Turning importance of more informed and timely determination devising in Build-To-Order Supply Chain, demands farther research on the modeling and analysis of Strategic Sourcing. Purchase monetary values fluctuate for a assortment of grounds as a consequence ; pull offing the stuff costs in volatile market is a ambitious undertaking. The Quantity Flexible ( QF ) contract theoretical account developed is based on limited information to stabilise the purchase cost under demand unsure and fluctuating monetary values by negociating the monetary value of merchandise. In order to understand the rational behavioral effects on QF contracts, we determine deductions of delimited reason on the public presentation of QF contracts. Rational behavior of the purchaser is studied under two different ineluctable restraints of determination doing comparing behavioral solution and optimum solution for two different scenarios in supply concatenation.

Keywords: Quantity flexibleness Contracts, Supply Chain Contracts, Build-To-Order Manufacturing, Bounded Rationality.


In recent old ages, Build-To-Order Supply Chain ( BTO-SC ) Management has become prevailing among hi-tech companies, including traditional fabrication companies. BTO-SC is defined by Gunasekaran and Ngai ( 2005 ) as ;

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The system that produces goods and services based on single client demands in a timely and cost competitory mode by leveraging planetary outsourcing, the application of information engineering and through the standardisation of constituents and delayed merchandise distinction schemes.

For the successful execution of the BTO-SCM, it is necessary to see demand-management techniques to pull off fluctuations in volume, pricing schemes, and increased flexibleness with providers in all sourcing contracts. A figure of contractual signifiers like Buyback, Quantity flexibleness, Backup, Revenue sharing, Net income sharing and Gross saless rebate have been extensively studied in literature ( e.g. , Tsay and Lovejoy 1999 ; Li and Kouvelis 1999 ;

Cachon and Lariviere 2005 ) these contracts have been shown to be effectual if demand is

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realized after the purchaser places its order.

Measure flexible ( QF ) contracts have been widely employed to better the efficiency of supply ironss by assorted companies such as Toyota, IBM and HP ( Tsay 1999 ) . With a QF contract, the provider charges the purchaser ( retail merchant ) a changeless unit sweeping monetary value but offers the purchaser limited flexibleness of seting his initial order measure without any punishment. If there is no flexibleness, that is, the purchaser ( retail merchant ) has to purchase precisely what he ab initio ordered, a QF contract degenerates into a sweeping monetary value ( WP ) contract. QF contract is a hazard sharing contract when demand is unknown and best suited for Build-To-Order Manufacturing patterns.

Research workers are fall backing to newsvendor jobs while planing Supply Chain contracts for covering with Build-To-Order merchandises which are characterized by unsure demand, long lead times, and fluctuating purchase costs. Many of the contracts developed in newsagent jobs are based on hazard neutrality premise but, under a stochastic environment like Build-To-Order fabricating significant sum of hazards like lost gross revenues, bringing undependability, obsolesce etc. resides for all its stakeholders and therefore the supply concatenation contracts needs to be studied in visible radiation of delimited rational behavior of stakeholders.

Literature Review

Perceived monetary value uncertainnesss in strategic sourcing are associated with many lending grounds like exchange rate motions, uncertainness of supply, deficiency of a hereafters market, information revelation, hyperinflation conditions, proficient developments, political convulsion, environmental influences, and altering hazard penchants of consumers. Out of these several grounds the major ground is exchange rate motion, where a purchaser can stop up paying well more or less than original contract monetary value ( Cater and Vickery 1988 ) . With hard prediction environments, like Build-To-Order fabrication coupled with fluctuating monetary values of merchandises, how does one happen a desirable solution for both sides? On extend of flexibleness in supply concatenation contracts as shown in Figure 1. We can reason that, Quantity Flexible ( QF ) contracts may supply one trade-off solution for pull offing volatile prediction with monetary value fluctuations.

In a QF contract, provider and the purchaser may accept some of the stock list and stock out cost load ( Arshinder et al.2007 ) . The provider requires the purchaser to do a committedness or topographic point an order earlier in order to guarantee markets and mitigate demand uncertainness. As a wages, the provider provides the purchaser with flexibleness to set the order measure subsequently. A supply contract with measure flexibleness can be explained with following illustration, Suppose the purchaser ( maker ) marks a contract of Q units with a provider and the contract has a limited flexibleness of factor say Aµ , where ( 0 & lt ; Aµ & lt ; 1 ) , Then the provider does non anticipate the purchaser to buy all Q units from it subsequently. The house can buy a sum of ten units from this provider, where ( 1 – Aµ ) Q & lt ; x & lt ; ( 1+ Aµ ) Q. Under QF supply contracts, similar “ entire minimal measure committedness ” contracts have been discussed by Bassok and Anupindi ( 1997 ) which deals with both clip and measure flexibleness.

One may sort such QF contract accommodations into two classs, i.e. , upward accommodation ( addition in order measure ) and downward accommodation ( lessening in order measure ) . Upward accommodation is designed to run into likely big demand. Such contracts allow the purchaser to increase order measure after detecting a coming monolithic demand. Down accommodation contracts are designed to react to a coming or realized demand lessening. It is clear that if, merely upward accommodation is allowed, the purchaser will put a lesser initial order or do a conservative committedness. Such policy tends to increase channel deficit cost. On the other manus, if merely downward accommodation is available, the purchaser will subject a larger initial order or do an aggressive committedness that may take to extra stock list in the supply concatenation.

QF contract couples the client ‘s committedness to buy no less than a certain per centum below the prognosis with the provider ‘s warrant to present up to a certain per centum above. Under certain conditions, this method can supply appropriate inducements to the purchaser and the provider, therefore leads to the channel coordination.

Important beginnings of uncertainness for any planning jobs with longer skylines are unpredictable demand and future monetary values of merchandises and the cost of natural stuffs ( Stefansson et al.2009 ) . Bassok and Anupindi ( 1997 ) look into prediction and buying behavior when the purchaser ab initio forecasts month-by-month demand over an full twelvemonth and so may revise each month ‘s purchase one time within specified per centum bounds. Bassok and Anupindi analyze a contract which specifies that cumulative purchases over a multiperiod skyline must transcend a antecedently specified measure, a signifier of minimum-purchase understanding. They besides study a rolling-horizon flexibleness contract concentrating on the purchasers ( retail merchants ) telling behavior when confronting an independent and stationary market demand procedure.

Typical research inquiries with regard to QF contract scenes include: ( 1 ) How should purchaser act ( i.e. prognosis and purchase ) given the available flexibleness? , ( 2 ) How should supplier act given the flexibleness promised to the purchaser? , ( 3 ) what would be cost or profit to each party of alterations to parametric quantities of the understanding, e.g. a flexibleness edge or pricing footings? To reply above inquiries we develop the similar sort of QF contract in demand unsure environment for procurance of critical constituents.

The remainder of paper is organized as follows. In following subdivision, we propose a contract theoretical account and discourse its theoretical account preparation including solution methodological analysis. In subdivision 4, we find consequences for a instance survey with two different solution attacks. In subdivision 5, we analyze the consequences under bounded reason based on behavioral solution and optimum solution and eventually in subdivision 6, we conclude and discuss hereafter research.

Proposed Model

3.1. Model preparation

Under the construction of BTO-SC, we study a houses determination on what should be contract measure to order? What should be its cost for a fixed period? See a purchaser ( maker ) confronting demand uncertainness and increased procurance cost following Build-to-Order Manufacturing scheme over a finite skyline. The aim of the contract is to minimise the purchase cost by placing optimal contract measure, which when negotiated for entire contract continuance will command the cost fluctuations in each order. The contract theoretical account negotiates the monetary value of constituents based on its quoted monetary value and repair the cost of sweeping cost and punishment cost for entire contract continuance.

The theoretical account is developed taking into history two purchase costs, one is sweeping cost for telling measure above lower limit committed contract measure and punishment cost for non telling the lower limit committed contract measure. The theoretical account identifies the minimal purchase cost for a period based on earlier forecasted demand measure and the negotiated contract costs i.e. , sweeping cost and punishment cost. Thus the Multi-objective theoretical account is based on the quoted monetary value provided by the provider as a primary parametric quantity. Two purchase costs are negotiated consequently which are fractions of quoted monetary value.

3.1.1. Premises: Following premises are made before explicating the multi-objective QF contract theoretical account:

Ordering cost, keeping cost and other hidden costs are negligible.

Contract measure ever lies between lower limit and maximal demand measure of contract period skyline.

As in QF contract there is limited flexibleness to alter the order measure, Similar flexibleness to change the order measure with regard to the fixed contract measure is given to purchaser, this will be a limited liability and this scope of flexibleness is ab initio decided based on Qmin and Qmax predicted from the forecasted demand for the contract period.

While negociating for the QF contract we are presuming the additive fluctuation of sweeping cost and punishment cost with regard to measure. For illustration, for telling higher measure sweeping cost benefit to purchaser would be more and frailty versa and likewise the higher the measure non ordered the higher will be the punishment borne by purchaser.

In order to accomplish the nonsubjective map the theoretical account is subjected to legion restraints as stated below.

In the nonsubjective map, x and y are the binary variables, for every ith period, there will be either overordering or underordering with regard to committed contract measure. This will be taken attention by binary variables for each period. In the nonsubjective map ( equation 1 ) the first portion calculates the purchase cost when measure ordered is above the contract measure for the ith period and 2nd portion takes attention of purchase cost when measure ordered is below contract measure for the said period. For every ith period, either of the one will be possible and binary maps will take attention of it along with other restraint ( equation 7 ) . Summation of ith periods gives the entire minimal purchase cost for entire contract continuance along with optimum contract measure to be ordered.

3.2. Solution Methodology

Quantitative research attack appeared to be most appropriate in order to turn to the research inquiries concentrating on the execution of a BTO-SCM scheme. ( Salvador et al. 2007 ) . Here we are seeking to unveil interactions that are taking topographic point in proposed theoretical account by taking attention of demand uncertainness and monetary value fluctuations.

The Fork-Lift Truck fabricating company selected for proving the developed theoretical account offered an appropriate research puting. In choosing the cardinal parametric quantities for theoretical account, we intentionally tried to let for multiple and divergent positions like demand measure, purchase cost, sweeping cost and punishment cost. The sourcing directors were identified for the activity and information was collected from cardinal beginnings of information viz. archival paperss, internal presentations, official purchase paperss and studies, etc.

After roll uping the desired information we used it in proposed theoretical account in two creases. First, in order to calculate the expected demand for future contract periods, from different calculating methods used in literature ( Miyaoka and Kopczak 2000 and Chen et Al. 2000 ) . We employed Holt-Winters exponential smoothing attack for solution which takes attention of degree, tendency and seasonality forms ( Peter R. Winters 1960 ) . Second, we used the forecasted informations in additive programming theoretical account to acquire the consequences by work outing it in widely used commercial optimisation convergent thinkers ( CPLEX, LINGO ) as shown in figure 2.

We have considered two different dimensions to catch the elaboratenesss of the proposed theoretical account observed during contract dialogues while obtaining the solution in two different instances in Results and findings subdivision.

3.2. Supply Chain stakeholders perspective

Trevelen and Schweikhart ( 1988 ) depict the assorted types of supply break like monetary value escalation, stock list and programming, engineering entree, and quality. The most often cited ground behind supply break is the increased uncertainness the opportunities of a supply break is reduced when a purchaser develops a strong relationship with a individual provider ( Elmaghraby 2000 ) , and this gives the maximal benefits to all its stakeholders. The theoretical account assumes a individual provider and a individual purchaser as its stakeholders negociating for the QF


In a finite-horizon QF contract theoretical account, the advantages associated with this contract from stakeholders ‘ position are given in Table 1.

Consequences and findings

The proposed theoretical account was implemented in a BTO Manufacturing Company and solved sing two different scenarios in sourcing.

Case 1: When I± and I? are independent of measure ordered. { I± and I? a‰ degree Fahrenheit ( Q ) }

Here sweeping cost and punishment cost are assumed to be independent of measure ordered and analysed for consequences. It was found that, for different combinations of values of I± and I? interesting consequences were obtained as represented in Figure 3 below.

The consequence shows a typical behavior refering to optimum measure. Based on the informations received for a provider of Forks maker, the optimal measure scope varied between 102 to 126 which was relatively a really smaller scope of fluctuation compared with earlier scope obtained from calculating technique ( i.e. , Qmin to Qmax ) . The behavior of optimum measure for different combination of I± and I? is shown in figure 4.

Purchase cost when plotted against sweeping cost factor ( I± ) for different combinations of punishment cost factor ( I? ) shows the interesting tendency with left side scope of I± demoing purchaser dominated contract dialogue and the right side, the provider dominated contract dialogue.

Figure 5 represents the dividing line for ruling scenarios for two outstanding stakeholders in Procurement. The observation from the line graph in figure 4 gives a purchaser optimum policy determination doing model. This gives purchaser the optimum contract scope for put to deathing sourcing determinations.

Measuring the theoretical account presuming dependence of I± and I? on measure ordered and we are seeking to happen out the multi-objective optimum consequences between measure to be ordered and the minimal purchase cost. Consequences obtained when, Wholesale cost factor, I± was linearly varied in the scope of 0.8 to 1 and Penalty cost factor, I? in the scope of 0 to 0.20 between upper and lower edge demands. i.e. , 90 and 140 for the instance studied showed multiple local optimum consequences.

The tabular array 2 shows the four different solutions obtained for the instance studied and we can deduce that, the consequences gives a crystalline position of entire purchase cost for best combinations of I± , I? for several local optimal telling measures. Here we are non obtaining planetary optimal solution ; since its good known fact that, one can accomplish it by paying lowest possible sweeping cost and without paying any punishment for the measure ordered. In order to better understand the construct the bounded rational behavior of purchaser in sourcing contracts, we need to compare the local optimum solutions with behavioral solutions as explained in the following subdivision.

Bounded Rational Behaviour of Buyer

The consequence of delimited reason on market fluctuations turns out to be complex, indeterminate in mark, and slightly self-contradictory ( Conlisk 1996 ) Decision shapers have to work under three ineluctable restraints: ( 1 ) merely limited, frequently undependable information handiness sing possible options and there effects. ( 2 ) Limited capacity of human head to measure and treat the information available. ( 3 ) Merely limited sum of clip available for doing determination. Therefore determination shapers who intend to do rational picks are bound to do hearty picks alternatively of optimum pick ( s ) in complex state of affairss. In this subdivision we investigate the consequence of bounded reason under restraints of limited, undependable information handiness and under restriction of human capacity of determination devising on contract measures.

How the behavioral mean order measure say, Qb differs from the optimum solution Q* ? Distinguishing the state of affairss in which the boundedly rational purchaser overorders ( i.e. , when Qb & lt ; Q* ) from the state of affairss in which he underorders ( i.e. , when Qb & gt ; Q* ) . We identify two implicit in effects that may do such deformations. First, when the purchaser is boundedly rational, order measures tend to be biased toward the center of the scope of possible demand realisations. The grounding heuristic ( Tversky and Kahnemann 1974 ) provides a behavioral principle for this consequence. When the demand denseness is usually distributed between lower edge a and upper edge B, so that a and B are the smallest and largest possible demand realisations, the center is m= a+b/2. The undermentioned consequence establishes this prejudice for the particular instance of unvarying demand.

In order to analyze this consequences, in a different attack, Let us see the purchaser has a extremely critical constituent or merchandise ( considered to be high net income merchandise ) with critical fractile I? =c/p & lt ; 0.05 and a derivable merchandise ( considered to be low net income merchandise ) if the critical fractile I? =c/p & gt ; 0.05 equivalently, P & gt ; 2c for a critical merchandise and P & lt ; 2c for a derivable merchandise. Then, for uniformly distributed demand, there is underordering for critical merchandises and overordering for derivable merchandises. Similar sort of nomenclature was foremost introduced by Schweitzer and Cachon ( 2000 ) , who besides provide experimental grounds for consequences of high net income merchandise versus low net income merchandises. They besides found that, in the high-profit status, the mean order was significantly lower than the optimum order, and in the low-profit status, the mean order was significantly higher than the optimum order. ( Schweitzer and Cachon 2000 ) . Similar consequences can be found for critical and derivable merchandises in our instance where purchaser tries to averse hazards associated with increased keeping cost and deficit cost. We find that, under bounded reason, the center prejudice provides a possible alternate account.

Here, 2nd determination prejudice sing the same instance where, the demand denseness is monotone. An increasing denseness suggests that, demand is likely to be high ; on reverse a decreasing denseness suggests that demand is more likely to be low. Here we find that, the behavioral solution is deformed in the way of low-probability demand realisations. Let us name this rare-event prejudice. One possible behavioral account is that determination shapers tend to put inordinate weight on rare happenings ( as in the chance weighing map of cumulative chance theory in Tversky and Kahneman ( 1992 ) . To command for center prejudice described earlier, we assume that the optimum solution occurs exactly at the center m.

Sing two illustrations, one with linearly increasing and other with linearly diminishing demand densenesss. Given that optimum solution Q* occurs at the center m, when degree Fahrenheit is diminishing, purchase cost falls from the optimum degree faster when Q is decreased below Q* compared to when Q is increased above Q* . This implies that overordering is less dearly-won compared to underordering, and therefore occurs more often.

The combined consequence is, the expected behavioral order Qb exceeds the optimum measure Q* , so there is overordering on norm. Similarly, the contrary is true when degree Fahrenheit is increasing. In the analysis above, we have made premises to insulate the two determination prejudices from each other. In Proposition 1, to command for the rare-event prejudice, we focus on unvarying demand with all realisations every bit likely. In Proposition 2, to stamp down the center prejudice, we assume that the optimum solution is located at the center. However, in most cases of the buyer-supplier job, both effects are present and may run in different waies.


In the paper we have considered Build-To-Order fabrication environment where the demand is unknown with contract negociating between individual purchaser and individual provider. An attempt has been made to develop a QF contract theoretical account for demand unsure monetary value fluctuating environment. The purchaser arranges for his demand based on prediction and by perpetrating to purchase the minimal contract measure from provider by constructing long term sourcing contract. The theoretical account would be best suited for BTO-SC environments like car and computing machine industry due to merchandise assortment, extremely unsure demand. The theoretical account developed will assist sourcing directors in doing strategic contract dialogues and will be able to warrant the benefits of the supply concatenation contract to its stakeholders in more crystalline and logical mode.

The attacks used in the model can be farther analyzed for their defects and restrictions. The QF contract theoretical account is complex, when we take into history keeping cost, telling cost and other hidden costs which are rather hard to explicate in bing theoretical account and the replies to these inquiries can take us to the future research. The construct of delimited reason, where the optimum measure and behavioral measure is besides studied in this paper can be compared for construing likewise for other types sourcing contracts which would be a good country for future research.


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