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1 Journal of the Faculty of Management and Information Systems, Prefectural University of Hiroshima 2014 No.6 pp The risk measure for resilience in the inventory control system Nobuyuki UENO, Yu KURISU, Koji OKUHARA and Hugang HAN 1 VaR AVaR Excel We propose risk measures for resilience in the inventory system. It is based on an expected stock-out for planning horizon. Resilience is powers of recovery against risk or business continuity. We research on risk measures in the inventory system to track the risk for resilience. Specially we investigate on risk measures concerned with multi-period. At first, we explain the representative risk measures, that is, VaR,AVaR and clarify the relationship between unfulfilled-order-rate and the representative risk measure. Next, we propose risk measures for multi-periods and clarify its validity by numerical experiences. Finally, future research is shown. VaR AVaR
2 VaR AVaR 4 5 Excel monitoring
3 45 Conditional level 1 ε tail probability ε distribution functionf X (x) VaR ε ( ) valueat-riskavar ε ( ) average value-at-risk AVaR ε ( )CVaR ε ( ) TVaR ε ( ) 9ε 1 VaR ε ( ) ε 1 AVaR ε ( )VaR ε ( ) ρ monotonicity : ( ) 1 ρ( ) ρ( ) subadditivity : ρ( ) ρ( ) ρ( ) positive homogeneity : c ρ(c ) cρ( ) translation invariance : c ρ(c ) ρ( ) c AVaR ε ( )VaR ε ( ) VaR ε ( ) AVaR ε ( ) VaR ε ( ) 9
4 46 6 ε VaR ε ( )(1)2 f (x) 1 ε 3 VaR ε ( ) 0 ε ε VaR ε ( )Excel NORMINV ε 1 SVaR( ) Expected Stock-out value-at-risk 3 4 (1)(2) 5
5 (5) 8 ε (8) 9 10 AVaR SVaR SVaRAVaR ε 4 2 (8)0 σ 2 f ( ) (11) 13
6 σ 2 (14) Excel1 5 AVaR SVaR e AVaR SVaRAVaR ω
7 E E E E E E E E E E E E E E E E E E E E
8 E E E
9 51 ε E E E E E E E E E E E E E E E E E E E E E E SVaR e AVaR AVaR i 14 i 4 3 i 15
10 52 6 AVaR O n 0 i 16 AVaR 2 1 AVaR AVaR Unfulfilled-order-rate for aggregation 17 2 AVaRUnfulfilled-order-rate for multi-period AVaR (agr) (multi) (16)(17) O n O n O n 1 (20) (17)(20) 2 AVaR AVaR
11 AVaR i SVaR(i) E E SOn(i) E E AVaR(i) SVaR(i) SOn(i) E E AVaR(i) SVaR(i) SOn(i) E E AVaR(i) SVaR(i) SOn(i) E E AVaR(i) SVaR(i) SOn(i) E E AVaR(i) SVaR(i) SOn(i) E E AVaR(i) SVaR(i) SOn(i) E E AVaR(i) SVaR(i) SOn(i) E E AVaR(i) SVaR(i) E SOn(i) E E AVaR(i) SVaR(i) SOn(i) E AVaR(i) SVaR(i) SOn(i) E AVaR(i)
12 54 6 (agr) (multi) O n O n (agr) (multi) O n O n AVaR 11
13 55 VaR AVaR (multi) AVaR O n 10 2 AVaR AVaR AVaR RMWG (C) pp N. Ueno K.Okuhara H.Ishii H. Shibuki and T. Kuramoto Multi-item Production Planning and Management System Based on Unfulfilled Order Rate in Supply Chain Journal of the Operations Research Society of Japan 50 3 pp pp
14 56 6 pp E.Hollnagel D.D.Woods N.Leveson S.T.Rachev, S.V.Stoyanov and F.J.Fabozzi : Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization, John Wiley & Sons,Inc R.T.Rockafellar and S.Uryasev : Conditional value-at-risk for general loss distributions, Journal of Banking & Finance, Vol.26, No.7, pp
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