Abstract. This paper surveies a individual merchandise scene in which a house can beginning from multiple providers. One provider has undependable capacity while other providers are dependable but have lower merchandise quality. The addressed context ( where a instance survey has been made ) is breaks due to countenances which cause failure in the supply from the undependable beginning. The of import inquiry which emerges here is how the companies should utilize different schemes for single/dual/multiple sourcing to manage those possible breaks.
In this paper two possible schemes are addressed and compared, which are double and ternary sourcing. Double sourcing provides the house with the chance of rerouting ( from a low quality provider ) after break. However, jobs of monopoly rise after the break and the purchasing house lose dickering power. Whereas, in ternary sourcing, the apparatus cost could be higher, but after the break at that place would still be competition between two providers and the monetary value would non increase unreasonably. The chief focal point of current work is on specifying the portion of each provider, and happening suited sourcing policy ( individual, double or ternary ) to use for different chances of break. The proposed theoretical account is applied in determination doing procedure of a studied supply concatenation in automotive industry.
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Keywords: supply concatenation break, sourcing scheme, dual-sourcing, triple-sourcing, countenance.
Uncertainty ( by and large termed “ hazard ” ) constitutes an inevitable portion of supply concatenation direction. Industrial companies depend on a scope of up-stream resources, which lie outside their control. Furthermore, directors have merely uncomplete information about their beginnings of supply which makes the buying procedure more hazardous. The reported dramatic results from hazardous events demonstrate the importance of proactively pull offing supply concatenation hazard [ 1-3 ] .
Juttner [ 4 ] emphasized supply concatenation hazards classification derived from their beginnings and effects. Among the supply concatenation hazards types are breaks that consequence from natural catastrophes, labour differences, supplier bankruptcy, Acts of the Apostless of war and terrorist act [ 5 ] . Break hazards by and large have a low chance and the potency for a great loss. Some documents refer to these as “ ruinous events ” [ 2 ] . These hazards can earnestly interrupt or detain stuff, information and hard currency flows, any of which can damage gross revenues, addition costs or both.
While a important sum of research has been conducted in the country of supply-chain systems, there has been comparatively small research [ 6-8 ] reported in the of import country of understanding the system-wide or planetary impacts of supply concatenation breaks [ 9 ] . How a company fares against such menaces depends on the type of break and the organisation ‘s degree of readiness [ 10 ] . Supply ironss may use divergent attacks to pull off breaks. They can procure their supply concatenation [ 11 ] , develop resilience [ 12 ] to execute recovery programs instantly after break or modify inventory direction policies [ 13 ] to diminish the effects of breaks. Along these lines, Lee and Wolfe [ 14 ] presented schemes for cut downing exposure to security losingss that may do breaks. Kleindorfer and Saad [ 15 ] introduced a conceptual model to gauge and cut down the effects of breaks. Norrman and Jansson [ 3 ] studied a fire accident at Ericsson Inc. ‘s sub-supplier and the company ‘s solution for extenuating the likeliness of such events as an proactive program. Tang [ 16 ] proposed robust schemes for extenuating break effects, and Pochard [ 10 ] discussed an empirical solution based on dual-sourcing to extenuate the likeliness of riotous events. Marley [ 17 ] discussed thin direction, integrative complexness and tight yoke, every bit good as their relationships with break effects.
Research workers addressed different extenuation [ 10, 16-19 ] and eventuality [ 20 ] schemes for cut downing the impacts of supply breaks. But the job is deadly when a individual beginning of the house is disrupted and can non go on its function any longer.
When there is a low chance of failure for a provider, it is sensible to work with it, but the on the job environment is dynamic and a provider with acceptable dependability in yesteryear may confront serious jobs which prevent it from deliver.
For case the planetary fiscal crisis contributed to the failure of keyA concerns, diminutions inA consumerA wealthA estimated in the millions ofA U.S. dollars, significant fiscal committednesss incurred byA authoritiess, and a important bead in economic activities [ 21 ] which caused declaration of bankruptcy by even major companies [ 22 ] . Another specific state of affairs caused by political issues, is when companies in different states are banned to collaborate and make concern with each other. This state of affairs, called countenance, is the context of this paper. Hence, the provider is non allowed to be in contact with maker. But this procedure is non based on a sudden event ; the chance of provider failure is really low in natural state of affairs but after the rise of political jobs, one possible reaction of states is seting countenance which causes serious jobs in supplier-buyer relationships. Sometimes the countenance is launched by a 3rd state that has economic power sufficiency to impede companies in a 2nd state to do concern with companies in the canonic state. After the specific political jobs, the chance of provider failure due to countenance grows quickly and purchasers should do determination on how they will go on sourcing after break ( figure 1 ) . In this instance, a break with really low chance and enormous impact becomes a break with high chance and important influence in a short period of clip, which is the critical clip for determination devising. Of class it is considerable that as the happening of countenances is still a probabilistic event, even after crisp addition in its likeliness it is possible that politicians reach an understanding and the job will be solved so the chance will fall down after it was peaked. Hence the determination doing becomes more important.
Please insert figure 1 here.
Similar job is the state of affairs of provider bankruptcy ; before bankruptcy declaration, the chance of supplier failure can be estimated and if the purchaser is cognizant, it can be after a utility supply policy.
Although, individual sourcing improves communicating due to shut buyer-seller relationship and could do lower cost as a effect of economic system of scale [ 23 ] ; the uncertainness of a specific buying-selling state of affairs makes dual/multiple sourcing a sensible scheme. But it is important to happen out with which degree of uncertainness, supply concatenation should switch to dual/multiple sourcing. One of the chief parts of this paper is to reply this inquiry which helps directors to do strategic determinations in appropriate clip.
This paper surveies a individual merchandise scene in which a house can beginning from multiple providers. One provider has the hazard of failure and undependable capacity while other providers are dependable but have lower merchandise quality. The addressed context ( where a instance survey has been made ) is breaks due to countenances that cause failure for an Persian automotive maker in the supply from the undependable European beginning. The of import inquiry which emerges here is how the companies should utilize different schemes of single/dual/triple sourcing to manage those possible breaks. Previous surveies represented the thought of double sourcing as a extenuation scheme [ 10 ] and rerouting as a eventuality scheme [ 20 ] , but in their survey break would non last until the terminal of study-horizon ; while in this research countenance is a rare but long break and influences the strategic determinations. In add-on chance of countenance in everyday state of affairs is truly low but in particular fortunes it rises so the determination devising should be done if this growing of chance occurs.
In this paper two possible schemes are addressed and compared, which are double and ternary sourcing. Double sourcing provides the house with the chance of rerouting ( supplied by a low quality Far-East provider ) after break. However, jobs of monopoly rise after the break and the purchasing house lose dickering power. In this state of affairs, the staying provider could increase/renegotiate the monetary values due to the monopoly state of affairs ( which has been seen in the instance survey ) . Whereas, in ternary sourcing, the apparatus cost could be higher due to an extra provider, but after the break at that place would still be competition between two staying providers and the monetary value would non increase unreasonably.
Further, already when inquiring for future monetary values, the purchaser could test the proposed monetary values offered for non-sanction and countenance scenarios and possible renegotiation closings. The scenarios of being one of two versus three providers would likely impact the providers ‘ offers.
The chief focal point of current work is on specifying the portion to give each provider, and define which sourcing policy ( individual, double or ternary ) to use for different chances of break. It is considerable that, if the company reroutes its supply to alternate providers, they may non supply the purchaser with its whole demand. Because they should increase their production capacity which faces some restrictions. Consequently, the measure of ciphering supply portion before break follows with look intoing supply portion after break. The above determinations are made to minimise the long tally norm cost and in both options, the chief costs are categorized into set-up cost, telling cost, quality cost and lost order cost. Research inquiries are to specify for which chances of break the single/dual/triple sourcing scheme would be more cost effectual and what is the portion of each provider?
The staying parts of this article are organized as follows: Following Section introduces the proposed theoretical account which is illustrated in afterward subdivision by an empirical survey ; it is followed by sensitiveness analysis of theoretical account to do determination on optimum break direction schemes. Finally, the paper concludes with a brief drumhead.
The chief focal point of this paper is on specifying the portion of each provider that minimizes the sum expected cost, when the purchaser chooses double or ternary sourcing scheme. In both conditions, the chief costs are categorized as:
C1- Ordering cost: The cost of purchasing parts from providers based on different unit-price of each provider.
C2- Quality cost: one premise is lower quality of alternate beginnings which imposes extra quality cost. So in this survey, if the whole demand is supplied by first beginning the base quality cost is zero, otherwise based on the sum of supplied parts from alternate providers this cost will be calculated. The consequence of low quality is by and large on the sum of broken parts and reworks so it has a additive relation with the figure of merchandise. Consequently, based on this ratio and portion monetary value, it is possible to delegate a cost as quality cost to each portion.
C3- Lost order cost: Based on the premise of this work, all the unmet demand is lost order. Lost orders are two types, ( a ) unmet demand due to the under-estimation of demand, ( B ) lost order as a consequence of deficiency of stuff due to jobs of break. The first type is the same in all sourcing policy and is based on the ordination policy and determination on sum of order in each period, so it would non be entered in theoretical account. But the cost of the 2nd circumstance is calculated.
C4- Set up cost: The more providers, the more set-up cost will be imposed. In this paper, set-up cost has a additive relation with the figure of providers so adding a new source/supplier imposed a fixed cost as set-up cost. This cost includes dialogue, dealing, tooling cost and etc.
C- Entire cost: amount of C1, C2, C3 and C4.
In this theoretical account the house operates an infinite skyline, with complete lost order for unmet demand where there is restraint on flexible capacity of alternate providers ; because the maximal capacity of alternate provider might be less than the entire demand or it can non make to its maximal capacity instantly after break. In a old work by writers [ 24 ] , this job without capacity restraint has been investigated.
In all sourcing schemes of this paper the undermentioned parametric quantities exist:
Dav: Average demand in each period.
B: The cost of lost order at the terminal of a period per unit.
P: The imposed quality cost if steadfast supplies from alternate providers per unit.
F: Set-up cost for each provider.
: Probability of break in a period.
: Probability of holding a period without break.
: The first whole number figure which is greater or equal to x.
The house has one undependable provider which may neglect down due to a break caused by countenance and if it goes down it will ne’er be available in clip skyline of planning. There are besides some option providers which offer the same parts with less quality and the low quality causes some re-workings and additions faulty parts, hence it imposes extra cost in comparing with base cost of undependable beginning. In following sub-sections, three options of sourcing will be illustrated.
The cardinal sourcing scheme in this survey is individual sourcing, and this subdivision presents the long-term mean cost of individual sourcing from each provider ( dependable and undependable ) . Part monetary values supplied from each provider are defined as follows:
copper: Part monetary value, supplied from first beginning ( which is undependable beginning )
chromium: Part monetary value, supplied from 2nd beginning ( which is dependable beginning with lower quality )
If the house chooses individual sourcing scheme with chief provider, the entire long-term norm cost includes ( 1 ) telling cost based on the portion monetary value which is calculated for the periods without break, ( 2 ) lost order cost based on the expected sum which can non be supplied during break, and ( 3 ) set-up cost for the periods without break. As the dialogue and dealing costs are included in set-up cost, these cost are imposed merely in the periods without break in which purchaser is working with provider. In this state of affairs the long-term norm cost would be:
( 1 )
But if the house chooses individual sourcing from alternate provider, the entire long-term norm cost includes ( 1 ) telling cost based on the portion monetary value, ( 2 ) quality cost, and ( 3 ) set-up cost, calculated as follows:
( 2 )
Imposed cost of the best solutions in double and ternary sourcing should be compared with the cost of individual sourcing by each provider.
Based on the primary premise, there are two alternate sourcing schemes: double and ternary sourcing ; and each of them has specific parametric quantities and determination variables. The double sourcing parametric quantities are as follows:
tungsten: Supply portion of 2nd provider before break.
copper: Part monetary value before break, supplied from first beginning ( which is undependable beginning ) .
chromium: Part monetary value before break, supplied from 2nd beginning ( which is dependable beginning with lower quality ) .
californium: Part monetary value after break, supplied from 2nd beginning.
Attention: Second beginning may forestall from providing with the chromium monetary value after break even for regular portion of provision, so the job should be divided into two portion with extra premise ; in other word, 2nd provider supplies the portion of tungsten before break with the monetary value of chromium, in some flexibleness preparation it remains fix after break and extra demand is supplied with higher monetary value ( californium ) , but sometimes 2nd provider will non provide with its base monetary value after break and increase the monetary value to cf. so the job should be solved in two different conditions.
: Constraint of flexible capacity of alternate provider in period I after break.
Based on the purpose of the theoretical account, the preparation can be categorized into two different scenarios: ( 1 ) D-A- 2nd provider keeps the monetary value of portion of tungsten, on chromium and supplies extra demand with the monetary value of californium and ( 2 ) D-B- 2nd provider increase the monetary value of whole demand to cf. In add-on based on the premises of or, four sub-scenarios ( D-A-1 and D-B-1 ; D-A-2 and D-B-2 ) merge here severally.
The two scenarios of ( D-A-1 ) and ( D-B-1 ) are the same ; because in the status of, lost order cost is less than imposed cost of rerouting and steadfast prefers to lose the order instead than providing from flexible capacity of 2nd provider. Hence, the inquiry is on finding the portion of each provider before break which will stay fixed after break for alternate provider. In both ( D-A-1 ) and ( D-B-1 ) , the determination is similar and the long-term norm cost ( Cav ) which should be minimized is:
( 3 )
For two scenarios of D-A-2 and D-B-2, the whole demand after break will be supplied from 2nd provider because of. The long-term norm cost for D-A-2 which should be minimized under the circumstance of chance of break is:
( 4 )
Similarly the long-term norm cost for the scenario of D-B-2 will be:
( 5 )
The purpose of introduced theoretical account is minimising expected cost, while there are some restraints on acceptable portion of each provider. In add-on to the restraint on flexible capacity of alternate provider, which determines the upper limit acceptable portion for alternate marketer after break, there is besides another restraint on lower limit acceptable portion for each provider as running production line for less than specific rate of merchandise is non economically tolerable for them. Furthermore, it is obvious that lower limit expected cost will be gained when the chance of break is zero and the house is individual sourced by chief provider, because there is merely one set-up cost and less portion monetary value. So, if the break does non happen and house remains individual sourced by chief provider, the expected cost would be its base cost ( I› ) , and if displacements to individual sourcing from alternate provider, the expected cost would be ( I›+I” ) . So, the company ever believe that extra cost equal to I” will be imposed if it shifts to individual sourcing from alternate provider and break does non happen.
In add-on if the company chooses 2nd provider as its sole beginning where break does non happen and it wants to return to the chief beginning, the renegotiating cost and clip should be added to regular cost. This cost is most of the clip a per centum of fixed cost, allow ‘s presume that this ratio is I± , so the expected extra cost would be summing up of these two cost which is called “ switching cost ” and can be calculated as equation ( 6 ) .
( 6 )
( 7 )
Consequently, the acceptable reply for double sourcing scheme would be gained through following LP theoretical account:
( 8 )
( 9 )
( 10 )
( 11 )
where, I?1 and I?2 are minimal acceptable portions for the chief and alternate provider.
While there are legion documents on single/dual sourcing [ 10, 23, 25, 26 ] to happen the proper reply for the best figure of providers, merely few research workers have worked on multiple sourcing [ 27, 28 ] and its mathematical preparations [ 29 ] . Most of the companies prefer to cut down the figure of providers to diminish the stuff providing cost by excluding the unneeded set-up and dialogue costs. Hence the dominant schemes are individual and double sourcing. When the hazard of provider default is high, companies tend to double sourcing but what if one provider goes down and the remained one causes serious job due to its place as a individual beginning. Problems of monopoly are important when because of political instability or high bargaining power of the marketer, the purchaser house should accept exceptional contract conditions to have the parts, e.g. the provider may set the statement of go oning relationship based on stableness of environmental and political issues in contract, which let them to renegociate or end the contract in the instance of mentioned state of affairss. One possible solution for this job is to put sourcing scheme on three-base hit sourcing which causes competition between two alternate providers and convey down the chance of renegotiation. In add-on, this scheme leads to monetary value competition to forestall from monetary value augmentation. Consequently, even if ternary sourcing increases the set-up cost, it reduces the hazard of monopoly jobs and as a portion of strategic determination doing on figure of providers, this option should besides be explored. In add-on to overall defined variables and parametric quantities, the ternary sourcing parametric quantities are as follows:
: Supply portion of chief ( undependable ) provider before break.
: Supply portion of first alternate provider before break.
: Supply portion of 2nd alternate provider before break.
: Additional supply portion of first alternate provider after break.
: Additional supply portion of 2nd alternate provider after break.
: Part monetary value before break, supplied from chief beginning ( which is undependable beginning ) .
: Part monetary value before break, supplied from first alternate beginning ( which is dependable beginning with lower quality ) .
: Part monetary value before break, supplied from 2nd alternate beginning ( which is dependable beginning with lower quality ) .
: Part monetary value after break, supplied from the first alternate beginning.
: Part monetary value after break, supplied from the 2nd alternate beginning.
: Constraint of flexible capacity of the first alternate provider in period I after break.
: Constraint of flexible capacity of the 2nd alternate provider in period I after break.
In similar manner to the old option ( double sourcing ) alternate beginnings may forestall from providing with their normal monetary value after break even for regular portion of provision, so the job should be divided into two portion with extra premise ; ( 1 ) option providers supply the portion of wr1 and wr2 before break with the monetary value of cr1 and cr2 severally which remains hole after break and extra demand is supplied with higher monetary value ( cf1 and cf2 ) ; ( 2 ) option providers will non provide with their base monetary value after break and increase the monetary value to cf1 and cf2. So the job should be solved in two different conditions: ( 1 ) T-A and ( 2 ) T-B which may organize 4 different sub-scenarios for each based on the premise of or or or. These premises represent T-A-1 and T-B-1 ; T-A-2 and T-B-2 ; T-A-3 and T-B-3 ; T-A-4 and T-B-4, severally.
With similar logical thinking in double sourcing for D-A-1 and D-B-1 ; T-A-1 and T-B-1 in ternary sourcing have the same preparation as good. The entire long-term norm cost for eight possible state of affairss, would be as follows:
( 12 )
( 13 )
( 14 )
( 15 )
( 16 )
( 17 )
( 18 )
Similar to double sourcing scheme, in ternary sourcing options there are some restrictions on lower limit acceptable portion of each provider and upper limit acceptable extra cost in comparing with switching cost. Furthermore, there exists another restriction on extra portion of alternate providers ( wf1 and wf2 ) which should be entered in the set of restraints for ternary sourcing theoretical account, while in double sourcing it was possible to unify this restriction in nonsubjective map. The preparation of this restraint is different for each scenario and the LP theoretical account is as follows:
( 19 )
( 20 )
/for all scenarios/
( 21 )
/for all scenarios/
( 22 )
/for all scenarios/
( 23 )
/for the scenario of T-A-3 and T-B-3/
( 24 )
/for the scenario of T-A-4 and T-B-4/
( 25 )
/for the scenario of T-A-2 and T-B-2/
( 26 )
/for the scenario of T-A-2 and T-B-2/
( 27 )
/for all scenarios/
( 28 )
where, and are extra portion of alternate providers in period ( I ) . As and may follow different forms for each instance ( e.g. a additive map or stepwise form based on I ) , accordingly, the values of and ( mean extra portion of alternate providers ) should be formulated and calculated based on particular status of that specific instance. This issue will be illustrated in following subdivision for studied supply concatenation.
1.3 Empirical Survey
The empirical instance survey of this paper has been done in the context of countenances while there are several trade barriers in supplier-manufacturer relationships. The investigated supply concatenation is in automotive industry in Iran. The critical parts can be supplied from undependable and dependable lower quality providers, the laters are non acceptable in normal state of affairss because of imposed excess quality-cost and extra set-up cost. Assume that, a critical portion is supplied from chief beginning with the monetary value of where there is besides an alternate provider with the offer of, but it imposes extra quality-cost of per portion. In add-on, we assume that the sum of volume flexibleness is fixed on. The other parametric quantities are, and lower limit acceptable portion for chief provider is 0.3. These parametric quantities signify to D’-A-2. Figure 1.1, exhibits the long-term norm costs based on the chance of break and portion of alternate provider.
If the concluding end of directors is to minimise the expected cost, when the sensed chance of break is, they can do proper determination which determines the sum of tungsten ( alternate provider portion ) to make the lowest cost.
For case, based figure 1.1, when the chance of break is less than 0.3 or more than 0.7, the perfectly best scheme is staying individual beginning with chief provider and alternate provider severally. It was besides the same for job without restraint on flexible capacity for alternate provider [ 24 ] . Because if the break does not/does happen and house remains individual sourced by main/alternative provider, the expected cost would be 200/220, so the company ever believe that extra 20 units cost will be imposed if it shifts to individual sourcing from alternate provider.
Fig. 1.1. Consequences for D-A-2
In add-on if the company chooses 2nd provider as its sole beginning where break does non happen and it wants to return to the chief beginning, the renegotiating cost and clip should be added to regular cost. This cost is most of the clip a per centum of fixed cost, assume that this ratio is 45 % , so the expected extra cost would be summing up of these two cost which is equal to 42 in this illustration, called “ switching cost ” . Consequently, w=1 dominates w=0, when the difference of expected cost for w=0 and 1 is more than 42.
Although, company may happen it cost-efficient to be individual sourced but some extra factors may take it to take double sourcing scheme, e.g. if the chance of break is 0.4 and the house finds it far excessively hazardous to hold one beginning, the lowest long-term norm cost ( 247 ) would be gained on w=0.3, which does non hold important difference with cost of individual sourcing options. So, company may happen it sensible to pay more but reduces the hazard of supply failure. If the company shifts to individual sourcing from alternate provider and break does non happen it may lose chance of future cooperation with chief provider. In this instance when maker wants to come to a determination on its sourcing scheme and being individual beginning on chief provider is far much hazardous. In add-on it has high expected future cost. So, it is wise to reserve an alternate provider for future and imposed cost of engaging 2nd provider should be considered as an insurance charge. Harmonizing to being of a constratint on flexible capacity of curative provider, if the house assigns less than w=0.3 to the alternate provider and break occurs, it can non reroute all the supply to the alternate provider and a portion of its demand will be lost. Hence, based on the imposed lost order and quality cost the optimized solution may stand in different value of w. For some chances of break, the rate of imposed cost based on the value of tungsten has wholly positive or negative rate which has been discussed wholly in [ 24 ] to find the best solution.
Fig. 1.2. Consequences for T-A-4 ( )
Because of particular status of monopoly for alternate provider after break, maker may waver to be dependent on it so the other option is to look into whether ternary sourcing is acceptable solution or non. Assume that, ; in this instance holding two competitory option provider causes portion monetary value and entire cost decrease ; this instance signifies to T’-A-4. While expected cost in for D’-A-2 ( dual sourcing ) is between 255 and 220 ( figure 1.2 ) and minimal cost of double sourcing option occurs on w=0.3 with the cost of 247, the company can look into if there is any executable option in ternary sourcing scheme or non. Based on defined parametric quantities, expected cost for different portion of providers is between 220 and 373. There are four sourcing options with the cost of less than 247 but as the portion of chief beginning is less than 0.3, these options are non acceptable and the concluding acceptable solution would be double sourcing with the portion of 0.3 for alternate provider.
In this survey double and ternary sourcing schemes are addressed and compared. Based on the illustrated empirical survey, minimal long-term norm cost are ever achieved in individual sourcing in which this provider is different for each chance of break ; and sourcing from alternate provider is more cost-efficient if the chance of break is higher than a specific sum.
But sing the addressed “ displacement cost ” the company may prefer to pay excess cost of dual/triple sourcing as an insurance cost for future supply failures and the best solution will non be individual sourcing. Consequently the determination of dual/multiple sourcing will be made when switching cost is less than the imposed cost of extra provider. Furthermore, there are some silent losingss due to lost demand, including client trueness and trust, which motivates houses to see extra cost of dual/triple sourcing as insurance cost. In add-on, the optimum portion of alternate provider would be wholly different for different chance of breaks. When the chance is lower ( in illustrated survey less than 0.5 ) , the lower limit expected cost is on portion of w=0.3 for alternate provider even though the house lose a portion of its demand due to miss of needed parts. And the more or less portion for alternate provider ( upper or lower than 0.3 ) causes the more cost. But for the higher chance of break, the expected cost has diminishing forms based on the addition in portion. So the more portion ends to the less expected cost and this form is the same for any value of tungsten between 0 and 1. Furthermore, the consequences of the theoretical account are really sensitive to set-up cost. So, based on different cost parametric quantities, there might be cost-efficient options in three-base hit sourcing which can be chosen by determination shapers to cut down the hazard derived by alternate provider monopoly. For case, in the illustrated survey, if the set-up cost is 15 alternatively of 50, there would be possible options of ternary sourcing with less expected cost in comparing with single/dual sourcing. Hence, one the chief efforts in future work would be sensitivity analysis on different parametric quantities including set-up cost and restraint of flexible capacity.