Multi Objective Ordering Planning for Multi Buyers Deteriorating Items

Zahra Attaei & Ahmad Makoui*

Zahra Attaei, M.Sc. graduate, Department of Industrial Eng., Azad University
Ahmad Makoui, Department of Industrial Eng., Iran University of Science & Technology

Keywords ABSTRACT

supply chain, joint replenishment, cooperative planning, multi objective
programming,
deteriorating items This paper is a research on the ordering planning of a supply chain with one supplier, multi buyer and multi deteriorating items. Items have fixed life time and expire dates. The ordering period is taken as variable and must be computed the proposed models. The problem is studied via two different approaches; the first is the joint replenishment, based on the Hwang and Chew’s model [3] and with some new assumptions. In the case that the life time is less than the ordering period, the cost of deterioration is considered in the model. The second approach is cooperative planning. In this approach transportation cost, inventory and shortage costs are considered in the proposed model. The models are studied for both single and multi period cases. The purpose of the models is an investigation about the influence of expire date on ordering periods’ lengths. The proposed models can compute these lengths and also the amounts of orders.
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ƽŹřŶƸĮƳƶƴƿżƷśŢſřƪƤƳƹƪưů ƭřƺţƽŻŚſźěŻŚŝƶƫƺƈŰƯŶƴģƵŹřŶƿźųŶƴģƪŗŚƀƯƽřźŝšLJŚƤƯŹŵ
ŻřŶƴţŹŚŞƗƶĩŢſřƵŶƃƶŤƟźĭźƔƳŹŵƾƷŵƁŹŚƠſƶƴƿżƷƕƺƳƹŵ ƂƳřŹŚĪưƷƹMinner>è@ƾƗźƟƹƾƬƇřƾƷŵƁŹŚƠſƽŚƷƶƴƿżƷ ƶƬŘƀƯ Ĩƿ Źŵ Ʊō ŹřŶƤƯ ƹ ƽŻŚſźěŻŚŝ ƱŚƯŻ ƲǀǀƘţ ŵŹƺƯ Źŵ >ææ@
ŵŹřŵ ŵƺūƹ ŚƌƟ ŢǀƟźƓ ŢƿŵƹŶŰƯ ƶĩ ƾƐƿřźƃ Źŵ ƾƫƺƈŰƯ Ŷƴģ ƵŵƺŝƾƟŵŚƈţŚƋŚƤţƱŚƄƿřƎſƺţƵŶƃƶŗřŹřƶƫŚƤƯŹŵŶƳřƵŵźƧŦŰŝ źƔƳŹŵźƠƇżǀƳƪƿƺŰţšŶƯŶƃŚŝƾƯƱƺſōƺěŶƴƿōźƟƢŞƏźŝƹ ƽźǀĭ Ʈǀưƈţ ƶƬŘƀƯ Ĩƿ ƱřƺƴƗ ƶŝ ƶƬŘƀƯ Ţſř ƵŶƃ ƶŤƟźĭ
ƁƹŹƲƿŶƴģźŤĭŹżŝƪƿŚƀƯƽřźŝŢſřƵŶƃƶŤƟźĭźƔƳŹŵƾƟƺĩŹŚƯ
ƹ ŶƳř ƵŵƺưƳ ƶŗřŹř ƁŹŚƠſ ƱŚƯŻ ƹ ŹřŶƤƯ ƲǀǀƘţ ƽřźŝ ĨǀŤƀƿŹƺǀƷ
ŶƳřƵŶƿŵźĭƶƀƿŚƤƯƮƷŚŝŚƷƁƹŹƲƿřƾƿřŹŚĩ ƹŵŹřŵŵƺūƹŹŚŞƳřƽŚƌƟŢƿŵƹŶŰƯƶƬŘƀƯŹŵŢſřźĩŷƶŝƭŻLJ ƾƯ ƑŚŰƫ ƩŶƯ Źŵ ƽŹřŶƸĮƳ ƹ Ŷƿźų  ƾƷŵ ƁŹŚƠſ ƽŚƷ ƶƴƿżƷ ƽŻŚſźěŻŚŝ ƁŹŚƠſ ƱŚƯŻ ŹřŶƤƯ ƲǀǀƘţ ƩŚŞƳŵ ƶŝ ƶƬŘƀƯ ŶƳƺƃ >æç@ Moon,ChaŵƺƃƮưǀƴǀƯƶƴƿżƷƎſƺŤƯƶĩƽƺŰƳƶŝŢſř ƱŚƄƿřŶƳřƵŵźĩƢǀƤŰţƱŚƯżưƷƽŻŚſźěŻŚŝƶƬŘƀƯĨƿƽƹŹźŝżǀƳ ƽŚƷ ƮŤƀǀſ Źŵ ƽŵŚƿŻ ƖŝŚƴƯ ƽŚƸŤƿŵƹŶŰƯ ƶĩ ŶƳŵƺưƳ ƱřƺƴƗ ƪƤƳƹƪưůŢǀƟźƓŚƌƟƶūŵƺŝźǀƔƳƾƘƣřƹƽŶǀƫƺţƹƽŵƺūƺƯ šŹƺƇƾţŚƤǀƤŰţƭřƺţƽŻŚſźěŻŚŝƪŗŚƀƯŹŵƾƫƹŶƳŹřŵŵƺūƹƹ ƲƿřŹŵŶƳřƶŤƟźĭźƔƳŹŵřŹƾƘƣřƹƽŚƸŤƿŵƹŶŰƯƾưĩŵřŶƘţƶŤƟźĭ ƪůƽřźŝĨǀŤƀƿŹƺǀƷŚŤƯƹĨǀŤƀƿŹƺǀƷƁƹŹƹŵƱŚĭŶƴƀƿƺƳƶƫŚƤƯ ŚŝřŹŚƸƳōƹŶƳřƵŵƺưƳƾƟźƘƯŚƷŢƿŵƹŶŰƯƵřźưƷƶŝƪƿŚƀƯƶƳƺĮƴƿř ƾƐƿřźƃŹŵŶƳŹřŵƾƘſ>æè@Goyal ,GiriŶƳřƵŵźƧƶƀƿŚƤƯƮƷ ƾƐų šŹƺƇ ƶŝ ŵƹŶŰƯ ƽżƿŹ ƶƯŚƳźŝ ƢƟř ƩƺƏ Źŵ ŚƋŚƤţ űźƳ ƶĩ
ƽŻŚſźěŻŚŝƱŚƯŻƲǀǀƘţƽřźŝĨǀŤƀƿŹƺǀƷƁƹŹƦƿŶŝŚƿƾƯƂƷŚĩ ĨţƽŻŚſźěŻŚŝƶƬŘƀƯĨƿƽƹŹźŝ>æé@AchuthanŶƴƿŚưƳƶŗřŹř ƶŝ ƭřŶƣř ŚŤƿŚƸƳ ƹ ƢǀƤŰţ Źřŵ ŢƿŵƹŶŰƯ ƽř ƵŹƹŵ Ŷƴģ ƾƫƺƈŰƯ ŵŹƺƯ ƽŻŚſźěŻŚŝ ƶƬŘƀƯ Ţſř Ƶŵźĩ ƶƴǀƸŝ śřƺū Ĩƿ ƶŝ ƱŶǀſŹ ƽżƿŹƶƯŚƳźŝƢƟřŚŝƵŶƴƃƹźƟŶƴģƹƽřƵŹƹŵŶƴģƶƫŚƀƯƦƿƾſŹźŝ ƾƯźŝŹŵřŹƾƷŵƁŹŚƠſƹŶƿźųƽŚƷƶƴƿżƷƩŶƯƹƵŵƺŝŵƹŶŰƯ
ŻřƹŵŹřŵŵƺūƹƁŹŚƠſŢƿŵƹŶŰƯżǀƳLJŚĩƁŹŚƠſƽřźŝŚƴưƋŵźǀĭ
ƶŤƟźĭźƔƳŹŵźƠƇżǀƳƵŹƹŵƽŚƸŤƳřƽŵƺūƺƯƹƶǀƫƹřƽŵƺūƺƯƾƟźƏ ƵŶƴƃƹźƟnƩŶƯźǀǀƜţĨƿŵŚŬƿřŚŝƶƫŚƤƯƲƿřŹŵƵŶƴƀƿƺƳŵƺƃƾƯ
ƽřźŝŚŤƿŚƸƳƹƪƿŶŞţƽřƵŹƹŵŶƴģƵŶƴƃƹźƟĨţƩŶƯĨƿƶŝřŹƽř
Yang,Zhao,Rand ŵŹƹō ƾƯ Ţſŵ ƶŝ řŹ ƶƴǀƸŝ ŹřŶƤƯ Ĩƿ Ʊō ƵŵźĩƢǀƤŰţƾƐųźǀƛƽŚƋŚƤţŚŝƽŻŚſźěŻŚŝƶƬŘƀƯƽƹŹźŝ>æê@ ƶƀƿŚƤƯ ĨǀŤƀƿŹƺǀƷ ƽŚƷ ƁƹŹ Śŝ ƹ ƶŗřŹř ƮŤƿŹƺĮƫř Ĩƿ ƱŚƄƿř ŶƳř ŚƋŚƤţƶĩƾƐƿřźƃŹŵřŹLJŚĩźƷƽŻŚſźěŻŚŝƱŚƯŻƶƫŚƤƯƲƿřŶƳřƵŵƺưƳ ƹƽźŤƄƯƎſƺţƁŹŚƠſƾŝŚƿŵŹŢǀƬŝŚƣƵŶƃƁŹŚƠſƭLjƣřŢƟŚƿŹŵ żǀƳ ƶƴƿżƷ źƔƳ Żř ŶƃŚŝ ƾƯ śƺƛźƯŚƳ ƽLJŚĩ Ʊŵřŵ žě ŢǀƬŝŚƣ
 ƪƤƳƹ ƪưů ƽŵƺūƺƯ ƽŚƷ ƶƴƿżƷ ƽƹŹ ƖƿŻƺţ ƶĪŞƃ ŹŚŤųŚſ
ŶƃŚŝƾƯŹřŸĭźǀŧŚţšŚƗLjƏřƹšLjǀƸƀţ
ƶŝ ƝřŶƷř ƹ ŚƸǀūƹźų ŚƸŤƿŵƹŶŰƯ šŚǀƋźƟ ŽŚſřźŝ ƖƿŻƺţ ƪŗŚƀƯ ŶƳƺƃƾƯƽŶƴŝƶŤſŵźƿŻšŹƺƇ
šŚƋƹźƠƯƹƶƬŘƀƯƞƿźƘţ
ƽżƿŹƶƯŚƳźŝŭƺƐſ  šLJƺƈŰƯŵřŶƘţ  ƶǀƫƹřŵřƺƯŵřŶƘţ 
ƵźǀŬƳŻŹŵƾſŹźŝŵŹƺƯƽŚƷƵŵŹ 
ŚƋŚƤţźƿŵŚƤƯŢǀƘƐƣƭŶƗŚƿŢǀƘƐƣ 
ŚƷƵŹƹŵŵřŶƘţ  ƾƷŵƁŹŚƠſƮŤƀǀſ 
ŚƸŤƿŵƹŶŰƯ
šLjǀƸƀţŢǀƟźƓŢƿŵƹŶŰƯ  ƪƯŚĩŹƺƏƶŝƱŚƿźŤƄƯƽŚƋŚƤţƲǀƯŚţƍźƃ  ƽźŤƄƯƶŝLJŚĩƪƿƺŰţƽřźŝŻŚŬƯƶƬƇŚƟƹƱŚƯŻŢƿŵƹŶŰƯ 
ŚƷŹŚŞƳřŢƯŶųŮƐſƽřźŝLJŚŝŶů  ƽŻřŶƳřƵřŹƶŝŻŚŬƯšLjǀƸƀţŵřŶƘţŹŵŢƿŵƹŶŰƯ 
ŚƸǀūƹźų
šLjǀƸƀţƾŝŚƿƱŚĪƯ  šLjǀƸƀţƆǀƈŴţ  šŚŬƳŚųŹŚĩŹŵšLJƺƈŰƯŶǀƫƺţƱřżǀƯ  ƞƬŤŴƯšLjǀƸƀţƲǀŝšLJƺƈŰƯƹƶǀƫƹřŵřƺƯƪưůƱřżǀƯ  ƶǀƬƤƳƎƿŚſƹƾŝŚƿźǀƀƯ  ƪưůƽŚƷŶƯƲǀǀƘţ  ƖƿŻƺţƽŚƷƩŚƳŚĩƲǀǀƘţ 
ƝŶƷƖŝřƺţ
ŵƺſƱŵźĩƮưƿżĩŚƯŚƿŚƷƶƴƿżƷƱŵźĩƮưǀƴǀƯ 
ŚƷƵŵŹƹšLjǀƸƀţƲǀŝƩŵŚƘţƽŹřźƣźŝ 
ŢƯŶųŮƐſƱŵźĩƮưƿżĩŚƯ  šŚưǀưƈţƽŹřƺŤſřƱŵźĩƮưƿżĩŚƯ 

ƭřƺţƽŻŚſźěŻŚŝçç
ƵƹźĭĨƿƲǀƯŚţƽŻŚſĬƴƷŚưƷƶƬŘƀƯƭřƺţƽŻŚſźěŻŚŝƶƬŘƀƯ
ƵŵřŵƁŹŚƠſľŚƯřƺţƵŶƴƴĩƲǀƯŚţĨƿŻřŢſřƲĪưƯƶĩŢſŚƷLJŚĩŻř ŵŹƺƯ ƾƫƺƈŰƯ Ŷƴģ ŢƫŚů Źŵ ƽŵƺūƺƯ ƽŚƸƫŶƯ ƕřƺƳř ŶƃŚŝ ƵŶƃ Ʊŵźĩ ƮưǀƴǀƯ LJƺưƘƯ ŚƷ ƩŶƯ Ʋƿř ƝŶƷ ŶƳř ƶŤƟźĭ Źřźƣ ƶƘƫŚƐƯ
ƾŗƺĩŚƯŶưůřƹƾŗŚƐƗřźƷŻŹřŶƿźųŶƴģŚŝźƿŸěŵŚƀƟƽŚƷLJŚĩƽřźŝƭřƺţƲǀƯŚţƶƟŶƷŶƴģƽżƿŹƶƯŚƳźŝçí

ƪĪǀſ źŝřźŝ ƵŶƳŻŚſ Ŷǀƫƺţ ƪĪǀſ ƶĩ ŵƺƃ ƾƯ ƉźƟ ƶƬŘƀƯ
ŶǀƫƺţƶǀƫƹřŵřƺƯƽŻŚſƮƷřźƟƪĪǀſƹŶƃŚŝƾƯƵŶƴƃƹźƟƽŻŚſźěŻŚŝ ƾƯŶǀƫƺţŚƿƽŻŚſźěŻŚŝƪĪǀſ ŻřƾŰǀŰƇśźƌƯƵŶƳŻŚſƵŶƴƴĩ ŹƺƏ ƶŝ ƾƿLJŚĩ Ŷƴģ ƶƬŘƀƯ ƽƹŹ źŝ >çæ@ Fung,MA,Lau ŶƃŚŝ R,T)ƩŶƯƶŤƟŹŹŚĩƶŝƩŶƯƶƫŚƤƯƲƿřŹŵŶƳřƵŵƺưƳƢǀƤŰţƱŚƯżưƷ ƾƯƵŵřŵƁŹŚƠſŹŶƣƱōTƾƳŚƯŻƪƇřƺƟŹŵƶĩŶƃŚŝƾƯ (T,S) Śƿ m ƩŶƯ ƶƫŚƤƯ Ʋƿř Źŵ Ŷſźŝ R Śƿ S ƶŝ ƽŵƺūƺƯ ŮƐſ Śţ ŵƺƃ ƹ ƵŶƃ ƮŤƀǀſ ŵŹřƹ Ʊƺſřƺě šŹƺƇ ƶŝ ŚƋŚƤţ ŶƃŚŝ ƾƯ ƾƫƺƈŰƯ ƪƿƺŰţšŶƯŶƃŚŝƾƯLJŚĩźƷƽřźŝŢƯŶųŮƐſŢƿŵƹŶŰƯƽřŹřŵ ŶƷřƺų ŢƟř žě ƽŵƺūƺƯ źŝ ŵřŻŚƯ ƽŚƋŚƤţ ƹ Ƶŵƺŝ ŢŞŨƯ ŚƷLJŚĩ LJŚĩźƷƽřźŝŶƳƺƃƾƯŵŹřƹƱƺſřƺ욏ƺƇƶŝƶĩƾƿŚƋŚƤţŢƃřŵ šƹŚƠŤƯ Ţſř ƲĪưƯ Ĩƿ źƷ űźƳ ŚƴưƋ ƹ Ƶŵƺŝ ƽźĮƿŵ Żř ƪƤŤƀƯ ƾƬĩƾƷŵƁŹŚƠſŢŝŚŧƶƴƿżƷƮŤƀǀſŹŵŵƺūƺƯƽŚƷƶƴƿżƷŶƃŚŝ źǀƛƩŶƯƪůƽřźŝƶƫŚƤƯƱŚĭŶƴƀƿƺƳŶƃŚŝƾƯƽŹřŶƸĮƳƾŗżūƹ
ƱřƺƴƗ ŢŰţ ĨǀŤƀƿŹƺǀƷ ƁƹŹ Ĩƿ ơƺƟ ŮǀŰƇ ŵŶƗ ƾƐų
ƾƯŢſŵƶŝřŹƶƴǀƸŝŹřŶƤƯƱōĨưĩƶŝƹŶƳřƵŵƺưƳƶŗřŹřHSTSP
ŶƳŹƹō
ƽŻŚſźěŻŚŝ ƶƴǀƸŝ ŹřŶƤƯ ƲǀǀƘţ ƽƹŹ źŝ >çç@ Yang-Fu ,Huang ƽŚƋŚƤţƶƬŘƀƯƲƿřŹŵŶƳřƵŵƺưƳƢǀƤŰţƾƃƹźƟƵŵźųƮŤƀǀſĨƿ
ƮƷƽŻŚſźěŻŚŝűźƳŚƴưƋŶƃŚŝƾƯŢŝŚŧƹƆŴƄƯƮŤƀǀſƶŝƵŵŹřƹ ŵƹŶŰƯŚƳƽżƿŹƶƯŚƳźŝƢƟřƹŶƃŚŝƾưƳŻŚŬƯŵƺŞưĩŢſřƆŴƄƯ ƵźƸŝ Żř ŹLJŵ źƷ ŢŝŚŝ ƾŤƟŚƿŹŵ ŵƺſ Ţſř ƵŶƃ ƶŤƟźĭ źƔƳ Źŵ ƽŹŚŬţƵŹƹŵƩƺƏƹŶƃŚŝƾƯźŤƄǀŝŹŚŞƳřŹŵŹLJŵźƷŢŝŚŝƾŤųřŵźě ƶƴƿżƷŶƃŚŝƾƯƽźŤƄƯƽŹŚŬţƵŹƹŵƩƺƏŻřźŤƄǀŝƾƃƹźƟƵŵźų
źƔƳŹŵŶƿźųƹƽŹřŶƸĮƳƾƷŵƁŹŚƠſŢŝŚŧƶƴƿżƷƮŤƀǀſƽŚƷ
ƁƹŹ Ĩưĩ ƶŝ >çè@ Chen,Hung, Weng Ţſř ƵŶƃ ƶŤƟźĭ
ŶƴƴĩƾƯƽŻŚſźěŻŚŝƶƴǀƸŝŹřŶƤƯƲǀǀƘţƶŝƭřŶƣřƆƫŚųƾƬƘƟƁŻŹř ƲǀǀƘţƝŶƷƱōŹŵƶĩƽŵƺūƺƯƩźŤƴĩƶƬŘƀƯĨƿŚŝƶƫŚƤƯƲƿřŹŵ ŚŤŝƖƿŻƺţŻřŚƋŚƤţƮǀŤƀƷƶūřƺƯŶƃŚŝƾƯƽŻŚſźěŻŚŝŹřŶƤƯƹƱŚƯŻ ŢſřŵƹŶŰƯƽżƿŹƶƯŚƳźŝƢƟřŶƿŚưƳƾƯŢǀƘŞţ,ƽŚƷźŤƯřŹŚěŚŝ ,źǀǀƜţŚŝŚƋŚƤţűźƳƂƿřżƟřŚƿƂƷŚĩƹŶƃŚŝƾưƳŻŚŬƯŵƺŞưĩ ƹ ƾƳŚƿŚě ƽŵƺūƺƯ ƹ ŶƃŚŝ ƾƯ ƾƫƺƈŰƯ Ĩţ ƩŶƯ ŶƷŵ ƾƯ űŹ ƶŤƟźĭźƔƳŹŵƩŶƯŹŵżǀƳƞǀƠŴţƹƭŹƺţŢſřźƠƇƶǀƫƹřƽŵƺūƺƯ ƹźƠƇƪƿƺŰţšŶƯŵźǀĭƾƯšŹƺƇřŹƺƟƽŻŚſźěŻŚŝŢſřƵŶƃ ĨƿƽƹŹźŝ>çé@RoseŵŹřŶƳŵƺūƹŢŝŚŝƲƿřŻřƾŤƿŵƹŶŰƯĢǀƷ Ĩƿ ŶƳř Ƶŵźĩ ƢǀƤŰţ ƁƹźƟ ƶƯŚƳŻƹŹ ƩŶƯ Źŵ ƽŻŚſźěŻŚŝ ƶƬŘƀƯ
ŶǀƴĩƉźƟŶƿźǀĮŝźƔƳŹŵřŹƁƹźƟƶƯŚƳŻƹŹƽŵƺūƺƯƩźŤƴĩƶƬŘƀƯ ƾƯ šŹƺƇ ƾƟŵŚƈţ šŹƺƇ ƶŝ ƽŻŚſźěŻŚŝ ƹ ŶƃŚŝ ƆŴƄƯ ŚƋŚƤţ ŵƺŞưĩƹŶƿźųƽŹřŶƸĮƳƶƴƿżƷƮŤƀǀſŹŵŵƺūƺƯƽŚƷƶƴƿżƷŵźǀĭ ƽřŹřŵƶĩŶƃŚŝƾƯƾƟŵŚƈţźǀƜŤƯĨƿƽŻŚſźěŻŚŝŹřŶƤƯŶƃŚŝƾƯ ƱōŹŚǀƘƯŻřƝřźŰƳřıƹƖƿŻƺţƲǀĮƳŚǀƯxŢſř( ,)ƽŚƷźŤƯřŹŚě ƾƷŵ ƁŹŚƠſ ŢŝŚŧ ƶƴƿżƷ ŶƃŚŝ ƾƯ ŶƷřƺų ƩźŤƴĩ ƪŝŚƣ ƹ Ţſř ƶƴƿżƷŢſřƵŵƺưƳƲǀǀƘţŢſřƂƿřżƟřƩŚůŹŵƾƐųźǀƛšŹƺƇƶŝ ŶƳřƵŶƃƶŤƟźĭźƔƳŹŵřƽŹřŶƸĮƳƹŶƿźųƾƷŵƁŹŚƠſźǀƔƳƾƿŚƷ Ţſř ƵŶƃ ƉźƟ ŵƹŶŰƯ ƽżƿŹ ƶƯŚƳźŝ ƢƟř Ţſř źĩŷ ƶŝ ƭŻLJ
CTPP,CLUC, ƮŤƿŹƺĮƫřèŻřƩŶƯźƷƽřźŝYang,Zhao,Rand
YZR electricƱřƺƴƗŚŝƾưŤƿŹƺĮƫřĨƿżǀƳŵƺųƹƵŵŚƠŤſřSilver
ŶƳŵźĩ ƶƀƿŚƤƯ ƮƷ Śŝ řŹ ŚƷ ƁƹŹ Ʋƿř ƾƯŚưţ ƹ ŶƳŵƺưƳ ƶŗřŹř
Źŵ ƽŻŚſźěŻŚŝ ƶƬŘƀƯ Ĩƿ ƽƹŹ źŝ >æë@ Schiltz,Johanser ŢǀƘŞţĬƴƫŹřƖƿŻƺţŻřƽŻŚſźěŻŚŝƹŵźƷƲǀŝƶƬƇŚƟƶĩƾƐƿřźƃ
źƔƳ ŵŹƺƯ ƶƬŘƀƯ Źŵ ƶƫŚƤƯ ƱŚĭŶƴƀƿƺƳ ŶƳř Ƶŵźĩ ƢǀƤŰţ Ŷƴĩ ƾƯ ƁŹŚƠſŢŝŚŧƽŚƷƶƴƿżƷƪƯŚƃƮŤƀǀſƶĩŶƳřƶŤƃřŵƲƿřźŝƉźƟ ŶƃŚŝƾƯŢƟřžěƽŚƷƁŹŚƠſƹƽŹřŶƸĮƳŵƺŞưĩŶƿźųƾƷŵ ŹƹźƯƽŵƺūƺƯƮŤƀǀſŶƃŚŝƾƯ(S.C.S)ƽŵƺūƺƯƩźŤƴĩŢſŚǀſ LJŚĩ ƪƿƺŰţ šŶƯ Ţſř źƔƳ ŵŹƺƯ Ʊƺſřƺě ƽŚƋŚƤţ Śŝ ƽř ƵŹƹŵ źƔƳŹŵżǀƳŢƯŶųŮƐſŢƿŵƹŶŰƯŚƴưƋŶƃŚŝƾƯŢŞŨƯƹƪƤŤƀƯ ƶƴǀƸŝŢſŚǀſĨƿƹƵŵƺŝƵŶǀĤǀ쏌ǀƀŝƶƬŘƀƯŢſřƵŶƃƶŤƟźĭ
ƽƹŹźŝ>æì@Sheng-Pen wangŢƟŚƿƱōƽřźŝƱřƺţƾưƳřŹƵŵŚſ ŶƳřƵŵźĩƢǀƤŰţƾƐųźǀƛƾƄƿřżƟřƽŚƋŚƤţŚŝƽŻŚſźěŻŚŝƶƬŘƀƯĨƿ Śŝ řŹ Ʊō ƱŚƿŚě Źŵ ƹ ŶƳř ƵŵƺưƳ ƶŗřŹř ĨǀŤƀƿŹƺǀƷ ƁƹŹ Ĩƿ ƱŚƄƿř řŹƽŻŚſźěŻŚŝƶƬŘƀƯĨƿWangŶƴƴĩƾƯƶƀƿŚƤƯźĮƿŵƽŚƷƁƹŹ ƾƐųźǀƛšŹƺƇƶŝŚƋŚƤţƶĩƾƐƿřźƃŹŵƹŶƳřƵŵřŵŹřźƣźƔƳŶƯ Ŷƴƴĩ ƾƯ ƲǀǀƘţ řŹ ƽŻŚſźěŻŚŝ ŹřŶƤƯ ƹ ƱŚƯŻ ŶŝŚƿ ƾƯ ƂƿřżƟř ƮưǀƴǀƯŹƺƔƴƯƶŝƭřƺţƽŻŚſźěŻŚŝƶƬŘƀƯĨƿƽƹŹźŝ>æí@Hoque ƁƹŹ ƲƿŶƴģ ƱŚƄƿř Ţſř Ƶŵźĩ ƢǀƤŰţ ƪĩ ƶƴƿżƷ Ʊŵźĩ
ƱŚƿŚěŹŵřŹŚƷƱōƶĩŶƳřƵŵźĩƶŗřŹřšLJŚƤƯźƿŚſŶƴƳŚưƷĨǀŤƀƿŹƺǀƷ Żř ƾƷƹźĭ Ţſř Źřźƣ ƶƬŘƀƯ Ʋƿř Źŵ Ŷƴƴĩ ƾƯ ƶƀƿŚƤƯ ƶƫŚƤƯ
ŢſřƾƐƿřźƃŹŵƲƿřƹŶƳƺƃƵŵřŵƁŹŚƠſƮƷŚŝƱŚƯżưƷšLJƺƈŰƯ źŝ>æî@Lo,Tsai,LiŢſřƮĩŚůƮŤƀǀſźŝƶūŵƺŝŢƿŵƹŶŰƯƶĩ śřƺūƶŝƾŝŚƿŢſŵŢƸūƽřƶƫŵŚƘƯƹŵƽŻŚſźěŻŚŝƶƬŘƀƯĨƿƽƹŹ ŹŵŶƳŵźĩƶŗřŹřƱōƪůƽřźŝƾưŤƿŹƺĮƫřƹŶƳŵƺưƳƢǀƤŰţƢǀƣŵƶƴǀƸŝ ƱřƺƴƗŚŝƽŻŚſźěŻŚŝƩŶƯĨƿƱŚĭŵźŞƯŚƳƶƬƤƯŹŵźƔƳŵŹƺƯƶƬŘƀƯ
ƱōŹŵŵƺūƺƯƾƫźŤƴĩƶƫŵŚƘƯƹŵƶĩŢſřźƔƳŶƯ ƽřƶƫŵŚƘƯƹŵ ƽźĮƿŵƹŵŹřŵƵŶƸƗźŝřŹƶƴǀƸŝƽŻŚſźěŻŚŝƱŚƯŻƲǀǀƘţƶƠǀƓƹƾĪƿ Jen-ming chen, ŶƴĩƾƯƲǀǀƘţřŹƽŻŚſźěŻŚŝŵřŶƘţƶƴǀƸŝŹřŶƤƯ źƔƳ Źŵ řŹ ƾŗżū ƹŵ ƲǀƯŚţ ƵźǀŬƳŻ Ĩƿ >çå@ Tsung-Hui chen ƵŶƴƃƹźƟŹřŶƿźųƹƵŶƴƴĩƲǀƯŚţƱŚĭŶƴƴĩŶǀƫƺţŵřŶƘţŶƳřƶŤƟźĭ ŹŵLJŚĩźƷƽřźŝŚƋŚƤţűźƳŶƴƴĩƾƯŹŚŞƳřřŹƭLjƣřƶĩŶƃŚŝƾƯƾĪƿ ƶŝ Śƿ řŹ ŹŚŞƳř ŚƷ ƵŶƴƃƹźƟ ŵƺƃ ƾƯ ƉźƟ ŢŝŚŧ ƁƹźƟ ƵŹƹŵ ƩƺƏ ĨƿŚƸƴţŻřżĩźưŤƯƱŚƯżưƷŹƺƏƶŝŚƿżĩźưţƭŶƗƶƳŚĭřŶūšŹƺƇ Ŷů Ĩƿ Śţ Ŷƴƴĩ ƾƯ ƽŻŚſźěŻŚŝ EOQ ŢſŚǀſ ŽŚſř źŝ ƖŞƴƯ ŶůƱōźŝŵřŻŚƯƽřźŝƹŢųřŵźěƾƷŵƁŹŚƠſŢŝŚŧƶƴƿżƷƅŚų ƾƯ ƉźƟ ƲǀƴĤưƷ ŵƺƃ ƾƯ Ţųřŵźě Ŷůřƹ źƷ ŢŝŚŝ ƾƿŚƷ ƶƴƿżƷ Ʋƿř ƅŚų Ǝƿřźƃ Źŵ ŵŹřŶƳ ŵƺūƹ ƾƷřŹ Źŵ ƁŹŚƠſ ĢǀƷ ƶĩ ŵƺƃ
çîƾŗƺĩŚƯŶưůřƹƾŗŚƐƗřźƷŻŹřŶƿźųŶƴģŚŝźƿŸěŵŚƀƟƽŚƷLJŚĩƽřźŝƭřƺţƲǀƯŚţƶƟŶƷŶƴģƽżƿŹƶƯŚƳźŝ

ŵźǀĭšŹƺƇŚƷƵŹƹŵƶưƷŚƿƾųźŝŻŚƛōŹŵŶƳřƺţƾƯƽŻŚſźěŻŚŝƶĩ ƱřżǀƯ ŶƃŚŝ ƾƯ ƾƫƺƈŰƯ Ĩţ ƽř ƵŹƹŵ ŹƹźƯ ƮŤƀǀſ Ĩƿ ƶƬŘƀƯ ƱŵźĩƮưƿżĩŚƯżǀƳƝŶƷŶƃŚŝƾƯŢưǀƣŻřƾƘŝŚţƎƤƟƽŻŚſźěŻŚŝ ƶƴƿżƷƪƯŚƃƮŤƀǀſƽŚƷƶƴƿżƷƶĩƾƐƿřźƃŹŵƵŵƺŝŵƺſƎſƺŤƯ źŝ >èæ@ Chi Chang ŶƃŚŝ ƾƯ Ŷƿźų ƹ ƾƷŵ ƁŹŚƠſ ƽŹřŶƸĮƳ ƪĪǀſƶĩƾƐƿřźƃŹŵƽŻŚſźěŻŚŝƽŵƺūƺƯƩźŤƴĩƶƬŘƀƯĨƿƽƹŹ ĨƿƩŶƯƹŢſřƵŶƃƪǀĪƄţĨģƺĩƵŹƹŵŶƴģŻřŵƺųƽŻŚſźěŻŚŝ
ƵŵŚƠŤſřŵŹƺƯƮŤƀǀſŶƳřƵŵƺưƳƢǀƤŰţŶƃŚŝƾƯŚƿƺěƽżƿŹƶƯŚƳźŝ
ƵŹƹŵŹŵƹƾƟŵŚƈţźǀƜŤƯĨƿŚƋŚƤţŶƃŚŝƾƯ(s,S)ƶƫŚƤƯƲƿřŹŵ ƲǀƯŚţƽřźŝƪƿƺŰţšŶƯŶƳƺƃƾƯƉźƟƮƷŻřƪƤŤƀƯƞƬŤŴƯƽŚƷ ŚƴưƋ ŶƃŚŝ ƾƯ ƵŹƹŵ ƩƺƏ Żř ƾŰǀŰƇ śźƌƯ ƹ Ƶŵƺŝ ŢŞŨƯ LJŚĩ ƵŹƹŵ ƲƿŶƴģ Żř ƽŻŚſźěŻŚŝ ƪĪǀſ źƷ Ŷƃ ƶŤƠĭ ƶĩ ŹƺƏ ƱŚưƷ
ƽżƿŹƶƯŚƳźŝƽźǀĭŹŚĩƶŝŚŝŢƿŚƸƳŹŵƶƬŘƀƯƩŶƯŢſřƵŶƃƪǀĪƄţ
ŵƺƃƾƯƆŴƄƯƶƴǀƸŝźƿŵŚƤƯƹƪůŚƿƺě Ŷƴģ ƽŻŚſźěŻŚŝ ƶƬŘƀƯ Ĩƿ ƽƹŹ źŝ >èç@ Yao, Chu, Lin ŶƳřƵŵƺưƳƢǀƤŰţŚƌƟŢƿŵƹŶŰƯŵƹŶŰƯƽŚƌƟŚŝƵřźưƷƾƫƺƈŰƯ ŹřŶƤƯƹƱŚƯŻźƔƳŻřƽŻŚſźěŻŚŝƽżƿŹƶƯŚƳźŝŢſřŹřźƣƶƬŘƀƯƲƿřŹŵ
nƽŻŚſźěŻŚŝƶƬŘƀƯĨƿŚŝŢƤǀƤůŹŵŵƺƃƲǀǀƘţƩƺƈŰƯnƽřźŝ ŵŹřŵ ŵƺūƹ ŚƌƟ ŢƿŵƹŶŰƯ Ʊō Źŵ ƶĩ ƮǀŤƀƷ ƹźŝƹŹ ƾƫƺƈŰƯ śźƌƯ ƶĩ ƱŚƯŻ Źŵ ƾƬĪǀſ ŹƺƏ ƶŝ ŶƴƳřƺţ ƾƯ ƞƬŤŴƯ ƽŚƷLJŚĩ
űźƳ ŚƴưƋ ŶƳƺƃ Ƶŵřŵ ƁŹŚƠſ ŶƃŚŝ ƾƯ ƽř ƶƿŚě ƪĪǀſ Żř ŮǀŰƇ
ŶƃŚŝƾƯƆŴƄƯƹŢŝŚŧƩƺƈŰƯźƷƽřźŝŚƋŚƤţ
Źŵ ŹŚŝ ƲǀŤƀŴƳ ƽŵƺūƺƯ ƮŤƀǀſ ŵźĪƬưƗ źŝ LJŚĩ ŜƿźŴţ źǀŧŚţ
ŶƿŵźĭƾſŹźŝæîëèƩŚſŹŵ>èè@SchraderƹGharešŚƤǀƤŰţ ƪǀƬŰţŚŝæîììƩŚſŹŵ>èé@JaiswalƹShahƎſƺţšŚƘƫŚƐƯƲƿř
źƔƳŹŵŚŝƹźƿŸěŜǀſōƭLjƣřƽřźŝƽŵƺūƺƯƮŤƀǀſĨƿƽŻŚƀƫŶƯƹ
ƹ Covert ŢƟŚƿ ƭƹřŶţ ƭLjƣř Ʋƿř ƽřźŝ ŢŝŚŧ ŜƿźŴţ űźƳ ƲŤƟźĭ
ŚŝźƿŸěŜǀſōƭLjƣřƽřźŝƽŵƺūƺƯƩźŤƴĩƩŶƯĨƿ>èê@Philip ŹŵŶƳŵƺưƳƾůřźƏŵƺŞưĩƱŵƺŞƳŻŚŬƯƉźƟŚŝƹźǀƜŤƯŜƿźŴţűźƳ źŝźƿŸěŜǀſōƭLjƣřŜƿźŴţűźƳƹŢŝŚŧšŹƺƇƶŝŚƋŚƤţƩŶƯƲƿř
ƵŶƃƶƿřŹřƩŶƯŢſřƵŶƃƶŤƟźĭźƔƳŹŵƩƺŞƿřƹƾƫŚĮģƖŝŚţŽŚſř ƶſ Śŝ ƩƺŞƿřƹ ƾƫŚĮģ ƖŝŚţ ƲŤƟźĭ źƔƳ Źŵ Śŝ >èë@ Philip Ǝſƺţ ƭLjƣř ƽřźŝ ƽŵŚƈŤƣř Ŷǀƫƺţ ƱřżǀƯ ƲǀǀƘţ Ŷƃ Ƶŵřŵ ƶƘſƺţ źŤƯřŹŚě ƽŚƸưŤƀǀſźŝƮĩŚůƽŚƸŤƿŵƹŶŰƯƹƎƿřźƃƶŝƶūƺţŚŝźƿŸěŜǀſō ƹ Elsayyed  æîìî ƩŚſ Źŵ >èì@ Dave Ǝſƺţ ƽŵƺūƺƯ æîíèƩŚſŹŵ>èî@KangƹKimæîíèƩŚſŹŵ>èí@Terasi æîîæƩŚſŹŵ>éæ@Raafat et al.ƹæîíçƩŚſŹŵ>éå@Make
ƾƫŶƯ æîîè ƩŚſ Źŵ żǀƳ >éç@ Wee ŢƟźĭ Źřźƣ ƶƘƫŚƐƯ ŵŹƺƯ źƔƳŹŵŚŝźƿŸěŵŚƀƟƭLjƣřƽřźŝƽŵŚƈŤƣřŶǀƫƺţŹřŶƤƯƲǀǀƘţŢƸū ƽŚƋŚƤţšŹƺƇƶŝŵƺŞưĩƱŵƺŞƳŻŚŬƯƉźƟƹŢŝŚŧŶǀƫƺţűźƳƲŤƟźĭ ŵƹŶƘƯŻřƱřƺţƾƯřŹ>éè@YangƹWee ƩŶƯŵƺưƳƶƿřŹřŢƟřžě ŵŹƹō ŹŚưƃ ƶŝ źƿŸěŵŚƀƟ ƭLjƣř ƽřźŝ ƾŰƐſ Ŷƴģ ƾƋŚƿŹ ƽŚƸƫŶƯ Chung,LinŢſřźƠƇƵŹƹŵƽŚƸŤƳřƹřŶŤŝřƽŵƺūƺƯƹŵŹřŶƳŵƺūƹ ƢƟř Ĩƿ Źŵ ƽŵƺūƺƯ ƩźŤƴĩ ƽŻŚſźěŻŚŝ ƶƬŘƀƯ Ĩƿ ƽƹŹ źŝ >çê@ ƩŶƯ ƶƫŚƤƯ Ʋƿř Źŵ ŶƳř ƵŵƺưƳ ƢǀƤŰţ ŢŝŚŧ ƹ ŵƹŶŰƯ ƽżƿŹ ƶƯŚƳźŝ ƱřƺƴƗŢŰţƾƃƹŹŻřƱŚƿŚěŹŵŵƺƃƾƯƵŵřŵƶƘſƺţChungƾƬŞƣ Ŷƴƴĩ ƾƯ ƵŵŚƠŤſř ƽŻŚſźěŻŚŝ ƱŚƯŻ ƹ ŹřŶƤƯ ƲǀǀƘţ ƽřźŝ DCF ƢǀƤŰţ ƽŻŚſźěŻŚŝ ƶƬŘƀƯ Ĩƿ ƽƹŹ źŝ >çë@ Elkafi Hassini ƲƿřŹŵŶƷŵƂƿřżƟřřŹŚƷƽŻŚſźěŻŚŝƲǀŝƱŚƯŻŚţŵŹřŵŶƈƣƹƵŵƺưƳ ƽŹřŶƸĮƳ ƶƴƿżƷ ƮǀŤƀƷ ƶūřƺƯ ƾƫƺƈŰƯ Ŷƴģ ƩŶƯ Ĩƿ Śŝ ƶƫŚƤƯ
ƶĩ ŶƷŵ ƾƯ űŹ ƾƳŚƯŻ ƽŻŚſźěŻŚŝ ƹ ŶƃŚŝ ƾƯ źƠƇ ƽŵƺūƺƯ
ƵŶƴƀƿƺƳƶƬŘƀƯƲƿřŹŵŵƺƃƾƯźƠƇźƔƳŵŹƺƯƩƺƈŰƯƽŵƺūƺƯ ƶŝřŹŹŚŞƳřƽŚƌƟŶƃŚŝƾƯƾƘƐƣƩŶƯƶĪƴƿřƶŝƶūƺţŚŝŵŹřŵŶƈƣ źĩŷƶŝƭŻLJŶŝŚƿƂƿřżƟřƽŻŚſźěŻŚŝƵŹƹŵƩƺƏŚţŶƿŚưƳƲǀǀƘţƽƺŰƳ ƵŶƃ ƶŗřŹř ƾƫŶƯ żǀƳ ŶƃŚŝ ƾƯ ƾƟŵŚƈţ ŚƋŚƤţ ƶĩ ƾƐƿřźƃ Źŵ Ţſř
Teng,Chang,Goyal ŵƺưƳ ƶƘūřźƯ ƶƫŚƤƯ ƶŝ Ʊřƺţ ƾƯ ƶĩ Ţſř ƂƟŶƷ ƶĩ ŶƳř Ƶŵźĩ ƢǀƤŰţ ƽŻŚſźěŻŚŝ ƶƬŘƀƯ Ĩƿ ƽƹŹ źŝ >çì@
ŶƃŚŝ ƾƯ ƶƴǀƸŝ ƁƹźƟ Ţưǀƣ ƹ ƽŻŚſźěŻŚŝ ƶƴǀƸŝ ƱŚƯŻ ƲǀǀƘţ
ŻŚŬƯŵƺŞưĩŶƃŚŝƾƯŢưǀƣŻřƾƫƹżƳƾƘŝŚţšŹƺƇƶŝLJŚĩƽŚƋŚƤţ ƁŹŚƠſƹŶƿźųƽŹřŶƸĮƳƶƴƿżƷƮŤƀǀſƽŚƷƶƴƿżƷƹŶƃŚŝƾưƳ ƮǀưƈţźǀƜŤƯĨƿŵƺųƁƹźƟŢưǀƣƶƫŚƤƯƲƿřŹŵŶƃŚŝƾƯƾƷŵ
ƶƫŚƤƯƲƿřƱŚĭŶƴƀƿƺƳŵƺƃƲǀǀƘţƱōƶƴǀƸŝŹřŶƤƯŶƿŚŝƹŶƃŚŝƾƯ ƽŚƷ ƁƹŹ Żř ƵŵŚƠŤſř Śŝ ƽŻŚƀƫŶƯ Żř žě źųō Ţưƀƣ Źŵ ŚŤƿŚƸƳ ŶƴƿŚưƳƾƯƶƴǀƸŝśřƺūƶŝƾŝŚǀŤſŵƹƶƬŘƀƯƪůƶŝƭřŶƣřƾƋŚƿŹ ƽŵƺūƺƯ ƩźŤƴĩ ƩŶƯ Ĩƿ ƽƹŹ źŝ >çí@ ƂƳřŹŚĪưƷ ƹ K.L.Mak SƹƁŹŚƠſƶƐƤƳsŶƳřƵŵźĩƢǀƤŰţ(s,S)ŢſŚǀſŚŝƽŻŚſźěŻŚŝ ƽŵƺūƺƯ ƩźŤƴĩ ƽƹŹ źŝ ƶƫŚƤƯ Ʋƿř Ţſř ƾƷŵ ƁŹŚƠſ ŮƐſ
ƮŤƀǀſŹŵŢſřƮƔƴƯŚƳƱŚƄƿŚƋŚƤţƶĩŶƴĩƾƯƢǀƤŰţƾƿŚƷLJŚĩ ŻŚŝ ƽřźŝ ƾƿŚƷ ŢƇźƟ ƹ ƾƷŵ ƁŹŚƠſ ŹřŶƤƯ źŨĩřŶů ŢƿŵƹŶŰƯ
ƽřźŝ ŶƃŚŝ ƾƯ (s,S) źƔƳ ŵŹƺƯ ŢſŚǀſ ŵŹřŵ ŵƺūƹ ƽŻŚſźě ƶŝ ƹ ŵƺƃ ƾƯ ƵŵŚƠŤſř ƝƺĩŹŚƯ ƽźǀĭ Ʈǀưƈţ ŶƴƿōźƟ Żř ƽŻŚƀƫŶƯ ƖƿŻƺţƖŝŚţŻřƽŵƺūƺƯŢǀƘƣƺƯƩŚưŤůřƾƫŚĮģƖŝŚţŻřƵŵŚƠŤſřƽŚū ŶƃŚŝƾƯƽŵƺūƺƯŢǀƘƣƺƯźĮƳŚǀŝƶĩŢǀƘƋƹƶƬůźƯźƷƩŚưŤůř
ƩźŤƴĩƩŶƯĨƿƽƹŹźŝ>çî@Hill,JohansenŢſřƵŶƃƵŵŚƠŤſř ŶƳřƵŵźĩƢǀƤŰţƶŤƟŹŢſŵŻřƁƹźƟŚŝƵřźưƷƽŻŚſźěŻŚŝƽŵƺūƺƯ űźƳ ŶƃŚŝ ƾƯ ƆŴƄƯ Ʊō ƖƿŻƺţ ƹ ƾƟŵŚƈţ ŚƋŚƤţ ƶƬŘƀƯ Ʋƿř Źŵ ŶƿŚưƳ ƾƯ ŢǀƘŞţ Ʊƺſřƺě ƖƿŻƺţ Żř ƹ ŢŝŚŧ ƮŤƀǀſ ƶŝ ŚƋŚƤţ ŵƹŹƹ Ŷƿźų ƽŚƷ ƶƴƿżƷ ƹ Ţſř ƶŤſƺǀě ŹƹźƯ ƽŵƺūƺƯ ƩźŤƴĩ ƮŤƀǀſ
(r,Q) ŢſŚǀſ ƹŵ ŵŹřŵ ŵƺūƹ ŵƺŞưĩ ƹ ƽŹřŶƸĮƳ ƾƷŵ ƁŹŚƠſ ƶŞſŚŰƯŢſŚǀſ ƹŵ źƷ źƿŵŚƤƯŶƿŚŝ ƹ Ƶŵřŵ Źřźƣ źƔƳ ŶƯ řŹ (s,S)ƹ
ŶƳƺƃ
ƽŵƺūƺƯƩźŤƴĩƶƬŘƀƯĨƿƽƹŹźŝ>èå@Ming-Chen,Tu Chen ƭřƺţƽżƿŹƶƯŚƳźŝƝŶƷƱōŹŵƶĩŶƳřƵŵźĩƢǀƤŰţƽřƵŹƹŵŹƹźƯŚŝ
ŢſřƾƐƿřźƃŹŵƕƺƋƺƯƲƿřƹŶƃŚŝƾƯƞǀƠŴţƶŗřŹřƹƽŻŚſźěŻŚŝ
ƾŗƺĩŚƯŶưůřƹƾŗŚƐƗřźƷŻŹřŶƿźųŶƴģŚŝźƿŸěŵŚƀƟƽŚƷLJŚĩƽřźŝƭřƺţƲǀƯŚţƶƟŶƷŶƴģƽżƿŹƶƯŚƳźŝèå

>æ@ƾŤĩŹŚƄƯƽżƿŹƶƯŚƳźŝçè
ƶƯŚƳźŝ ŶƿŚŝ ƽźŤƄƯ šŚƃŹŚƠſ ƱŵŹƹōźŝ ŹƺƔƴƯ ƶŝ ƾƳŚƯŻŚſ źƷ Źŵ
ƶƯŚƳźŝ ƶƨƴƿř Śŝ . ŵƺƃƭŚŬƳř Źřżŝř ƹ šLJōƲǀƃŚƯ ƱŚƴƧŹŚƧ ŵřƺƯƽżƿŹ ŹŚǀƀŝ ƶŤƃŸĭ ƽŚƷ ƶƷŵ Źŵ Ŷƿźų ƲǀƴĤưƷ ƹ ƖƿŻƺţ ƹ Ŷǀƫƺţ ƽżƿŹ ƽŻŚſ ĬƴƷŚưƷ ƽŚƷ ƶƯŚƳźŝ ŻƺƴƷ Ţſř ƶŤƟźĭ Źřźƣ ƶƘƫŚƐƯ ŵŹƺƯ ƂƫŚģ ŶƴŤƀƷ řżŬƯ ƾƳƺƳŚƣ źƔƳ Żř ƶƧ ƱŚƯŻŚſ Ŷƴģ ƹ ƪŰƯ Ŷƴģ ƽżƿŹ ƶƯŚƳźŝ ƮƸƯ ƽŚƷ ƶŞƴū Żř ŵŹřŸĭ ƾƯ ƂƿŚưƳ ƶŝ řŹ ƽŶƿŶū źƷ ƶŝ ŶƳřƺţ ƾƯ ƪƯŚƧ”ƲǀƯŐţ ƵźǀŬƳŻ ƶƨŞƃ”.ŵƺƃƾƯƾƤƬţ ƶŤƟźƄǀě ƶŝ ŵƺƃ ƦǀƨƠţ ƾƬųřŵ ƲǀƯŐţ ƽŚƷ ƵźǀŬƳŻ ŠƨŞƃ Źŵ ŌŚƧźƃ Żř ƭřŶƧ ƹ) ƲǀƯŐţ ƵźǀŬƳŻ ƾƬƇř ŶƴƿōźƟ ŹŚƸģ Żř Ʀƿ źƷ ƦƿźƃźƷ ƶƨƿřƶƳƺĭ ƾƯ ƪƯŚƃ řŹ (ƞƬŤŴƯ ƽżƿŹ ƶƯŚƳźŝ ƞƿŚƓƹ ƶĈūƺţ ƪŝŚƣƽř ƶƳƺĭ ƶŝ .ŶƴƃŚŝƾƯ ƁƹźƟ ƹ ƖƿŻƺţ Ŷǀƫƺţ šŚƧŹřŶţ ƪƯŚƃ ŚƷŶƴƿōźƟ Ʋƿř.ŶƳƺƃ ƹ ƖƿŻƺţ ƽżƿŹ ƶƯŚƳźŝ Żř ƾƤǀƠƬţ ƶƫŚƤƯ Ʋƿř ƾţŚƘƫŚƐƯ ƵŵƹŶŰƯ ƪŗŚƀƯ Ʋƿř Żř . ŵƺƃƾƯƪƯŚƃřŹ ( ƁŹŚƠſ ƵŻřŶƳř ƲǀǀƘţ) ƽŵƺūƺƯ Żř ƶĩ ŵƺƃƾƯ ŵŚƿ” ƾŤĩŹŚƄƯƽżƿŹ ƶƯŚƳźŝ “ƱřƺƴƗ ŢŰţ šŚǀŝŵř Źŵ ƂƿřżƟř řĆŶƿŶƃ źǀųř ƩŚſŶƴģ Źŵ Ʊō ƶŝ Ƃƿřźĭ ƶĩ Ţſř ƾŨůŚŞƯ šŚƘƫŚƐƯ ƲǀƴĤưƷ. ŵƺƃ ƶƘūřźƯ >ì@ƶŝƶƳƺưƳ ƱřƺƴƗ ƶŝ Ţſř ƶŤƟŚƿ Źŵ ŚľƇƺƈų ƖƿŻƺţ ƹ ƽŵƺūƺƯ ƶģŹŚĜĪƿ ƽżƿŹƶƯŚƳźŝ Ţưſ ƶŝ ƽŹŚǀƀŝ ŵƺūƹ Ʊō Ţưſ ƶŝ ƽŹŚǀƀŝ Ƃƿřźĭ ƹ Ţſř ƵŶƃ ƭŚŬƳř źǀųřƩŚſ Ŷƴģ >ç@ŵŹřŵ

ƵźǀŬƳŻƽŻŚƀƫŶƯè
:ƭřƺţƽŻŚſźěŻŚŝƽŚƴŞƯźŝƽŻŚƀƫŶƯèæ
ƶĩ Ţſř ŹřŶƿźų ƽŵřŶƘţ ƹ ƵŶƴƴĩ ƲǀƯŚţ Ĩƿ ƪƯŚƃ ƶƬŘƀƯ
ƁŹŚƠſƽŚƷLJŚĩŶƳŹřŵřŹLJŚĩƕƺƳŶƴģƪƯŚƃƾƿŚƷŚƋŚƤţƱřŹřŶƿźų ƾƯ ŌŚƌƤƳř ŲƿŹŚţ ƹ ŢŝŚŧ źưƗ ƽřŹřŵ ƹ Ƶŵƺŝ źƿŸě ŵŚƀƟ ƵŶƃ Ƶŵřŵ ŵƺƃƾƯƪƿƺŰţƱřŹřŶƿźųƶŝƲǀƯŚţřŶŞƯŻřŚưǀƤŤƀƯŚƷLJŚĩŶƴƃŚŝ
źƷŹŵƹŵƺƃƾƯƭŚŬƳřƽřƵŹƹŵšŹƺƇƶŝŚƷLJŚĩƲǀƯŚţƽżƿŹƶƯŚƳźŝ ƹŵŵźĭƆŴƄƯŹřŶƿźųźƷƶŝLJŚĩźƷŻřƁŹŚƠſƱřżǀƯŶƿŚŝƵŹƹŵ ƩŶƯƽřźŝƵŶƃƶŤƟźĭźƔƳŹŵƝřŶƷřƶŝƶūƺţŚŝƵŹƹŵƩƺƏƲƿźŤƸŝ
ŢſŵƶŝŌŚƌƤƳřŲƿŹŚţƱŶƃƭŚưţŻřƪŞƣŶƿŚŝŚƷLJŚĩŶƿōƾƯŢſŶŝ ƽŹřŶƸĮƳƱŚƯŻšŶƯƹƁŹŚƠſƱŚƯŻƽƹŹƶƬŘƀƯƲƿřŶƴſźŝŹřŶƿźų ƽřŶŤŝř Źŵ ƁŹŚƠſƱŚƯŻ Źŵ ŚƷLJŚĩ ŵŹřŸĭ ƾƯźǀŧŚţ ŹŚŞƳř Źŵ ŚƷLJŚĩ

ƽřŹřŵŵŵźĭƾƯƾƟźƘƯƂŴŝƲƿřŹŵƶĩƾƫŶƯŶƴŤƀƷŚƌƤƳřšŶƯ
ŶƃŚŝƾƯźƿŻšŚƋƹźƠƯ
ƭƺƬƘƯƶĩŢſřƵŶƃƉźƟŹřŶƿźųƽLJŚĩźƷŹŵƱŚƯŻŶůřƹźŝŚƋŚƤţ
ŶƃŚŝŢŝŚŧƹ
ŢſřŢŝŚŧLead time-
ŢƀǀƳŻŚŬƯƽŵƺŞưĩĢǀƷ
ƶĩŵƺƃƾƯƮǀƀƤţƾƗźƟƹƾƬƇřŢưƀƣƹŵƶŝƾƷŵƁŹŚƠſƶƴƿżƷ
ŵŹřŵŵƺūƹƁŹŚƠſźƷŹŵƾƬƇřŢưƀƣ
i=1,2,…,I)ŚƷLJŚĩŵřŶƘţi ƵŶưƗŹŵƁŹŚƠſƽŵŚƈŤƣřƱřżǀƯƶŞſŚŰƯƩŶƯƲƿřƾůřźƏŻřƝŶƷ ƮŤƀǀſ ƽŚƷ ƶƴƿżƷ ƶĩ ƽƺŰƳ ƶŝ ŶƃŚŝ ƾƯ ƁƹźƟ Ƶŵźų ƹ ƁƹźƟ ŵŵźĭ ƶƴǀưĩ ƱŚƯżưƷ šŹƺƇ ƶŝ ƹ ŮƐſ ƹŵ źƷ Źŵ ƽŵƺūƺƯ ƹWee ƩŶƯ ƶƘſƺţ çååæ ƩŚſ Źŵ >éé@ Wu ƹWee ƲǀƴĤưƷ ƹ ƂŴŝ ƲƿŶƴģ ƶŝ ƽŵŚƈŤƣř ƁŹŚƠſ ƱřżǀƯ ƮǀƀƤţ Śŝ řŹ Yang Leeƹ ChenŹŵŶƳŵřŵŹřźƣƾſŹźŝŵŹƺƯƵŹƹŵĨƿƾƏŹŵƩŚſŹř ƵŶƃƾſŹźŝƾƟŵŚƈţźưƗƩƺƏƹƾƄƷŚĩƁŻŹřŚŝƾţLJƺƈŰƯ>éê@ Ĩƿ ƽŵƺūƺƯ  Ŷƴĩ ƽƹźǀě ƾƿŚưƳ ƖƿŻƺţ Żř ƽŵƺūƺƯ ŵŚƀƟźĭř ŶƳř  ŵƺƄƳ ƵŵżƳ Ţſŵ Ʊō ƶŝ ƹ ŶƃŚŝ I źŝřźŝ t ƱŚƯŻ Źŵ LJŚĩ ƮƬƣ ƶĩŵƺŝŶƷřƺųIe-xźŝřźŝt+xƶƔŰƫŹŵLJŚĩƮƬƣƲƿřƽŵƺūƺƯ ŵŚƀƟƶĩŚŬƳōŻřŵƺƃƾƯƞƿźƘţƱŚƯŻŶůřƹŹŵLJŚĩŵŚƀƟűźƳƱōŹŵ ŹŵŚƣŶƴĩƾƯƪǀưŰţƽŵƺūƺƯƽŹřŶƸĮƳźŝřŹƾƟŚƋřƽŚƷƶƴƿżƷ
ƪƬų ƽźǀĭ Ʈǀưƈţ ŶƴƿōźƟ ŹŵƱŶƃ ƶŤƟźĭ ƵŶƿŵŚƳ šŹƺƇ Źŵ Ţſř
ŶƳŚƄĪŝƶƷřźǀŝƶŝřŹLJŚĩƩŚſŹřƽĦţřźŤſřƹƵŵźĩŵŚŬƿř ƩŶƯĨƿƱřƺƴƗŚŝƽřƶƫŚƤƯŹŵ>éë@BanerjeeæîíëƩŚſŹŵ
ƩŶƯĨƿƵŶƴƃƹźƟƹŹřŶƿźųƽřźŝħźŤƄƯƽŵŚƈŤƣřƁŹŚƠſƶŤſŵ
ŵźĩŵŚŬƿřƵŶƴƃƹźƟƹŹřŶƿźųƽřźŝħźŤƄƯƽŵŚƈŤƣřƁŹŚƠſƶŤſŵ
ƩŶƯ Ĩƿ ƱřƺƴƗ Śŝ ƽř ƶƫŚƤƯ Źŵ >éì@ Goyal  æîíë ƩŚſ Źŵ
ƶŤĪƳĨƿƵŶƴƃƹźƟƹŹřŶƿźųƽřźŝħźŤƄƯƽŵŚƈŤƣřƁŹŚƠſƶŤſŵ
ŚƷŹƽřźŝřŹæîíëƩŚſŹŵBanerjeeƎſƺţƵŶƃƶŗřŹřƩŶƯŹŵ
ŹŵŵřŵƮǀưƘţƵŶƴƃƹźƟƽřźŝƶŤſŵƶŝƶŤſŵŢſŚǀſƉźƟƽŻŚſ
ƽŵƺūƺƯƆǀƈŴţƱřƺƴƗŚŝƽřƶƫŚƤƯŹŵ>[email protected]æîíîƩŚſ ĨƿƽŻŚſƶǀŞƃŻřƵŵŚƠŤſřŚŝƾƃƹźƟƵŵźųƵźǀŬƳŻĨƿŹŵŹŚŞƳř ŵƺưƳƶŗřŹřƁƹźƟƵŵźųƽŵřŶƘţƹƽżĩźƯŹŚŞƳřĨƿŻřƪĪƄŤƯƩŶƯ ƽŚƸƃƹŹƱřƺƴƗŚŝƽřƶƫŚƤƯŹŵ>éî@Posner ,LuæîîéƩŚſŹŵ ƮŤƿŹƺĮƫř ƹŵ ƁƹźƟ Ƶŵźų Ŷƴģ ƹ ŹŚŞƳř Ĩƿ ƮŤƀǀſ ƽřźŝ ƾŞƿźƤţ Ƶŵźų Ŷƴģ ƹ ŹŚŞƳř Ĩƿ Żř ƪĪƄŤƯ ƾưŤƀǀſ ƽřźŝ řŹ ĨǀŤƀƿŹƺǀƷ ƽřƶƫŚƤƯŹŵ>êå@Kim , HaæîîìƩŚſŹŵŶƳŵřŵƶŗřŹřƁƹźƟ ƶģŹŚĜĪƿ ƶģŹŚĜĪƿ ƁƹŹ Ĩƿ ƖƣƺƯ ƶŝ Ŷǀƫƺţ ƭŚƔƳ ƽŻŚſ ƵŵŚǀě ƾſŹźŝŵŹƺƯƾƋŚƿŹƩŶƯĨƿŵŚŬƿřŚŝřŹŹřŶƿźųƹƵŶƴƃƹźƟƱŶƃ
Ĩƿ ƢƿźƏ Żř ƵŶƴƃƹźƟ ƽŵƺūƺƯ ƽŚƷ ƶƴƿżƷ Ʊō Źŵ ƶĩ ŶƳŵřŵ Źřźƣ Wee, æîîíƩŚſŹŵŶƿōƾƯŢſŶŝƶŤſƺǀěźǀƛŹřŵƶƳřŶƳŵƖŝŚţ
ƽřźŝ ƽř ƶŤſŵ Ŷƴģ Ŷǀƫƺţ ƽřźŝ řŹ ƽř ƶģŹŚĜĪƿ ƩŶƯ >êæ@ Jong ŵŚƀƟƽŚƷŹƺŤĩŚƟŵƺųƩŶƯŹŵŚƸƳōŶƳŵřŵƶŗřŹřźƿŸěŵŚƀƟšLJƺƈŰƯ źƔƳ Źŵ ƱŚƯżưƷ šŹƺƈŝ řŹ ƵŶƴƃƹźƟ ƹ ŹřŶƿźų Ʋǀŝ ƾĮģŹŚĜĪƿ ƹ šŚƤǀƤŰţ Źŵ řŹ ƽŵƺūƺƯ ŵŚƀƟ Ʊƺƴĩ Śţ ƽŵŶƘŤƯ ƱŚƤƤŰƯ ŶƴŤƟźĭ Ghare SchraderæîëèƩŚſŹŵŶƳřƵŵřŵŹřźƣƾſŹźŝŵŹƺƯŵƺų ƽŵƺūƺƯ Źŵ řŹ ŵŚƀƟ ƶƬŘƀƯ ƶĩ ŶƳř Ƶŵƺŝ ƾƳŚƤƤŰƯ ƲǀŤƀŴƳ >êç@ Covert ,PhilipƱƺģƱŚĭŶƴƀƿƺƳźƿŚſŶƳřƵŵřŵŹřźƣƾſŹźŝŵŹƺƯ ŹŚŤƟŹ æîîæ ƩŚſ Źŵ >êé@ Raafat  æîíè ƩŚſ Źŵ >êè@
ŵŹƺƯŵƹŶŰƯŚƳŚƿŵƹŶŰƯŶǀƫƺţƭŚĮƴƷŹŵřŹźƿŸěŵŚƀƟšLJƺƈŰƯ ŶƳŵřŵŹřźƣƾſŹźŝ
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ƶĪƿŹƺƐŝ kijt ŚŝŢſřźŝřźŝ j ŹřŶƿźųŹŵ i ƽLJŚĩƽŻŚſźěŻŚŝ
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ƱŚƯŻŶůřƹźŝƪưůƶƴƿżƷƪĩ:Cc
ƱŚƯŻŶůřƹźŝƾƷŵƁŹŚƠſƶƴƿżƷƪĩCs ƲƿřźŝŚƴŝ Ţſř j ŹřŶƿźų ƽřźŝ i ƽLJŚĩ ƁŹŚƠſ ŹřŶƤƯ kij
Qij dijkijt
ƁŹŚƠſ ƶƴƿżƷ ƪĩ Cs ƹ Ţſř ƱŚƯŻ Ŷůřƹ źŝ ƪưů ƶƴƿżƷ ƪĩ Cc
ŢſřƱŚƯŻŶůřƹźŝƾƷŵ
ŶƃŚŝƾƯ i ƽLJŚĩźưƗI
ŢſřƩƺěŶůřƹƶŝŵŚƀƟźŧřźŝLJŚƧŵƺŞưƧŶůřƹƶƴƿżƷi
ƶŤƀŝřƹƪĩƶƴƿżƷƶĩŶƴƿōƾƯŢſŵƶŝƽřƶƳƺĭƶŝtƹ kijŜƿřźƋ śŶŰƯ źǀƛ ƶƴƿżƷ ƖŝŚţ ƶĩ Ţƃřŵ ƶūƺţ ŶƿŚŝ ŵƺƃ ŶƷřƺų ƪƣřŶů ƾĮŤƀŝƁřkijƶŝƶĩŮǀŰƈţŹƺŤĩŚƟĨƿ>çí@Dagpunar ŶƃŚŝ ƶƬưūŹŵŢſřĨƿŻřźŤĭŹżŝkijƲƿźŤĪģƺĩƶĩƾƯŚĮƴƷřŹŵŹřŵ
ŻŚŝĢǀƷŢſřƲĪưƯŚƷƶųźģƾƌƘŝŹŵŢſřƶŤƟźĭźƔƳŹŵS/t
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>ë@ŶƃŚŝƵŶƃƶƴƿżƷŶƿŚŞƳ ƹPorras ƱřƺţƾƯřŹŮǀŰƈţŜƿźƋƲƿřŻřƵŵŚƠŤſřŻřƩŚŨƯĨƿ źƿŵŚƤƯƮưǀƴǀƯŚŝƭřƺţƽŻŚſźěŻŚŝƶƬŘƀƯƪůƽřźŝ>çî@Dekker ŶƴģƹŹřŶƿźųŶƴģƶƳƺưƳŹŵŵƺưƳƶƔůLjƯƵŶƃŢƟŚƿƁŹŚƠſ ŚƷ kij Żř ĨǀĤǀƷ ƶĩ ƾŤƫŚů  ƭřƺţ ƽŻŚſźěŻŚŝ ƶƬŘƀƯ ƽ LJŚĩ
ƱŵřŵŹřźƣƩŚůƲƿřŚŝŶƃŚŝŹŵŚƳŢſřƲĪưƯŶƴƃŚŞƳĨƿƽƹŚƀƯ >êë@ Chan ƶƬǀſƹ ƶŝ ƵŶƃ ƵŵŚƠŤſř ƁƹŹ Źŵ ŮǀŰƈţ ŹƺŤĩŚƟ Ʋƿř
ŻřƶƯřŵřŹŵƹŶƃŚŝƾƯźţƵŵŚſŢſřƵŶƃƶŗřŹřçååèƩŚſŹŵƶĩ
C ƝŶƷ ƖŝŚţ ŹƺƔƴƯ Ʋƿř ƽřźŝ Ŷƃ ŶƷřƺų ƵŵŚƠŤſř ƁƹŹ Ʋƿř ŵƺƃƾƀƿƺƳŻŚŝźƿŻšŹƺƇƶŝŶƳřƺţƾƯ
ƮǀƴĩƾƯƾſŹźŝŢƫŚůƹŵŹŵřŹƶƬŘƀƯ Ʋƿř ƽƹŹ ƽźǀŧŚţ ƩƺƈŰƯ źưƗ ŶƃŚŝ i  t ,i źĭř æ
šŹƺƇ ƶŝ  C ƱŚƯŻ Ŷůřƹ źŝ ƪĩ ƶƴƿżƷ ƲƿřźŝŚƴŝƹ



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