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Operations Management, Supply Chain Management
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Lineare Regressionskoeffizienten Euklidische Distanzen M/M/1-Warteschlange∑𝑁 2 𝑁 𝑁 𝑁
𝑛=1 𝑥𝑛 ∑𝑛=1 𝑦𝑛 − ∑𝑛=1 𝑥𝑛 ∑𝑛=1 𝑥𝑛 𝑦𝑛 ∑𝐽𝑗=1 𝑎𝑗 𝑔𝑗 (𝑥, 𝑦) ∑𝐽𝑗=1 𝑏𝑗 𝑔𝑗 (𝑥, 𝑦) Warte- 𝜌2 𝜌2 𝑃0 = 1 − 𝜌2
𝑎= 𝑥= 𝑦= schlange 𝐿𝑄 = 𝑊𝑄 = 𝑛+1
𝑁 ∑𝑁 𝑁 𝜆(1 − 𝜌) 𝑃𝑛 = 𝜌 (1 − 𝜌)
𝑛=1 𝑥𝑛 − (∑𝑛=1 𝑥𝑛 )
2 2 (1 − 𝜌)
∑𝐽𝑗=1 𝑔𝑗 (𝑥, 𝑦) ∑𝐽𝑗=1 𝑔𝑗 (𝑥, 𝑦)
𝑤𝑗 𝜆 1 𝑃0 = 1 − 𝜌
𝑁 ∑𝑁 𝑁 𝑁
𝑛=1 𝑥𝑛 𝑦𝑛 − ∑𝑛=1 𝑥𝑛 ∑𝑛=1 𝑦𝑛 Server 𝜌= 𝑆=
𝑏= 𝑔𝑗 (𝑥, 𝑦) = 𝜇 𝜇 𝑃1 = 𝜌
𝑁 ∑𝑁 𝑁
𝑛=1 𝑥𝑛 − (∑𝑛=1 𝑥𝑛 )
2 2 2
√(𝑎𝑗 − 𝑥) + (𝑏𝑗 − 𝑦)
2
𝜌 𝜌
System 𝐿𝑆 = 𝑊𝑆 = 𝑃𝑛 = 𝜌𝑛 (1 − 𝜌)
Transformationen (1 − 𝜌) 𝜆(1 − 𝜌)
Trans-
Bestellmengenmodell λ
Ursprungsform Lineare Form 𝜇 𝑥 Rekursion λ∗ = (1−p)
formation
𝑍(𝑥) = 𝑐𝜇 + 𝐾 + ℎ
Potenz: 𝑦̃ = 𝑙𝑛(𝑦) 𝑥 2 Regelkarten
𝑥̃ = 𝑙𝑛(𝑥) 𝑦̃ = 𝑎̃ + 𝑏𝑥̃
𝑦 = 𝑎𝑥 𝑏 Endliche Produktionsrate
𝑎̃ = 𝑙𝑛(𝑎) 𝐱̅-Karte R-Karte p-Karte c-Karte
Exponential:
𝜇 𝜇 𝑥
𝑦̃ = 𝑙𝑛(𝑦) 𝑍(𝑥) = 𝑐𝜇 + 𝐾 + ℎ (1 − )
𝑦̃ = 𝑎̃ + 𝑏𝑥 𝑥̿ + 𝐴2 𝑅̅ 𝐷4 𝑅̅ ̅ + 𝑍 ⋅ 𝜎𝑝̅
𝑝 𝑐̅ + 𝑍√𝑐̅
𝑦 = 𝑎 ⋅ 𝑒 𝑏𝑥 𝑎̃ = 𝑙𝑛(𝑎) 𝑥 𝜓 2 OE
Logarithmisch: 𝑥̃ = 𝑙𝑛(𝑥) 𝑥̿ − 𝐴2 𝑅̅ 𝐷3 𝑅̅ ̅ − 𝑍 ⋅ 𝜎𝑝̅
𝑝
𝑦 = 𝑎 + 𝑏𝑥̃ Newsvendor-Modell UE 𝑐̅ − 𝑍√𝑐̅
𝑦 = 𝑎 + 𝑏 ⋅ 𝑙𝑛(𝑥)
Hyperbolisch:
𝑆 ∗ = 𝜇 + 𝑧𝜎 Standardtabelle für einen Stabilitätsbereich von ±3 σ
1 𝑍(𝑆 ∗ ) = (𝑐𝑢 + 𝑐𝑜 ) ⋅ 𝑓𝑁(0,1) (𝑧) ⋅ 𝜎
𝑏 𝑥̃ = 𝑦 = 𝑎 + 𝑏𝑥̃ A D D
𝑦=𝑎+ 𝑥 n
𝛱(𝑆 ∗ ) = (𝑟 − 𝑐)𝜇 − 𝑍(𝑆 ∗ ) 2 4 3
𝑥 2 1,880 3,268 0
3 1,023 2,574 0
Einfache Exponentielle Glättung
4 0,729 2,282 0
𝑦̂𝑡,𝑡+1 = 𝛼𝑦𝑡 + (1 − 𝛼)𝑦̂𝑡−1,𝑡 5 0,577 2,115 0
Doppelte Exponentielle Glättung Tabelle Standardnormalverteilung
𝑦̂𝑡,𝑡+𝜏 = 𝑎𝑡 + 𝑏𝑡 𝜏 z fN(0,1)(z) FN(0,1)(z) z fN(0,1)(z) FN(0,1)(z) z fN(0,1)(z) FN(0,1)(z) z fN(0,1)(z) FN(0,1)(z)
𝑎𝑡 = 𝛼𝑦𝑡 + (1 − 𝛼)(𝑎𝑡−1 + 𝑏𝑡−1 ) -3,2 0,0024 0,0007 -1,6 0,1109 0,0548 0,0 0,3989 0,5000 1,6 0,1109 0,9452
-3,1 0,0033 0,0010 -1,5 0,1295 0,0668 0,1 0,3970 0,5398 1,7 0,0940 0,9554
𝑏𝑡 = 𝛽(𝑎𝑡 − 𝑎𝑡−1 ) + (1 − 𝛽)𝑏𝑡−1
-3,0 0,0044 0,0013 -1,4 0,1497 0,0808 0,2 0,3910 0,5793 1,8 0,0790 0,9641
Dreifache Exponentielle Glättung -2,9 0,0060 0,0019 -1,3 0,1714 0,0968 0,3 0,3814 0,6179 1,9 0,0656 0,9713
-2,8 0,0079 0,0026 -1,2 0,1942 0,1151 0,4 0,3683 0,6554 2,0 0,0540 0,9772
𝑦̂𝑡,𝑡+𝜏 = (𝑎𝑡 + 𝑏𝑡 𝜏) ⋅ 𝑐𝑡+𝜏−𝑃 -2,7 0,0104 0,0035 -1,1 0,2179 0,1357 0,5 0,3521 0,6915 2,1 0,0440 0,9821
𝑦𝑡 -2,6 0,0136 0,0047 -1,0 0,2420 0,1587 0,6 0,3332 0,7257 2,2 0,0355 0,9861
𝑎𝑡 = 𝛼 + (1 − 𝛼)(𝑎𝑡−1 + 𝑏𝑡−1 ) -2,5 0,0175 0,0062 -0,9 0,2661 0,1841 0,7 0,3123 0,7580 2,3 0,0283 0,9893
𝑐𝑡−𝑃
-2,4 0,0224 0,0082 -0,8 0,2897 0,2119 0,8 0,2897 0,7881 2,4 0,0224 0,9918
𝑏𝑡 = 𝛽(𝑎𝑡 − 𝑎𝑡−1 ) + (1 − 𝛽)𝑏𝑡−1
-2,3 0,0283 0,0107 -0,7 0,3123 0,2420 0,9 0,2661 0,8159 2,5 0,0175 0,9938
𝑦𝑡
𝑐𝑡 = 𝛾 + (1 − 𝛾)𝑐𝑡−𝑃 -2,2 0,0355 0,0139 -0,6 0,3332 0,2743 1,0 0,2420 0,8413 2,6 0,0136 0,9953
𝑎𝑡 -2,1 0,0440 0,0179 -0,5 0,3521 0,3085 1,1 0,2179 0,8643 2,7 0,0104 0,9965
-2,0 0,0540 0,0228 -0,4 0,3683 0,3446 1,2 0,1942 0,8849 2,8 0,0079 0,9974
Tracking Signal -1,9 0,0656 0,0287 -0,3 0,3814 0,3821 1,3 0,1714 0,9032 2,9 0,0060 0,9981
𝑆𝐸𝑡 = 𝜙 ⋅ 𝜀𝑡 + (1 − 𝜙) ⋅ 𝑆𝐸𝑡−1 -1,8 0,0790 0,0359 -0,2 0,3910 0,4207 1,4 0,1497 0,9192 3,0 0,0044 0,9987
-1,7 0,0940 0,0446 -0,1 0,3970 0,4602 1,5 0,1295 0,9332 3,1 0,0033 0,9990
𝑆𝐴𝐸𝑡 = 𝜙 ⋅ |𝜀𝑡 | + (1 − 𝜙) ⋅ 𝑆𝐴𝐸𝑡−1
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