2010Available online 2 February 2010
Keywords:
Quantity discounts
Inventory control
JIT
Fashion retail supply chain
Quick Response strategies
Markdown pricing
73/$ - see front matter & 2010 Elsevier B.V. A
016/j.ijpe.2010.01.025
esponding author.
ail addresses: [email protected] (R. Patil), b
tathur), [email protected] (J. Shah).
a b s t r a c t
Firms that sell very short life cycle products often receive quantity discounts from their suppliers and
transporters for placing larger orders. Practitioners and researchers have begun to recognize the need to
decide the end of the season markdowns by studying the sales pattern. The use of these options can
affect supply chain mismatch risks and costs. In this paper, we study the impact of quantity discounts
and transportation cost structures on procurement, shipment and clearance pricing decisions through a
stochastic programming with recourse formulation. We propose a solution procedure that efficiently
solves this stochastic non-linear problem. Our computational experiments suggest that it is not always
necessary to select the most complex action plan. Under some business environments, the conventional
strategy of placing and transporting a single large order is a better option. We then identify situations
where options such as markdowns and the use of quick response suppliers could be useful.
& 2010 Elsevier B.V. All rights reserved.
1. Introduction
Very short life cycle products such as fashion and seasonalproducts have life cycles ranging between 3 and 6 months (Sen,2008; US Office of Technology Assessment, 1987), and theseproducts exhibit high demand uncertainty before their launch. Inthe past, firms that procured and sold such products to endcustomers or retailers usually ordered the entire order quantitywell before the selling season due to the demand uncertainty,the short lifespan and quick obsolescence of the products, thedifficulties in repeated negotiations and procurement, and thelong procurement lead-time. Depending upon how the productsperformed vis-�a-vis the original forecast, the firms used to incurmismatch costs due to either short supply or surplus supply. Sincethe last decade, these firms have been using quick responsestrategies to reduce the mismatch costs for such products (Fisheret al., 2001). The initial business volume could be between 60%and 100% of the total anticipated order (Subrahmanyan, 2000).For example, suit buyers procure 80% before season, keeping theremaining 20% of the budget back until after the season starts(Daily News Record, 1993). The various trade-offs involved in theordering of such products are shown in Fig. 1.
ll rights reserved.
Research that uses analytical methods to design quickresponse strategies is referred to as the two period or two stageproblem in the extant literature (Cattani et al., 2008; Cheaitouet al., 2009; Fisher et al., 2001; Fisher and Raman, 1996; Li et al.,2009). In this paper, we further investigate this research stream,taking into consideration the following practical issues.
Vendors often offer discounts to get economies of scale inpurchasing, manufacturing, and transportation (Munson andRosenblatt, 1998). In the fashion industry in particular, intensecompetition has prompted vendors to increasingly use monetarysupport such as quantity discounts to attract retailers (Kincadeet al., 2002). In the shipping industry, custom fees and containercharges are fixed costs that are incurred for each shipment, whichcan be considered as quantity discounts because the averageshipping cost per unit decreases with the increase in the shippedquantity (Popken, 1994). In the road and rail transportationindustry, transporters often provide discounts on full truck loadsand full wagon loads (Munson and Rosenblatt, 1998). Hence, itwould be interesting to study the role of both the procurementand the transportation quantity discount structures in the twostage model.
Given that the demand for these products is stochastic innature, instead of offering a predefined markdown price, themarkdown offered at the end of the season needs to be rationallydetermined by the unsold quantity at the end of the season(Cachon and Kok, 2007). The markdown price should dependupon the number of unsold units at the end of the product lifecycle, among other factors. We attempt to study the behaviour of
Order Variable Ordering Continuum
Initial business volume (before product launch)
Second business volume (during product life cycle)
Shipments
Price markdown (during product life cycle)
100% of total volume less than total volume
No
Single
No
←--------------→
Yes
Multiple
Yes
Lower ←material cost shipping cost
responsiveness→ Higher
Impact on metrics →
Higher ←
(at
inventory cost stock outs
clearance salesend of product life
→ Lower
cycle)
Fig. 1. The ordering continuum.
R. Patil et al. / Int. J. Production Economics 128 (2010) 3–104
the clearance price as a function of the leftover inventory and thediscount cost structures.
Though the traditional practice was to receive all merchandisebefore the start of the season, retailers nowadays are usingdifferent delivery windows during the season. For example, suitretailers use two delivery windows in a season (Sen, 2008). Takinginto consideration that the cost of retail shelf space is progres-sively increasing, we explore the possibility of computing theoptimal delivery schedule for these products. This will allow us toexplicitly study the trade-offs between the cost and responsive-ness dimensions of the quick response supply chain. We propose anon-linear (sometimes discontinuous) stochastic programmingwith recourse formulation to model this problem with theobjective of maximizing the retailer’s expected product life cycleprofit by keeping the initial business promised, and by usingsubsequent replenishment orders, transport batch sizes, andmarkdowns as recourse decision variables. We subsequentlypropose an efficient numerical procedure to solve this complexproblem.
In the next section, we present a review of the relevantliterature, and lay out the motivation for the problem under study.In Section 3, the stochastic programming with recourse model andthe proposed algorithm are presented. Section 4 discusses theresults of the numerical study, and the managerial implications.The final section reports the conclusions of our study.
2. Literature review and motivation
The problem of sourcing new products that face stochasticdemand has been investigated from different viewpoints. Earlierresearch assumed that the procurement decision had to be madebefore the realization of the demand, as in the case of the classicnewsboy problem where the entire demand for a style productoccurs in a single period. Khouja (1999) provides a detailedreview of the newsboy problem.
Though the demand for the product is highly uncertain andunpredictable at its launch, it becomes more predictable after ananalysis of the early demand pattern (Fisher and Raman, 1996).The quick response supply chains research stream used this morerefined demand information and suggested some sourcingstrategies by representing the resulting problem as a two stagestochastic program (Fisher and Raman, 1996; Bradford andSugrue, 1990).
Several variations and enhancements to this problem havebeen proposed. Fisher et al. (2001) suggest an efficient heuristic tocompute the first and the second period order quantities for acatalogue retailer’s products when the replenishment lead-timewas positive. Choi and Li (2003) suggest an optimal two stageordering policy based on the Bayesian information updating usingdynamic programming. They further discuss the impact of theoptimal policy on service level and profit uncertainty. Cheaitouet al. (2009) investigate the two period problems under a capacityconstraint situation, and slower and faster production modeoptions. Cattani et al. (2008) consider a two product, two stageproblem, and identify those situations where speculative, reactive,and mixed strategies could be optimal. Li et al. (2009) generalizethe Fisher et al. (2001) model by taking into consideration timedependent inventory holding and backorder costs.
Earlier research on the quick response supply chains hasassumed that the unit product cost and the unit transportationcost would not change with the quantity that was ordered ortransported. However, a customer could receive a price discountwhen placing large orders as was discussed earlier (Silver et al.,1998). In the single period newsboy context, Lin and Kroll (1997)investigate the impact of all unit and incremental quantitydiscount policies on the optimal ordering quantities and profitsusing a numerical procedure taking into account positive shortagecosts. Pantumsinchai and Knowles (1991) compute the optimalnumber of newsboy containers required in the newsvendorproblem under container size discounts.
Prior research shows that in situations where quantitydiscounts exist, the unit sourcing and transportation costs shoulddecrease with an increase in the ordered quantity; the monetaryrisk is lower here compared with situations where there are noquantity discounts. This gives rise to an interesting question: Howwill the reduced monetary risk influence the reactive and thespeculative ordering quantities? In this paper, we investigatethe impact of quantity discounts on both the initial and thereplenishment order quantities in the general two stage problem.
Scenario dependent markdowns can reduce the risk of unsoldinventory at the end of the season. A popular product with lessclearance inventory will need a smaller discount while anunpopular product having higher clearance inventory will requirea higher markdown (Cachon and Kok, 2007). We propose that thispractice would influence both the initial and the replenishmentorder quantities. The second objective of this research is to testthis hypothesis and study its interaction with the quantity
Table 1Possible ARRP decisions.
Product launch
scenario
Tactical decisions Operational decisions
1. More successful
than expected
Maintain launch price
Determine the optimal
number of
replenishments and
replenishment
quantities based on
trade-off between
inventory carrying
cost, and fixed costs in
ordering and
transportation
Negotiate with quick
response supplier for
increasing overall
purchases
2. More or less as
expected
Maintain launch price
3. Less successful
than expected
Reduce launch price
Plan for clearance sale
R. Patil et al. / Int. J. Production Economics 128 (2010) 3–10 5
discounts. In the next section, we propose a two stage non-linearstochastic programming formulation to study these questions.
3. Model formulation
3.1. Stochastic programming with recourse model
Placing an accurate order for the very short life cycle productsis a challenge for retailers owing to the high volatility in demandand the inability to accurately forecast the total life cycle demandat the time of initial negotiations with the supplier (before thelaunch of the product). For such products, the accuracy of demandforecasting improves considerably by the time the maturity phaseof the product life cycle is reached. Raman (1999) reports that theproduct life cycle demand—the demand up to the product phase-out time—can be forecasted quite accurately towards the end ofthe first quarter of the total time between launch and phase-out.We will refer to this time point as the accurate response reviewpoint (ARRP). Table 1 describes the tactical and operationaldecision making processes involved at the ARRP. Table 1 suggeststhat the speculative procurement and shipment decisions aretaken before the launch of the product while the reactiveprocurement, shipment and markdown decisions are taken atthe ARRP. It represents the two stage decision making frameworkreported in prior research. The operations planning horizon istypically very short. We include additional periods in the secondstage of the planning horizon to provide the flexibility requiredwhile deciding the shipment plan. The ARRP is located in the firstperiod such that the first shipment of the reactive order placed atthe ARRP arrives at the start of the second period.
We use general quantity discount functions to represent bothprocurement and transportation costs. Thus, our model canincorporate most of the commonly used discount models suchas all units, incremental and fixed fees to represent reactive andspeculative procurement and transportation functions.
Notations used:
(1) Model parameters
T ={t|t=1,y,T}, where T is the set of planning timeperiods over the product life cycle.
K ={k|k=0, 1}, where K is the set of procurementorder placement decision time points (DTPs); 0represents initial and before product launch; 1represents at the ARRP (happens in period 1).
S
={s|s=1,y,S), where S is the set of demandscenarios.fs
represents the probability of occurrence of scenarios.Ds
represents the total demand of the product at unitretail price p under scenario s.dts
represents the demand of the product in period t atunit retail price p under scenario s.d/Ts
represents the demand of the product in period T atmarkdown price qs such that d/Ts=dTs(1+e(p�qs)/p),
where e is the price elasticity.
p represents the unit retail price planned at thelaunch of the product.
q represents the unit clearance price in period T suchthat 0oqop.
wt
represents the backorder cost per unit in period t.ht
represents the inventory holding cost per unit inperiod t.ck(x)
represents the procurement quantity discountfunction that computes the per unit procurementcost of the product for business volume xnegotiated in DTP k. We assume that ck(x) x is anon-decreasing function of x.
uk(x)
represents the transportation quantity discountfunction that computes the per unit transportationcost of the product for a batch size x for volumenegotiated in DTP k. We assume that uk(x) x is anon-decreasing function of x.bts
represents the backorder at the end of period tunder scenario s.
its
represents the inventory at the end of period tunder scenario s.
(2) Decision variables
x0 represents the procurement order placed at DTP 0(speculative order).
x0t represents the quantity shipped in period t of thespeculative order placed at DTP 0.
x1s represents the procurement order placed at DTP 1under scenario s (reactive order).
x1st represents the quantity shipped in period t of thereactive order placed at DTP 1 under scenario s,where t41.
qs
represents the unit markdown price in period Tunder scenarios s, such that 0oqsop.
(3) Mathematical formulation
MaximizePSs ¼ 1
fsðpPT�1
t ¼ 1
dtsþqsd=TsÞ�c0ðx0Þx0
�XS
s ¼ 1
fsc1ðx1sÞx1s�X
t
uoðxotÞx0t
�XS
s ¼ 1
fsfXT
t ¼ 2
u1ðx1stÞx1stþXT�1
t ¼ 1
ðhtitsþwtbtsÞ�hT iTsþwT bTsg
ð1Þ
subject to
x0 ¼X
t
x0t ð2AÞ
x1s ¼XT
t ¼ 2
x1st 8s ð2BÞ
x01�i1sþb1s ¼ d1s 8s ð3Þ
x0tþx1stþ iðt�1Þs�bðt�1Þs�itsþbts ¼ dts 8s 8t41 ð4Þ
ðDs�XT�1
t ¼ 1
dtsÞð1þe½p�qs�=pÞ ¼ d=Ts 8s ð5Þ
where x0, x0t, x2s, qs represent non-negative constraints.
R. Patil et al. / Int. J. Production Economics 128 (2010) 3–106
The mathematical model has a stochastic (non-smooth for thediscrete discount function) non-linear objective function (Eq. (1))that maximizes expected profit by subtracting expected sourcing,transportation, inventory, backorder, and lost sales costs fromexpected revenue. Eqs. (2A) and (2B) ensure that the totalshipment quantity over all periods is equal to the initial(speculative) order and reactive (replenishment) orders, respec-tively. The inventory balance equations for period 1 and for theremaining periods are indicated by Eqs. (3) and (4), respectively.These equations suggest that under each scenario order backlogsor inventories may be built over the product life cycle, dependingupon the realized demand and procurement and shipmentquantities in each period. Eq. (5) captures the impact ofmarkdown in the last period on demand. Firms may have someexcess inventory or unfulfilled demand at the end of the finalplanning period T. Fashion firms typically salvage excess inven-tory, and treat unfulfilled demand as lost sales because the lengthof the planning period is defined and fixed (Li et al., 2009). Hence,for the last planning period, backorder cost and inventory holdingcost definitions are adjusted as follows. wT, the unit backordercost in the last period T, is the unit lost sales cost. hT, the unitinventory holding cost in the final period T, denotes the salvagevalue per unit. The salvage value is zero if the firm has to disposethe unsold units at the end of the season for free. In situationswhere the firm can sell the unsold units through other channels,the salvage value would be positive. Supplier capacity constraintscan be easily incorporated into the formulation by adding upperbounds on both the speculative and the reactive orders placed.
The solution to the mathematical model thus provides theoptimal speculative order quantity, the speculative order’sshipment schedule, and the recourse plan (consisting of theoptimal reactive order quantity, the reactive order’s shipmentschedule and the markdown price) for each scenario. We nowdevelop a solution procedure that efficiently solves the mathe-matical problem to optimality.
3.2. Proposed solution procedure
The mathematical model can become non-linear and discon-tinuous when practical discount functions such as all units andincremental are used. Hence, we develop a general solutionprocedure which is independent of the structure of the discountfunctions. We start the algorithm development with a completeexplicit enumeration where a solution vector is used for theobjective function evaluation and feasibility check. We firstdevelop a series of lemmas and corollaries as described below,to reduce the computational time required.
We partition the solution vector into two: the procurementand shipment decision vector and the markdown decision vector.We assume that we have selected the procurement and shipmentdecision vector for evaluation. Let ZTs be the number of unitsavailable for sale in the final period T for the scenario s.
Lemma 1. Markdown is an optimal policy only when
e41=ð1�ðhT=pÞÞ.
Proof. In the final period, when all the procurement decisionshave been taken, we have the following revenue optimizationproblem:
Maximize qsdTs 1þe p�qs
p
� �� �þ ZTs�dTs 1þe p�qs
p
� �� �� �hT
ð6Þ
subject to ZTsZdTs 1þe p�qs
p
� �� �ð7Þ
Differentiating Eq. (6) with respect to qs and setting the
result to 0, we get the optimal markdown price, q�s ¼ ðp=2eÞð1þeþeðhT=pÞÞ. &
Rearranging the terms and doing some algebraic processing, themarkdown is meaningful when e41/(1�(hT/p)).
Lemma 2. When markdown is an optimal policy, q�s ¼ ðp=2eÞð1þeþeðhT=pÞÞ for ZTs�dTs(1+e(p�qs
*/p))Z0. Else, q�s is such that
dTs(1+e(p�qs*)/p)=ZTs.
Proof. If the optimal markdown price violates constraint 7, thenit is optimal for the firm to set the markdown price such thatconstraint 7 becomes active, because the objective function isstrictly decreasing in the markdown price. Hence, the optimalmarkdown price obeys the following equality:
ZTs ¼DTs 1þe p�q�sp
� �� �
When the optimal markdown price satisfies constraint 7, its
calculation is as shown in Lemma 1. &
Lemma 2 computes the optimal markdown price for eachscenario (given the speculative and reactive order decisions) usingclosed form expressions, and thus saves computational time ascomplete enumeration over markdown variables is no longerneeded. Now, we propose a few corollaries to strengthen both thelower and upper bounds for the procurement and shipmentdecisions.
Let,
D|max=maximum possible total product demand in theproduct life cycle;D|min=minimum possible total product demand in the productlife cycle;Ds|max=maximum possible total product demand under sce-nario s;dTs= demand during time period T without markdown underscenario s; andd0T|max=maximum possible demand during time period T withmarkdown.
From Eq. (5),
d=Ts ¼ dTsð1þe½p�qs�=pÞ
Maximum possible demand occurs in period T under scenario s
when qs=0:
d=Tsjmax ¼ dTsð1þeÞ d=T jmax ¼Maxsðd=TsjmaxÞ
Therefore, D|max=PT�1
t ¼ 1
dtS +d=T |max, and Ds|max =PT�1
t ¼ 1
dts +d=Ts|max.
Djmin ¼MinsðDsÞ:
Let, u0(0) and c0(0) denote the maximum per unit transporta-tion cost and procurement cost, respectively, that the firm pays tothe low cost supplier and the slower transport mode in DTP 0.u0(0)+c0(0)op such that the low response supplier and theslower transport mode are feasible alternatives.
Corollary 1. D|minrx0*rD|max.
Proof. The lower bound simply follows from the observation thatwhen x0oD|min, the firm can always increase the profits byincreasing x0 up to D|min under all scenarios because u0(0)+c0(0)op. The upper bound exists because when x04D|max, thefirm only increases costs without increasing revenue therebydecreasing the profits. &
Corollary 1 significantly reduces the search space for x0 andhence for x0t variables.
R. Patil et al. / Int. J. Production Economics 128 (2010) 3–10 7
Now, we assume that x0 is given and compute the lower andupper bounds for x1s and thus for x1st variables. Then for thereduced problem, let, u1(0) and c1(0) denote the maximum perunit transportation cost and procurement cost, respectively, thatthe firm pays to the quick response supplier and the fastertransport mode. u1(0)+c1(0)op such that the quick responsesupplier and the faster transport mode are feasible alternatives.
Corollary 2. (Ds�x0)+ rx1s*r(Ds|max�x0)+.
Proof. Given that the firm has committed an initial businessvolume of x0, if (Ds�x0)+
Zx1s, under scenario s, the firm canalways increase x1s up to (Ds�x0)+ and increase the profitsbecause c1(0)+u1(0) p p. The upper bound comes fromthe observation that under scenario s, when x1s4(Ds|max�x0)+ ,the procurement cost and transportation cost increase, and therevenue remains constant. As a result, the profits strictly decrease.Thus, Corollary 2 considerably reduces the search space for x1s andx1st variables. &
We consider a three period problem (T=3) which is similar tothe two period problem considered in earlier research. We use thesecond period to represent the first reactive order shipment, andthe third period to represent the final period (where markdownsare planned). We use the constraints (2A and 2B), and chosenvalues of x0 and x1s to strengthen the upper bounds on both thespeculative and the reactive order shipment variables as follows.The upper bound for x01 is set as x0. The upper bound forx02=x0�x01 while for x03=x0�x01�x02 and thus is fixed. Similarly,we compute the upper bounds for the recourse shipmentvariables, and fix the final period shipment variable for eachscenario. These bound strengthening and variable fixing processesallow us to remove constraints 2A and 2B from the optimizationproblem. We then remove constraints 3 and 4, and instead usethem to represent the inventory and backorder variables of eachperiod under each scenario as follows:
i1s ¼ ðx01�d1sÞþ8t¼ 1
its ¼ ðx0tþx1stþ iðt�1Þs�bðt�1Þs�dtsÞþ8t41
b1s ¼ ðd1s�x01Þþ8t¼ 1
bts ¼ ðdtsþbðt�1Þs�x0t�x1st�iðt�1ÞsÞþ8t41
Lemma 2 calculates the optimal markdown price under eachscenario for given speculative and reactive order quantities, andthus simultaneously satisfies constraint 5. Therefore, we nowhave an unconstrained optimization problem with a significantlyreduced search space. The objective function (even the discontin-uous one) can be easily evaluated for a given free procurementand shipment decision variable vector. As a result, the problemcan be solved to optimality in a reasonable amount of time bydoing an explicit search over only free procurement and shipmentdecision variables. The proposed solution procedure is shown below:
Step 1: Set initial values of x0=D|min.Step 2: Set x1s=(Ds�x0)+.Step 3: For a given combination of x0 and x1s values, determinethe best solution by explicit enumeration on the shippingdecision variables and the optimal markdown price. Optimalmarkdown price is determined is follows:If er1=ð1�ðhT=pÞÞ replace the SS
s ¼ 1fsðpST�1t ¼ 1dtsþqsd
=TsÞ term
in objective function with SSs ¼ 1fspS
Tt ¼ 1dts. Else, determine qs*
and corresponding d=Ts as described in Lemma 2.Step 4: For x0rD|max set x0=x0+D and go to Step 2. Else, go toStep 5.Step 5: Stop. The overall optimal solution is the optimalcombination of the x0 and x1s values, and the optimal shippingdecisions, and the markdown corresponding to this combina-tion.
In the next section, we discuss the numerical setup, theexperimental design and the experimental results.
4. Numerical experiments and discussion
4.1. Numerical setup
We assume that three demand scenarios—low, medium, andhigh—can occur with the probabilities 0.3, 0.3, and 0.4, respec-tively. As was mentioned in the previous section, we consider athree period problem (T=3). The first, second, and third perioddemand forecasts are assumed as follows: (low: 50, medium:70, and high: 100) for the first period, (low: 100, medium: 140,and high: 200) for the second period, and (low: 100, medium: 140,and high: 200) for the third period. The first period demand is lowcompared with the other periods as the product is at the start ofits life cycle. The launch price is set at 20. Backorder costs for thefirst two periods are kept at 1.5 per unit per period. The thirdperiod backorder is lost sales which is equal to 20 per unit. Thesalvage value is kept as zero.
Linear quantity discount functions were used to representprocurement and transportation costs in our experiments. Theprocurement cost term is ck(x)=a0k�a1k x, where a1k such thatck(x) is a non-decreasing function of x and a00ra01. The shippingcost term is uk(x)=e0k�e1k x, where e1k such that uk(x) is a non-decreasing function of x and e00re01. The DTP 1 procurement coststructure is represented as 8�0.002x, while the transportationcost structures for DTP 0 and DTP 1 are represented as 1�0.001x
and 2�0.002x, respectively.
4.2. Experimental design
Our objective is to understand the impact of differentoperations and marketing characteristics—the inventory holdingrate, the price elasticity of demand, and the speculative order coststructure—on the performance of different supply chain strate-gies. Hence, in the 2�2�2�2 experimental design, we variedthese parameters along the following lines. The inventory holdingrate per unit per period is kept at two levels: low=1 and high=3.For a product life cycle of about 6 months, each period would befor about 2 months, and the inventory holding rates consideredare in line with the low and high values observed in reality. Wefollow prior research trends in assuming that the launch price isretained as the first and second period price, and that the thirdperiod demand can be increased by reducing the retail price.Eq. (5) represents this relationship between demand and price.The price elasticity of demand used in this equation depends uponfactors such as competition (presence of substitutes), necessity,gender, and characteristics of the product such as blend and origin(Fadiga et al., 2005; Jones and Hayes, 2002). Recent studies havefound that the price elasticity is usually between 0 and 2 forfashion products (Fadiga et al., 2005; Jones and Hayes,2002). Hence, in the experiments, we have considered twotypes of markets—price inelastic and price elastic—keeping theprice elasticity of demand (e) at two levels—low=0.25, andhigh=2.0. The DTP 0 procurement cost structure is varied usingthe values low=4, high=8 for a01, and low=0.002, high=0.004 fora11. The parameter values were chosen in such a way as tobring out the characteristics of the optimal policies with greaterevidence (Cantamessa and Valentini, 2000). We implementedthe algorithm discussed in the previous section in Microsoft-Excel using macros coded in Visual Basic programminglanguage.
R. Patil et al. / Int. J. Production Economics 128 (2010) 3–108
4.3. Supply chain strategies
Traditionally, firms have used speculative ordering, a combi-nation of speculative and reactive ordering (quick response), andmarkdown pricing options to manage the supply chains in thefashion industry. Our experiments test the effectiveness of thefollowing four strategies, which are essentially combinations ofthe above options and JIT delivery under quantity discountssituations:
1.
TabSim
E
Figu
Speculative order only: Only initial business volume, no ordersplitting, no recourse procurement, and no markdown.
2.
Speculative order and JIT delivery: Initial business volume,order splitting, no recourse procurement, and no markdown.3.
Quick response strategy using speculative and reactive ordersand JIT delivery: Initial business volume, order splitting,recourse procurement, and no markdown.4.
Quick response strategy with JIT delivery with markdown:Initial business volume, order splitting, recourse procurement,and markdown.The first strategy is similar to the traditional method ofspeculative ordering which is easier to execute. The secondstrategy needs some amount of effort to manage just-in-timetransportation. The third strategy further requires the identifica-tion of quick responsive suppliers and faster transportationmodes. The fourth strategy additionally requires efforts to planand execute the markdowns. The implementations of the thirdand fourth strategies involve forecast updating at the ARRP basedon actual sales data. Hence, an investment in an informationtechnology system is required to collect the necessary retail leveldata on a real time basis. In general, the efforts and the expensesinvolved increase as the complexity associated with the strategyincreases. Our experiments also test the benefits associated withthese supply chain planning strategies. Using such an analysis,managers would be able to study the trade-offs and take the finaldecisions.
4.4. Results
We first carried out base experiments with strategy 1 toevaluate the relative value associated with the other tactical andoperational strategies (strategies 2–4). Table 2 shows the optimal
le 2ulation results.
xp. no. Business environment Optimal supply chain decisi
e a01 ht= 1, 2 a11 Order split (t=1, 2, 3) S
1 0.25 8 3 0.002 (70,40,140) (
2 0.25 8 3 0.004 (70,80,200) (
3 0.25 8 1 0.002 (100,10,140) (
4 0.25 8 1 0.004 (70,140,290) N
5 0.25 4 3 0.002 (70,80,350) N
6 0.25 4 3 0.004 (70,80,350) N
7 0.25 4 1 0.002 (70,140,290) N
8 0.25 4 1 0.004 (70,140,290) N
9 2 8 3 0.002 (70,80,150) (
10 2 8 3 0.004 (70,80,200) (
11 2 8 1 0.002 (100,50,150) (
12 2 8 1 0.004 (70,140,290) N
13 2 4 3 0.002 (70,80,350) N
14 2 4 3 0.004 (70,80,350) N
15 2 4 1 0.002 (70,140,290) N
16 2 4 1 0.004 (70,140,290) N
res in parentheses in the last column indicate strategy 1 profit.
supply chain planning decisions in the different situations understrategy 4. In the last column, we compare the improvement inprofitability with strategy 4 to the profitability obtained in thebase case (strategy 1); strategy 1 profits are reported inparentheses. The results indicate that the use of tactical andoperational responses led to improvements ranging from 8.1% to74.4%. Given that the net profits for the apparel firms which sell toretailers or end customers are about 3% of total sales (Fisher andRaman, 1999), such an improvement would be of great value tofirms operating in these markets.
Depending upon the business environment, the optimalsolutions differ in terms of the use of the combination of therecourse actions. When the procurement cost at DTP 0 is low, thenit would be optimal to place a single order at DTP 0, and the firmdoes not benefit by using the other recourse actions. This suggeststhat the conventional practice of placing a single large order hasmerits if low cost suppliers are available. However, even when asingle large order is placed and discounts are available for bulkshipping, it would be optimal to transport the products in smallbatches across the periods. The optimal batch sizes would alsodepend on the inventory holding rates. As the inventory holdingrate increases, firms transport smaller batches in the initialperiods followed by larger batches in the later periods.
When low cost suppliers are not available, and the purchasediscounts are not high, it would be optimal for the firms to orderas per the scenario. The firm places an initial order at DTP 0 tomeet some demand. The firm then places another order at DTP 1in high and medium demand scenarios to meet the extra demand(experiment 3). But when the vendor offers a steep discount, thefirm chooses to place a single large order in DTP 0 when inventoryholding costs are low (experiment 4). Though this strategy resultsin excess stock in low and medium demand scenarios, the benefitsobtained from the discounts are substantial enough to justify asingle large order in DTP 0.
In the price elastic market, firms choose to markdown pricesonly under low and medium demand scenarios. Markdown underlow demand case is greater than under medium demandsituation. Thus the optimal markdown price would depend uponthe units available for sale in the final period. In contrast, in theprice inelastic market, even in situations where a firm has excessinventory, it would not be optimal for the firm to reduce prices toclear the inventory. Therefore, a firm should estimate andconsider the price elasticity of the demand for its product beforemaking the markdown decision.
ons Increase in profit (%)
on strategy 1econd order (s=1, 2, 3) Markdown (s=1, 2, 3)
0,100,250) N 73.4 (2429)
0,0,150) N 63.2 (2674)
0,100,250) N 30.7 (3221)
N 19.9 (3654)
N 45.7 (3829)
N 42.7 (4262)
N 8.9 (5154)
N 8.1 (5654)
0,50,200) (15, 20, 20) 74.4 (2429)
0,0,150) (15, 20, 20) 66.2 (2674)
100,50,200) (15, 20, 20) 31.9 (3221)
(15, 15, 20) 31.1 (3654)
(15, 15, 20) 50.4 (3829)
(15, 15, 20) 46.9 (4262)
(15,15, 20) 12.4 (5154)
(15, 15, 20) 11.3 (5654)
R. Patil et al. / Int. J. Production Economics 128 (2010) 3–10 9
Table 3 shows the percentage of increase in the profits withthe use of strategies 2, 3, and 4 over strategy 1. This is alsodepicted graphically in Fig. 2. As it would not make sense for afirm to use the markdown option in a low price elasticitysituation, we restricted our focus to experiments 9–16. As wasdiscussed earlier, the costs and the complexity of implementationincrease as we move from strategies 2 to 4. So based on the natureof the cost structure, the firms may choose only that combinationof levers which provides them sufficient benefits. For example,when the premium paid to the responsive supplier is high(experiments 13–16), the recourse option of placing the secondorder at ARRP has not been exercised, but the recourse action ofmarkdown is exercised in all the four experiments; the value ofthe markdown differs across the four experiments. But in asituation where the premium paid to the responsive supply isrelatively low, profitability improves significantly whenappropriate combinations of the recourse actions are used. Themanagers of such firms need to understand the businessenvironment, and then choose the optimal strategy, instead ofalways choosing the complex strategies. Even though it is possibleto understand how each parameter affects the optimal mix of
2000
3000
4000
5000
6000
7000
3.0 3.0 1.0 1.
0.002 0.004 0.002 0.0
8 8 8 8
2.00 2.00 2.00 2.0
9 10 11 1
Ex
Ret
aile
r O
ptim
al P
rofi
t
Stgy 1 Stg
ht = 1, 2
a11
a01
ε
Exp No
Fig. 2. Comparison
Table 3Performance of the studied supply chain strategies.
Exp. no. Profit increase (%) over strategy 1 with
Strategy 2 Strategy 3 Strategy 4
9 47.4 73.4 74.4
10 52.6 63.2 66.2
11 12.1 30.7 31.9
12 12.5 19.9 31.1
13 45.7 45.7 50.4
14 42.7 42.7 46.9
15 8.9 8.9 12.4
16 8.1 8.1 11.3
strategies individually, it is difficult for firms to work out intuitivesolutions for various combinations of the relevant parameters.The model in this paper provides a comprehensive framework fordetermining the optimal decisions.
5. Conclusion
In this paper, we developed a mathematical model to computethe procurement, transportation and markdown plans for the newshort life cycle products taking into consideration the discountsassociated with larger purchases and bulk transports. Theproposed solution procedure is capable of handling most of theprocurement and transportation discount structures. We showhow pre processing (using bound strengthening and variablefixing), and mathematical program decomposition (computingthe optimal markdown prices for given procurement decisions)can be used to solve a complex discontinuous non-linear model tooptimality within a reasonable amount of time.
The numerical experiments suggest that the conventionalstrategy of placing a single large order becomes dominant whenlow cost sourcing options are available, and when higherdiscounts are offered for the additional purchases. Thus, quantitydiscounts can play an important role in the procurementdecisions even for short life cycle products. In situations wherethe inventory holding costs are high, the profits increase when thefirm ships the products in smaller batches (even though discountsare available for larger shipments). From an operations perspec-tive, we would recommend that managers should simultaneouslydecide both the procurement and the transportation plans fortheir products, instead of focusing only on the procurementdecisions. Our experiments also suggest that identifying andplacing the orders with quick response suppliers is not always theoptimal solution. And contrary to popular belief, the results showthat it is not always necessary to markdown prices in the finalperiod to clear the excess inventory. Moreover, the markdown
0 3.0 3.0 1.0 1.0
04 0.002 0.004 0.002 0.004
4 4 4 4
0 2.00 2.00 2.00 2.00
2 13 14 15 16
periments
y 2 Stgy 3 Stgy 4
of strategies.
R. Patil et al. / Int. J. Production Economics 128 (2010) 3–1010
prices would depend upon the excess inventory available in thefinal period. Therefore, managers need to understand theirbusiness environment before expending efforts on tactical andoperational decisions such as identifying quick response suppliersand planning for markdowns.
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