A Robust Optimization Approach to Resources Allocation in Maintained Systems

A. H. Shokouhi & H. Shahriari

Amir H. Shokouhi, PhD student, Industrial Engineering Department, K.N. Toosi University of Technology
Hamid Shahriari, Assistance professor, Industrial Engineering Department, K.N. Toosi University of Technology

Keywords ABSTRACT

Robust Optimization,
Availability;
Redundancy Optimization;
Maintenance Resources Optimization of maintenance resources to maximize the system availability is a major concern in different manufacturing systems. Therefore, a lot of effort is put to construct optimization models to reach the maximum availability level and to reduce the costs of lack of availability. However, despite these efforts, data uncertainty in the real world problems was neglected in proposed models which results models with sophisticated nonlinear constraints. In this article the budget uncertainty model of optimization is considered and its counterpart in resources allocation for maintained systems is presented. The proposed model takes into account the degrees of conservativeness to introduce a robust model of optimization. This model is capable of maximizing the availability for the maintained system under certain conditions. The capability of the model in controlling the effects of uncertainty is investigated by means of simulation studies and reasonable results concluded.

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ƽƶºƴǀƸŝśřƺūŚƷƵŵřŵŢǀƘƐƣƭŶƗŢƬƗƶŝŵŹřŵƱŚĪƯřŜǀţźţƲƿŶŝ ƽřźºŝĨǀſLjĩƽŚƷƁƹŹŹŵŶƴƃŚŞƳƶūƺƯơƺƟƽŚƷƩŶƯŻřƪƇŚů
ŢǀſŚƀºůƪǀƬŰţƽŚƷŵźĪƿƹŹŻřŚƷƵŵřŵŢǀƘƐƣƭŶƗƲŤƟźĭźƔƳŹŵ

1Reliability
çìƽŹŚƿźƸƃŶǀưůƹƾƷƺĪƃƲǀƀůźǀƯřƽŚƷƮŤƀǀſŹŵƖŝŚƴƯƆǀƈŴţŹŵŹřƺŤſřƽŻŚſƶƴǀƸŝŵźĪƿƹŹ

n reci creci  n qi T  yicmi  CM ë
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ƽƵŶºƴƷŵƱŚƄºƳ y i ƾůLjƇřšřźǀưƘţƖŝŚƴƯƱřżǀƯreci ƱōŹŵƶĩ ƾůLjºƇřźºǀưƘţƖŝŚƴƯƽƶƴƿżƷcreci  i ƮŤƀǀſźƿŻŌřżūřŵřŶƘţ
qi T  ƹ i ƮŤƀ ǀſź ƿŻŹŵƾůLj Ƈřšřź ǀưƘţƽƶ ƴƿżƷ cmi
ƱŵƺºŝƾƿŚºưƳƉźºƟŚºŝƶĩŢſř i ƮŤƀǀſźƿŻŌřżūřƾŝřźųƩŚưŤůř
ŢſřƶŞſŚŰƯƪŝŚƣìƽƶƫŵŚƘƯŻřƱōŹřŶƤƯŚƷƾŝřźųƖƿŻƺţ
qi T 1eiT
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šřźºǀưƘţƖŝŚºƴƯƂƤƳƱŵřŵƱŚƄƳŹƺƔƴƯƶŝ[æç]ŚĪƫřƹŚĩƹƹźŤſŚĩ Ƶź Ƹŝ I ƾĭŵźƄ ƟƆųŚºƃŻřƾ ſźŤſŵŮƐ ſƽƹŹź ŝƾůLj Ƈř
ŹŵšřźºǀưƘţƱŚƯŻƲǀĮƳŚǀƯƂƷŚĩŹřŶƤƯƽƵŶƴƴĩƱŚǀŝƶĩŶƳřƶŤƟźĭ ƶŤƟŚƿżĩźưţƾƇŚųŌżūƽƹŹźŝƖŝŚƴƯŶƇŹŵæååƶĩŢſřƾƐƿřźƃ
řŹ d  i ƮŤƀǀſźƿŻŌřżūřŵŚưŤƗřŢǀƬŝŚƣŢŞƀƳŜǀţźţƲƿŶŝŶƴƃŚŝ
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di  I 1reci  1 d1i í
šřźºǀưƘţƖŝŚºƴƯŻřƶºĩŢſřƾƳŚƯŻŹŵŵŚưŤƗřŢǀƬŝŚƣŢŞƀƳ d1i ƶĩ ƢºǀƠƬţŚºŝŜºǀţźţƲƿŶºŝŢºſřƵŶƄºƳƶŤƟźĭƽř ƵźƸŝĢǀƷƾůLjƇř
Ĩ ƿƾºſźŤſŵŮƐºſ[æç]ŚºĪƫřƹŚĩƹƹźŤºſŚĩíƹçšLJŵŚºƘƯ ƖŝŚºƴƯƹŌřżūřƲƿřŵřŶƘţŻřƾƘŝŚţƱřƺƴƗƶŝřŹƾƟŚƋřŌřżūřŚŝƮŤƀǀſ
ŶƿōƾƯŢſŵƶŝîƽƶƐŝřŹŻřƶĩŶƴŤƟźĭźƔƳŹŵƾůLjƇřšřźǀưƘţ
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n 1 yi  î
AS  i1 11 I 1reci 1d1i  
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ŵƺŝŶƷřƺųźƿŻšŹƺƇƶŝƶƿŚěƩŶƯƵŶƃƵŵřŵšŚŰǀƋƺţƶŝƶūƺţŚŝ max AS in1 11I 11reci 1d1i yi   
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n recicreci n qi T yicmi  CM
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1268732040128Downloaded from ijiepm.iust.ac.ir at 16:53 IRST on Saturday November 4th 2017

Downloaded from ijiepm.iust.ac.ir at 16:53 IRST on Saturday November 4th 2017

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ƾſźŤſŵŮƐſŹřƺŤſřƽŻŚſƶƴǀƸŝƩŶƯè
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ƵŶƃƵŹŚƃřŵźĪƿƹŹƹŵŻřŹƺĩŸƯƶƫŚƀƯŹŵŚƷƵŵřŵŢǀƘƐƣƭŶƗƱŵźĩ ƮǀƴĩƾƯƵŵŚƠŤſřŹřƺŤſřƽŻŚſƶƴǀƸŝŹŵ
ƽřƵŻŚŝŢǀƘƐƣƭŶƗƽřźŝŹřƺŤſřƩŶƯèæ
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ŶƴĩƾƯƪưƗ ƽŚƷƵŵřŵƶưƷƽřźŝŢƫŚůƲƿźţŶŝƶĩŵƺƃƾƯƉźƟƁƹŹƲƿřƢŞƏźŝ ƩƺƈůƾſŹźŝŵŹƺƯƶƫŚƀƯŹŵźĮƿŵšŹŚŞƗƶŝŶƷŵƾƯűŹƾƘƐƣźǀƛ
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