Emergency Procurement Based on Supply Disruptions: Single-Sourcing or Dual-Sourcing

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1 Send Orders for Reprints to 68 The Open Cyernetis & Systeis Journal, 04, 8, 68-6 Open Aess Eergeny Proureent Based on Supply Disruptions: Single-Souring or Dual-Souring Xinjun Li * and Xiaonan Zhang Shool of Eonoi and Manageent, Yantai University, Yantai, Shandong, 64005, China Astrat: Reent years have witness the pervasive supply disruptions and their ipats on supply hain perforane. We investigate single or dual souring eergeny odel with partial supply disruptions. Introduing the onept of disruption proportion and delivery alloation, we first explore partial interrupted proportion of ain supplier and delivery proportion of akup supplier. Under partial disruption, we then exaine the expeted profit of the anufaturer for single souring and ultiple souring ased on different disruption risk. Furtherore, we deonstrated the ipat of delivery proportion etween ajor supplier and akup supplier on eergeny proureent strategy of the anufaturer. Finally we deonstrate the ipat of delivery proportion etween ajor supplier and akup supplier on anufaturer s eergeny proureent strategy. Nuerial exaples show that the anufaturers should hoose the est proureent strategy to axiize expeted profit in different situations. Keywords: Dual souring, eergeny proureent, partial disruption, supply disruptions.. INTRODUCTION With the developent of lean prodution and eonoi gloalization, supply hains eoe ore and ore oplexity and vulnerale. Manufaturers tend to redue the nuer of suppliers so as to inrease eonoies of sale to ahieve ost redution and onvenient anageent. Under this irustane, one one of suppliers annot delivery for disruption, it is possile ring the huge loss to downstrea anufaturers or distriutors and the entire supply hain. Faing with the supply disruption of the fire on Marh 000 at the Philips plant in Aluquerque, NM, Nokia seek proatively other eergeny suppliers, gaining great arket share, and Erisson waited passively, losing huge arket share. On Otoer 0, Apple Ma Book Air's ain supplier of etal hassis was ordered to suspend prodution for retifiation y the loal governent eause of environent destrution. These ases illustrate the neessary of dual-souring or akup suppliers. There has een a growing strea of literature on supply disruptions. C. Bloe [] provides an review of the literature on supply hain disruption anageent and a detailed qualitative analysis. O. Tang and S. Musa [] provide detailed presentation of the risk fators faed y suppliers, and provide reoendations for different proureent strategies. J. Burke and Janie E. Carrillo [3] exaine shows that, unless the supplier's apaity is greater than the produt deand, or the purhaser annot otain diversifiation enefits, single-soure proureent doinant, otherwise doinant dual-soure proureent. In Wang et al. [4], assuing two suppliers are unstale with different ost strutures, the expeted profit funtions of four senarios are estalished, using the approxiation ethod to otain the optial ordering quantity. G. Yu et al. [5] argue that when supplier hoogeneity degree is higher, dual-souring in response to supply disruptions have the advantage. Traditional ultisouring is onduive to prooting opetition aong suppliers, resulting to the lowest purhase prie. K. Chen [6] study the anufaturers to retailers to adjust the prie or give allowane to ope with Deand Disruptions. Faian et al. [7] analyses the orrelation etween supply and deand unertainty ipats on the optial proureent strategy. X. Li et al. [8] explore dual-souring strategies to itigate disruption risk, dividing disruptions into oon ause failure and supplier-speifi inident. Our study is also related to the literature on akup suppliers. H. Jing [9] study on the advantages of akup supplier strategy and dual souring strategy. B. Tolin [0] exaine the dual souring flexiility and reliaility using the newsoy odel, and analyze the influene fators of seondary suppliers. WenJie Zhang [] develop anufaturer s expeted profits under different interruption proaility. Li Xinjun et al. [] present optial ordering ehaniss ased on options ontrats for a triadi supply hain. Chen Junlin [3] researh an unreliale supplier and a akup supplier of apaity onstraints, the uyer how to hoose the order strategy. Baih [4] study the influene fators of seleting akup supplier when supply disruptions. Most of these douents fous on how to deal with soe proles of supply and deand ialane, with few artiles aout supply disruptions. In this paper, we explore the ipat of the disruption proportion of ajor supplier and delivery proportion of akup supplier on the deision on anufaturer s eergeny proureent strategy. In what follows, we will develop a set of anufaturer s expeted profit of 874-0X/4 04 Bentha Open

2 Eergeny Proureent Based on Supply Disruptions The Open Cyernetis & Systeis Journal, 04, Volue 8 69 Tale. Pries under different souring and orresponding deand funtion. - Pries Market deand Pries Market deand Single souring Dual souring M k M + M k M k,, M + M k single-souring and ultiple-souring, respetively in the presene of supply hain disruption risks. We provide the est proureent strategy that the anufaturers should hoose to axiize expeted profit in different situations.. MODEL ASSUMPTIONS AND SYMBOL DESCRIP- TION.. Model Assuptions We onsider a two-stage supply hain onsisting of one anufaturer and two suppliers, where the wholesale pries offered y the two suppliers are different. The ajor supplier ( offers opetitive wholesale prie ut lower reliaility. The akup supplier ( offers ore reliale ut ore expensive. Assuing supplier s apaity unrestrited, the wholesale pries hanges with the anufaturer purhase quantity. The wholesale prie of ajor supplier in single souring is lower than that in dual souring. The wholesale prie of akup supplier in noral state is lower than that in disrupted state. Let as define disruption proportion and delivery proportion. Major supplier ay e partially interrupted or opletely interrupted. Disruption proportion is defined as the ratio of the rest supply apaity to all the ordering quantity with partially interruption. In dual souring anufaturer assigns a akup supplier to a ertain proportion of orders and this proportion is alled y delivery proportion... Syol Desription M : axiu arket sale M : arket sale shifting when disruption ours D : realized deand, D = M k k : oeffiient of prie sensitivity, k > 0 : disruption proaility of ain supplier p : unit sales prie of final produt : ain supplier s unit wholesale prie in singlesouring : ain supplier s unit wholesale prie in dual-souring : akup supplier s unit wholesale prie in noral state : akup supplier s unit wholesale prie in disrupted state v : anufaturer s unit loss of unsatisfied deand : ain supplier disruption proportion in disrupted state, 0 : akup supplier delivery alloation in dualsouring, 0 < < < 3. SOURCING STRATEGY SELECTION BASED ON SUPPLY DISRUPTIONS The anufaturer has two souring ethods to hoose fro, one is single souring and the other is dual souring. Different purhasing strategies have different pries, depited in Tale. We use the average of their wholesale pries to alulate the arket deand in dual souring. 3.. The Benhark with Single Souring and Dual Souring The expeted profit funtion of the anufaturer with single souring, E, is given y ( E( = ( ( p ( M k + [( M + M k v + (( p ( M k ] ( The expeted profit funtion of the anufaturer with dual souring, E, an e alulated as ( E( = ( ( M k [( p ( ] + [( ( p ( M + (( ( p ( M + ( p ( M k + (M k v] When the akup supplier is the sole soure, =0, =. The expeted profit funtion of the anufaturer is given y E( 3 = ( [( p ( M k ]+ {( p ( M k + [( M + M k ( M k ]v} = ( p ( M k (3 +[( M + M k ( M k ]v (

3 60 The Open Cyernetis & Systeis Journal, 04, Volue 8 Li and Zhang When dual souring ethod outperfors the single souring with the ain supplier as the sole soure, E > E(, ( ( ( M k [( p ( ]+ [( ( p ( M + (( ( p ( M + ( p ( M k + (M k v] > ( ( p ( M k + [( M + M k v + (( p ( M k ] > = The expression an e written as, ( p ( M k ( M k [( p ( ] ( M k ( ( [M k + ( M + M k ]v +( p ( M k If >, then E ( > E(. In this ontext, dual souring is etter than single souring with the ain supplier. When the single souring with the akup supplier as the sole soure doinates the dual souring, then E > E(, ( 3 ( p ( M k + [( M + M k ( M k ]v > ( ( M k [( p ( ]+ [( ( p ( M + (( ( p ( M +( p ( M k + (M k v] We an get the following expression, ( M k [( p ( ] ( p = ( M k ( M k [( ( ( p ]+ (7 (k + k k v The odel of akup supplier as the sole soure is superior to dual souring. Therefore, we an hoose the appropriate proureent strategies aording to the disruption proaility: If <, then hoose ain supplier as the sole soure. If < <, then hoose dual souring. (4 (5 (6 If >, then hoose akup supplier as the sole soure. 3.. Analysis of the Disruption Proportion The derivatives of E with respet to is given y, E( ( = (k M M v ( p ( M + M k (8 It is ovious of p >, so E( < 0. When disruption proportion inreases in single souring, the anufa- v turer's expeted profit dereases. The derivatives of E with respet to eoes, E( ( = ( ( ( M k (9 If ( ( ( M k < 0, then E ( < 0. The anufaturer's expeted profit dereases in disruption proportion. Beause the disruption portion of ain supplier is opleentary y the akup supplier, akup supplier s unit wholesale prie in disrupted state is higher than ain supplier s unit wholesale prie. The anufaturer's expeted profit dereases with disruption proportion Analysis of the Delivery Proportion The derivatives of E( with respet to an e written y E( = ( ( M k + ( ( M k Considering that < (0, we an otain that as >, then E( 0 > ; as <, then x( x( E( < 0. When the delivery alloation satisfies < <, the anufaturer's expeted profit dereases with delivery alloation in dual souring. When the ( delivery alloation satisfies < <, the anufaturer's expeted profit inreases in delivery proportion. ( When the delivery alloation is greater than a ritial value, the anufaturer inreases order quantity froakup souring, although this leads to higher proureent osts, ut the total expeted profit is heightened.

4 Eergeny Proureent Based on Supply Disruptions The Open Cyernetis & Systeis Journal, 04, Volue 8 6 Tale. Paraeter assignents. Paraeter v p M M K Values ANALYSIS OF NUMERICAL EXAMPLE In this setion, analyze the anufatures expeted profit of adopting single souring and ultiple souring, the ipat of the disruption proportion of ajor supplier and delivery alloation of akup supplier on the anufaturer s proureent strategy. Paraeter assignents are shown in Tale. The horizontal axis is disruption proaility of ain supplier, the vertial axis is anufaturer s expeted profit funtion, denoted y E (, E( and E ( 3. With the inrease of disruption risk, anufaturer s expeted profit redues in three souring. There have two values of the disruption proaility for deision-aking, =0.5 or =0.74. The value 0.5 is the intersetion of E ( and E (, while the value 0.74 is the intersetion of E ( and E ( 3. If <0.5, then hoose ain supplier as the sole soure. If 0.5<<0.74, then hoose dual souring. If >0.74, then hoose akup supplier as the sole soure (Fig.. dual-souring to the two key paraeters (,. Then an alulated the anufaturer s expeted profit against (,, where takes values fro 0.3 to 0.7, and takes values fro 0. to 0.9 with the inreent 0.. These points are plotted in Fig. (3. It shows the anufaturer's expeted profit under different delivery alloation and different disruption proaility in dual souring. When <0.55, the anufaturer's expeted profit dereases with delivery alloation. When =0.55, the anufaturer s expeted profit reains unhanged even if the value of varies. When >0.55, the expeted profit inreases with delivery alloation. When disruption proaility low the threshold, onsidering the akup supplier wholesale prie higher than ain suppliers of wholesale prie, inreasing the distriution proportion of akup supplier will lower the expeted profit. When disruption proaility exeed the threshold, onsidering the akup supplier wholesale prie in disrupted state higher than other in noral state, then the anufaturer an inrease the distriution proportion to inrease expeted profit (Fig E( E(3 E( Disruption proaility Fig. (. Expeted profits under different purhasing strategies. The horizontal axis is disruption proportion of ain supplier, the vertial axis is anufaturer s expeted profit funtion in dual souring E (. We use nuerial exaples to show the sensitivity of anufaturer's expeted profit in dual-souring to the two key paraeters, (,, whih takes values fro 0. to 0.6 with the inreent 0., takes values fro 0. to 0.9 with the inreent 0.. These points are plotted in Fig. (. It shows that anufaturer's expeted profit dereases in disruption proportion, and with the inrease of disruption proaility, the trend of deline gets faster. Beause the disruption partial of ain supplier is opleentary y the akup supplier, akup supplier s unit wholesale prie in disrupted state is higher than ain supplier s. Thus anufaturer expeted profit dereases in disruption proportion (Fig.. The horizontal axis is distriution proportion of akup supplier, while the vertial axis is anufaturer s expeted profit funtion in dual souring. We use nuerial exaples to show the sensitivity of anufaturer's expeted profit in _=0. _=0.3 _=0.5 _=0. _=0.4 _= Disruption proportion of ain supplier Fig. (. Expeted profits under different disruption proportion in dual souring _=0.3 _=0.45 _=0.55 _=0.4 _=0.5 _= Distriution proportion of akup supplier Fig. (3. Expeted profits under different delivery alloation in dual souring.

5 6 The Open Cyernetis & Systeis Journal, 04, Volue 8 Li and Zhang CONCLUSION We study eergeny proureent odel ased on inoplete supply disruptions, and analyze the anufaturer s expeted profit of single souring proureent strategy and ultiple souring proureent strategy under different risk of disruption. Furtherore, we argue the ipat of the disruption proportion of ajor supplier and delivery alloation of akup supplier on the anufaturer s proureent strategy, and find out the est proureent strategy that the anufaturers should hoose to axiize expeted profit in different situations. We find that anufaturer s expeted profit dereases in disruption proportion, and sharply redued with disruption proaility. As the disruption proaility is elow the ritial value, the expeted profit dereases with delivery alloation. As the disruption proaility is higher than the ritial value, the expeted profit inreases with delivery alloation. There are other avenues to extend this artile. First, ased on the anufaturer's profit, we an exaine the entire supply hain profits. Seond, we an investigate liited supplier s apaity. Finally, our fraework an e extended to onsider ore qualified suppliers. CONFLICT OF INTEREST The authors onfir that this artile ontent has no onflit of interest. ACKNOWLEDGEMENTS This work is supported y the National Soial Siene Fund of China (No. CGL04, the National Natural Siene Foundation of China (No. 737, and REFERENCES [] C. Blae, and M. Henke, Supply hain risk: a handook of assessent, anageent and perforane, Springer-Verlag: New York, USA, 009. [] O. Tang, and S. Nuraya, Identifying risk issues and researh advaneents in supply hain risk anageent, International Journal of Prodution Eonois, vol., pp. 5-34, 0. [3] G. Burke, J. Carrillo, and A. Vakharia, Single versus ultiple supplier souring strategies, European Journal of Operational Researh, vol., pp. 95-, 007. [4] W. Wang, The Effet on Optial Ordering Quantity Under Disruption Risk of Two Supplier, PhD Thesis of Taiwan University, 0. [5] H.Yu, and A. Z. Zeng, Single or dual souring: deision-aking in the presene of supply hain disruption risks, OMEGA- International Journal of Manageent Siene, vol. 4, pp , 009. [6] K. Chen, and P. Zhuang, Disruption anageent for a doinant retailer with onstant deand-stiulating servie ost, Coputers & Industrial Engineering, vol. 4, pp , 0. [7] F. J. Sting, and A. Huhzereier, Dual souring: responsive hedging against orrelated supply and deand unertainty, Naval Researh Logistis, vol., pp , 0. [8] X, Li, J. Ji, and S. Wang, Coordination and optiization of dual souring under supply disruptions, Journal of Industrial Engineering and Engineering Manageent, vol. 3, pp. 4-47, 04. [9] B. Tolin, and Y. Wang, On the value of ix flexiility and dual souring in unreliale newsvendor networks, Manufaturing & Servie Operations Manageent, vol., pp , 005. [0] J. Hou, and A. Z. Zeng, Coordination with a akup supplier through uy-ak ontrat under supply disruption, Transportation Researh Part E, vol. 5, pp , 00. [] W. Zhang, Analysis on supply eergeny anageent ased on dual soure, Journal of Shanghai Jiao Tong University, vol. 3, pp , 03. [] X. Li, J. Ji, and S. Wang, Perforane analysis of akup supplier for supply disruptions with stohasti deand, Operations Researh and Manageent Siene, vol. 4, pp. 4-49, 03. [3] J. Chen, X. Zhao, and Y. Zhou, A periodi-review inventory syste with a apaitated akup supplier for itigating supply disruptions, European Journal of Operational Researh, vol., pp. 3-33, 0. [4] V. Baih, Vulnerale options in supply hains: effets of supplier opetition, Naval Researh Logistis, vol. 7, pp , 006. Reeived: Septeer, 04 Revised: Noveer 30, 04 Aepted: Deeer 0, 04 Li and Zhang; Liensee Bentha Open. This is an open aess artile liensed under the ters of the Creative Coons Attriution Non-Coerial Liense ( lienses/y-n/3.0/ whih perits unrestrited, non-oerial use, distriution and reprodution in any ediu, provided the work is properly ited.