Coordinating a Supply Chain Consisted of One Supplier and One Retailer When Demand Disruption Happens

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1 Management Science and Engineering Vol., No., 07, pp. 9-3 DOI:0.3968/947 ISSN [Print] ISSN X [Online] Coordinating a Supply Chain Conited of One Supplier and One Retailer When Demand Diruption Happen ZHANG Jun [a],[b] ; CHEN Hong [a],* [a] School of Management and Economic, Univerity of Electronic Science and Technology of China, Chengdu, China. [b] Logitic Engineering and Management Faculty, Kunming Metallurgy College, Kunming, China. *Correponding author. Supported by Reearch Fund for the Doctoral Program of Higher Education of China (008500). Received 0 December 06; accepted March 07 Publihed online 0 March 07 Abtract In thi paper, a upply chain conited of one upplier and one retailer i tudied. The retailer ell the product to cutomer by uing e-commerce platform and cutomer receive the product offline. Ditributing product i outourced by the retailer. The upply chain i coordinated under the revenue-haring contract in the tatic cae. The upplier oberve that the market cale change after the production plan in the upply chain i formulated. In centralized upply chain, the upplier only need to adjut the retail price the change of the market cale i in a certain range. The upplier need to adjut the retail price and production quantitie the change i large enough. In decentralized deciion, the upply chain cannot be coordinated. Thi mean that the original revenue-haring contract cannot coordinate the dirupted upply chain. An improved revenue-haring contract i put forward to coordinate the dirupted upply chain. The reearch how that the improved contract can coordinate the original upply chain and the dirupted upply chain, which mean that the contract ha robutne when facing the market cale diruption. Finally, ome numerical example are alo given. Key word: Supply chain coordination; E-commerce; Demand diruption; Supply chain contract Zhang, J., & Chen, H. (07). Coordinating a Supply Chain Conited of One Supplier and One Retailer When Demand Diruption Happen. Management Science and Engineering, (), 9-3. Available from: URL: DOI: INTRODUCTION The e-commerce market grow rapidly all over the world in recent year. E-commerce market in Europe i a relatively mature market and evolve contantly. However, diruption uch a natural diater, terrorim attack, major public health event, financial crii, machine fault and trike may affect buine operation and upply chain management. An originally-coordinated upply chain cannot be coordinated becaue of ome diruption, and the urvival of the upply chain member can be influenced by other diruption. For example, a large number of airport in the United State were forced to cloe becaue of 9 terrorim attack. Raw material upply in many companie all over U.S.A. wa delayed becaue of the accident. Some upply chain are almot damaged due to thi diruption and it reult in a heavy lo. Large companie like Ford are alo influenced by diruption. Supply of engine and drive part of Ford upend for a long time due to the low repone of it procurement ytem, which make five companie affiliated with Ford in North America cloe temporarily. Diruption will make market demand change greatly. For example, the pread of foot-and-mouth dieae make the demand for beef in Europe decreae dramatically, which affect the operation of the beef upply chain in Europe. The demand for tent and moving helter increae dramatically in the diater area after the Wenchuan Earthquake, 008, and a lot of enterprie manufacturing tent have to work overtime in order to 9 Copyright Canadian Reearch & Development Center of Science and Culture

2 Coordinating a Supply Chain Conited of One Supplier and One Retailer When Demand Diruption Happen meet the demand, which affect the operation of their upply chain ytem. Recently, with the development of e-commerce, online hopping i widely pread all over China. Cutomer buy what they want online and evaluate the product after they receive them offline. According to ome tatitic, total ale volume in Taobao and Tmall, two companie ubordinated to Alibaba, i about 9. billion RMB on th November, 0, which ha great impact on the upply chain ytem. Retailer need to preorder a large number of product in order to meet the huge coming demand and the logitic ytem i greatly influenced by logitic activitie uch a purchaing, toring, tranporting and ditributing. A can be een above, upply chain member behavior, total upply chain profit and the urvival of enterprie in upply chain can be affected by diruption. The impact i o eriou that it i neceary to tudy the trategy about how to coordinate upply chain when facing diruption and thi ha been paid much attention by many companie and academic world. A upply chain coniting of one upplier and one retailer i tudied in thi paper. The ret of thi paper i organized a follow. The related reearche are reviewed in Section. Benchmark model i etablihed in Section 3. Section 4 coordinate the centralized upply chain with demand diruption. How to coordinate the decentralized upply chain with demand diruption i tudied in Section 5 and an improved revenue-haring contract i preented in thi ection. Numerical tudie are illutrated in Section 6. Section 7 conclude thi paper and ome poible reearch opportunitie in the future are alo dicued.. LITERATURE REVIEW Reearche related to thi paper are known a diruption management. The concept diruption management i firtly put forward by Clauen (00). It i ued to olve the operation of Continental Airline when it face emergency. A conceptual model to analyze upply chain diruption i put forward by Kleindorfer et al. (005). A two-tage upply chain with demand diruption i tudied by Xu (003), i (004) and Huang (006), and the quantity dicount contract i ued to coordinate the upply chain. Giannoccaro (004) tudie a three-tage upply chain coordination by uing revenue-haring contract. Tomlin (006) dicue a upply chain in which there exit two upplier and one manufacturer when the upply chain face diruption rik. Xu (006) tudie upply chain coordination when the production cot function i a convex function. Xiao (005, 008) tudie a upply chain with one-manufacturer and two-retailer when the demand diruption occur and extend the tudy to a more complex problem in which there exit competition between the two retailer. Lei (0) examine how to coordinate a two-tage upply chain under aymmetric information with a linear contract when demand and cot diruption happen imultaneouly. Compared with previou tudie, there are ome dference in thi paper. Firtly, it analyze a upply chain under e-commerce, a new background. We analyze the impact of the market cale on the e-commerce upply chain. Secondly, there exit retailer ale cot in the upply chain. Thirdly, thi paper examine the effect of the revenue-haring contract in upply chain coordination, which i alo dferent from previou tudie.. BENCHMARK MODEL Thi paper examine a upply chain compoed of one upplier (he) and one retailer (he), in which the upplier i the price leader and the retailer i the price follower. The tranaction between the upplier and the retailer i done under ymmetric information, which mean that the upplier know the retailer cot tructure and profit function, and vice vera. The upplier ell a kind of hortle-cycle product to the retailer according to a production plan which i baed on market forecat. The retailer ell the product online and cutomer receive the product offline. The retailer outource hi product ditribution buine to a third-party logitic company. The retailer decide whether or not to buy the product according to the revenue-haring contract the upplier offer. Suppoe that p i the retail price and the demand function that the retailer face i a nonlinear function, i.e., d=dp -. D i the market cale and c i the upplier unit production cot. The retailer unit ale cot i c r which include the unit cot of uing e-commerce platform and the unit cot of ditributing hi product. The unit retail price i p and k (k>0) i the price enitivity coefficient. i the realized demand under the retail price p. The demand function i =Dp - and the retail price i p ( D/ ) k. The total profit of the upply chain i f ( ) ( D/ ) k c cr. () According to the firt-order condition, we obtain that the optimal retail price i kc ( cr ) p, () the optimal production quantity i D kc ( c r), (3) and the optimal upply chain profit i Dc ( c) r f( ) kc ( cr). (4) Lemma. The upply chain compoed of one upplier and one retailer can be coordinated under the revenueharing contract ( w, ), where w ( c cr ) and 0< <. ) Copyright Canadian Reearch & Development Center of Science and Culture 0

3 ZHANG Jun; CHEN Hong (07). Management Science and Engineering, (), 9-3 PROOF. By ubtituting w ( c cr ) (0< <) ) into the upplier profit function, i.e., f ( ) p ( w c), we eaily obtain that f ( ) f( ). It how that the revenue-haring contract (w,φ ) coordinate the upply chain (Burguera, 003; Cachon, 005). 3. COORDINATING CENTRALIZED SUPPLY CHAIN WHEN DEMAND DISRUPTION OCCURS Centralized upply chain i a ytem which it deciion are made by the ame deciion-maker, the upplier. The upplier oberve that demand diruption occur after her production plan i formulated. It reult in the change of the market cale. The diruption i captured by the term of ΔD and only D+ΔD>0, which enure it i meaningful in the real world. Thu, the dicuion followed are baed on the condition mentioned above. After the diruption occur, the demand function i d=(d+δd)p -. The realized demand i =(D+ΔD)p - and DD the retail price i p ( ) k. The correponding total upply chain profit function i written a DD f ( ) ( ) c cr b( ) b( ). (5) The parameter b >0 and b >0 in Equation (5) are the marginal cot related to the change of the market cale and (x) + =max{0,x}. b i the extra increaed unit cot due to increae production plan and b i the extra unit dipoal cot due to elling the remained product in the econdary market at the price lower than the marginal production cot when the upply i greater than the demand. In order to further dicu the impact of the demand diruption on the original production plan, we put forward Lemma. Lemma. When the demand diruption occur, we aume that * i the optimal production quantity which maximize the upply chain profit function hown in Equation (5). Then, ΔD>0, and ΔD<0. Lemma illutrate the following reult. If the market cale increae, the upply need to increae production quantitie. If the market cale decreae, the upplier need to decreae production quantitie. According to Lemma, ΔD>0, then. Thu, optimizing the total upply chain profit function f() i equal to optimize the trictly concave function DD f( ) ( ) c crb( ), (6) ubject to. If ΔD<0, then. Thu, optimizing the total upply chain profit function f() i equal to optimize the trictly concave function DD f( ) ( ) c crb( ) (7) ubject to. Theorem i obtained by uing the methodology imilar to Xu (003, 006) and i (004), which how the optimal deciion in the centralized upply chain when the demand diruption occur. Theorem. When the market cale diruption occur and the demand function i d=(d+δd)p -, the upplier in the centralized upply chain need to adjut the optimal retail price and the optimal production quantitie in order to optimize the total upply chain profit and coordinate the upply chain. According to dferent diruption, the optimal retail price p * and the optimal production quantity * are hown a follow: Theorem how the following reult. When diruption make the market cale change, there exit robutne in the original production plan. When ΔD i in certain range, the original production quantity doe not need to be changed but the correponding retail price need to be adjuted in order to compenate for the extra cot derived from the diruption. If ΔD exceed certain value, the original production quantity need to be adjuted and the correponding retail price alo need to be adjuted according to the change of the market cale. It i alo hown that the original revenue-haring contract cannot coordinate the upply chain when the demand diruption occur. We need to redeign the contract in order to coordinate the upply chain, which will be dicued in the next ection. If the upplier doe not notice the impact of the diruption and continue to ue the original retail price (p p) when the realized demand in the upply chain i d DD ( DD) p and the retail price i p ( ) k, the total upply chain profit in thi cae i (8) (9) Copyright Canadian Reearch & Development Center of Science and Culture

4 Coordinating a Supply Chain Conited of One Supplier and One Retailer When Demand Diruption Happen f D D p c c p b b. (0) ( ) ( )( r) ( ) ( ) Thu, we obtain that ( D D)( p c cr) b D p, D 0; f ( ) () ( D D)( p c cr) bd p, D COORDINATING DECENTRALIZED SUPPLY CHAIN WHEN DEMAND DISRUPTION HAPPENS Decentralized deciion mean that each member in the upply chain doe hi buine according to hi own maximum profit. In the centralized deciion, when the market cale change, the optimal trategy for the retailer i to chooe the retail price p * and the procurement quantity *. In decentralized deciion, the upply chain member ign an appropriate contract which alo make the retailer chooe p * and *, the decentralized upply chain obtain the optimal upply capacity which i equal to that in the centralized upply chain. Thi mean that the upply chain i coordinated. The revenue-haring contract i ued to coordinate the decentralized upply chain. Let T( ) b( ) b( ). Concerning a given revenue allocation ratio (0 ), the upplier offer the retailer an improved revenue-haring contract in which T ( ) the wholeale price i w ( ) ( c cr ). Theorem. When the market cale change in the decentralized upply chain, the upply chain can be coordinated by the revenue-haring contract ( w ( ), ) and the optimal total upply chain profit can be allocated between the upplier and the retailer in any given ratio. PROOF. Concerning a given revenue allocation ratio (0 ), the retailer profit function under the improved revenue-haring contract ( w ( ), ) i hown below. DD fr( ) ( ) w ( ) c r. By ubtituting w() into the equation mentioned above, we eaily obtain that fr( ) f( ). Thu, the upply chain i coordinated by the contract and the optimal upply chain profit can be allocated between the upply chain member in any given allocation ratio by adjuting the parameter φ. Thi mean that the improved revenue-haring contract ( w ( ), ) can coordinate the decentralized upply chain. Furthermore, ΔD=0, then b =b =0. The upply chain profit function in thi cae i f ( ) f( ) and the wholeale price i w()=w. Thi mean that the improved revenue-haring contract ( w ( ), ) can coordinate the upply chain when the diruption of the market cale doe not occur. In other word, there exit anti-diruption ability in the improved contract. 5. NUMERICAL STUDIES When the market cale diruption take place, the optimal production quantity and the optimal retail price in the upply chain will be influenced, and the optimal upply chain profit and the allocation of the profit between the upply chain member will alo be influenced. We will analyze the effect of the demand diruption on the upply chain performance, the upplier profit and the retailer profit by uing numerical example in thi ection. Let D=,500, c =3, c r = and k=. The upplier and the retailer ign an agreement in which the upplier take 40% of the total channel revenue and the retailer take the remainder part. Thi mean that φ =0.6. In the tatic cae, it i hown that the upplier optimal production quantity i 3.44, the optimal retail price i p 8 and the optimal upply chain profit i f Suppoe that b =0.5 and b =0.. When the market cale change, there exit two type of demand diruption in the upply chain. We analyze two dferent trategie, the original trategy and the adjuted trategy, which are ued in the upply chain after the demand diruption take place. If the upplier doe not recognize the impact of the diruption on the upply chain and doe not make timely deciion, he will continue to ue the original retail price trategy which i called a the original trategy. We compare upply chain performance under the original trategy with that under the improved revenue-haring contract, which i hown in Table. Table Supply Chain performance Under Demand Diruption Cae ΔD p p * * w w * f f * Note. x i the original trategy and x * i the adjuted trategy. A it can be een from Cae and Cae in Table I, the optimal retail price are the ame while the optimal wholeale price and the optimal production quantitie need to be adjuted. The retail price here i larger than the original retail price. It how the following reult. If the diruption of the market cale aty certain condition, the retailer doe not need to adjut the retail price while the upplier need to increae the production quantity and the wholeale price. Thi can balance the upplier profit when facing enlarged market demand. A i hown in Cae 3 and Cae 4, both the optimal production quantitie and the optimal wholeale price are the ame while the optimal retail price need to be adjuted. Thi mean that there exit robutne in the optimal production quantity Copyright Canadian Reearch & Development Center of Science and Culture

5 ZHANG Jun; CHEN Hong (07). Management Science and Engineering, (), 9-3 decided at firt and the revenue-haring contract when dealing with the diruption. When the demand increae, the retailer increae the retail price in order to balance the impact of the diruption. The retail price here i larger than the original retail price. When the demand decreae, the retailer decreae the retail price in order to balance the impact of the diruption. The retail price here i lower than the original retail price. The upplier doe not need to adjut the production quantity and the wholeale price in both cae. A can be een from Cae 5 and Cae 6, the optimal retail price are the ame while the optimal wholeale price and the optimal production quantitie need to be adjuted. The retail price here i lower than the original retail price. It how the following reult. If the diruption of the market cale aty certain condition, the retailer doe not need to adjut the retail price while the upplier need to decreae the production quantity and increae the wholeale price. Thi can decreae the upplier lo when facing hrunk market demand. Lat but not leat, when the demand diruption occur, the total upply chain profit under the improved revenueharing contract are alway larger than thoe under the original price trategy. It illutrate that there are better performance in uing the revenue-haring contract when dealing with the diruption. CONCLUSION A one-upplier-one-retailer upply chain i tudied in thi paper when the market cale change. In centralized deciion, the upplier need to increae the production quantity when the market demand increae. The upplier need to decreae the production quantity when the market demand decreae. There exit robutne in the original production plan. In other word, when the diruption aty a given condition, the original production quantity doe not need to be adjuted and the upplier only need to adjut the correponding retail price in order to deal with the demand diruption. The retail price and the production quantity need to be adjuted when the demand diruption exceed certain value. An improved revenue-haring contract i ued to coordinate the decentralized upply chain, which can maximize the total upply chain profit. It i noted that the reult derived in thi paper alo illutrate the generality of the revenueharing contract. Finally, ome numerical example are alo given to analyze the upply chain performance when the original price trategy in baic model and the adjuted price trategy in the demand diruption are carried out repectively. There are abundant opportunitie in the future. For example, it i intereting to tudy more complex upply chain when the information of profit and cot between the participant i aymmetric. It i worth coordinating the ame upply chain ytem when the demand diruption and the upplier production cot diruption occur imultaneouly. Another direction i to tudy the problem which the demand function the retailer face i an exponential and more complex function. More complex upply chain tructure with other diruption i alo worth tudying. REFERENCES Cachon, G. P., & Larivere, M. A. (005). Supply chain coordination with revenue haring contract: Strength and limitation. Management Science, 5(), Clauen, J., Hanen, J., & Laren, J., et al. (00). Diruption Management. OR/MS Today, 8(5), Giannoccaro, I., & Pontrandolfo, P. (004). Supply chain coordination by revenue haring contract. International Journal of Production Economic, 89(), Huang, C. C., Yu, G., & Wang, S., et al. (006). Diruption management for upply chain coordination with exponential demand function. Acta Mathematica Scientia, 6B(4), Kleindorfer, P. R., & Saad, G. H. (009). Managing diruption rik in upply chain. Production and Operation Management, 4(), Lei, D., Li, J. B., & Liu, Z. X. (0). Supply chain contract under demand and cot diruption with aymmetric information. International Journal of Production Economic, 39(), 6-6. i, X., Bard, J. F., & Yu, G. (004). Supply chain coordination with demand diruption. Omega, 3(4), Tomlin, B. (006). On the value of mitigation and contingency trategie for managing upply chain diruption rik. Management Science, 5(5), Xiao, T., & i, X. (008). Price competition, cot and demand diruption and coordination of a upply chain with one manufacturer and two competing retailer. Omega, 36(5), Xiao, T., Yu, G., & Sheng, Z., et al. (005). Coordination of a upply chain with one-manufacturer and two-retailer under demand promotion and diruption management deciion. Annal of Operation Reearch, 35(), Xu, M. H., i, X. T., & Yu, G., et al. (003). The demand diruption management problem for a upply chain ytem with nonlinear demand function. Journal of Sytem Science and Sytem Engineering, (), Xu, M., i, X., & Yu, G., et al. (006). Coordinating dyadic upply chain when production cot are dirupted. IIE Tranaction, 38(9), Copyright Canadian Reearch & Development Center of Science and Culture