1, 2, 4 2, 3, 4 4 2, 3, 4, 10 2, 6, 7, 10 2, 3, 6, 10 3, 4, 8, 10 2, 4, 7, 10 3, 6, 8, 10 5 4, 6, 11, 14, 30 5, 8, 12, 16, 30 4, 6, 11, 16, 30 5, 8, 14, 18, 30 4, 6, 14, 19, 30 5, 8, 16, 18, 30 4, 6, 16 [...] matrices and number of feasible IPs. n W1, . . . , Wn 1 1, 2 1, 2, 3 1, 2, 4 2, 3, 4 4 2, 3, 4, 8 2, 4, 5, 8 3, 4, 6, 8 5 3, 5, 7, 11, 17 6 4, 5, 10, 13, 16, 30 7 5, 17, 21, 25, 31, 37, 55 8 5, 17, 21, 25, 31 [...] number system with base n # 4 matr. # enum. 4 matr. # feas. IPs 1 1 1 1 2 1 1 2 3 3 3 8 4 125 22 46 5 1.2 · 105 372 442 6 3.4 · 109 10.936 6.395 7 4.2 · 1015 479.064 131.711 8 2.4 · 1023 30.846.418 3.658.432 …

2] [,3] # [1,] 1 4 7 # [2,] 2 5 8 # [3,] 3 6 9 class(x) # [1] "matrix" str(x) # int [1:3, 1:3] 1 2 3 4 5 6 7 8 9 mode(x) # [1] "numeric" x[1,2] # Eintrag in Zeile 1 und Spalte 2 # [1] 4 4 x[x > 5] # Einträge [...] Z # Levels: X Y Z Daten[,1] # [1] X Y Z # Levels: X Y Z 5 Fehlende Werte: x <- c(4, NA, 19) # NA: Not Available x # [1] 4 NA 19 x == NA # [1] NA NA NA is.na(x) # [1] FALSE TRUE FALSE Daten einlesen: daten [...] 5 rep(3,5) # 5-maliges Wiederholen der 3 # [1] 3 3 3 3 3 1:5 # ganze Zahlen von 1 bis 5 # [1] 1 2 3 4 5 x <- seq(1,5,2) # jede zweite ganze Zahl von 1 bis 5 x #[1] 1 3 5 length(x) # Wie lang ist x? # [1] …

Bulk-Robust Assignment Problems: Hardness, Approximability and Algorithms

as uniform. a b c d 1 2 3 4 a b c d 1 2 3 4 a b c d 1 2 3 4 a b c d 1 2 3 4 a b c d 1 2 3 4 Figure 4: From left to right: a Card-E-RAP instance with S = { {a, 1}, {d, 3}, {d, 4} } (orange); three scenario [...] Basic Properties 4.2 Deciding Feasibility 4.3 Complexity of V-RAP 4.4 An (lnn + 2)-Approximation for V-RAP 4.5 Complexity of Card-V-RAP 4.6 Constant-Factor Approximation for Card-V-RAP 4.7 Card-V-RAP with [...] nodes a b c 1 2 3 4 5 6 1 2 3 4 5 6 a b c 1 2 3 4 5 6 3 4 6 1 Figure 13: On the left: A non-uniform Card-V-RAP instance with four failure scenarios given by the uncertainty set S = {1, 2, 4, 6} (orange). On …

both derivatives (4.4.1) and (4.4.2) are Fréchet-derivatives if det(Ñg) 2 L¥ (W), jjÑgjjF 2 L¥ (W), jj (Ñg) 1jjF 2 L¥ (W) and # ((Ñg) T)(x) # ((Ñg) T)(x) 2 L¥ (W) (see Theorem 2.4). Symmetry of the second [...] 69E+00 1.00 0.30 - - 1479 TRUE 3 0 4.55E-01 1.16E+02 8.07E-02 0.97 0.36 1 3.27E-05 1446 FALSE 4 0 1.49E-01 2.24E+01 4.22E-03 0.99 0.50 1 1.06E-05 1466 FALSE 5 0 4.09E-02 4.33E+00 9.85E-05 0.99 0.69 1 2.88E-06 [...] useds 1 0 4.35E+00 4.84E-01 2.48E-01 0.98 0.30 1 2.28E-04 22 FALSE 2 0 1.63E+00 1.32E-01 2.00E-01 0.99 0.40 1 6.81E-05 21 FALSE 3 0 5.87E-01 4.24E-02 1.94E-01 1.00 0.55 1 4.28E-05 21 FALSE 4 0 1.66E-01 …

(B)(t) and L̂4(u, t) = m̂(u, t)− r̂4(t) , Û4(u, t) = m̂(u, t) + r̂4(t) where r̂4(t) = √ 2T⌊(1−α)B⌋(t)√ nbn √ m′ n(2⌈nbn⌉ −m′ n) Output: Cn(t) = { f : [0, 1]2 → R | L̂4(u, t) ≤ f(u, t) ≤ Û4(u, t) ∀u ∈ [0 [...] + w1/2n−1/2τ−1/2−4/q′ n + w−1 + τ 2n ) , ∥∥∥ sup u∈[0,γn)∪(1−γn,1] t∈(0,1) |σ̂2(u, t)− σ2(u, t)| ∥∥∥ q′ = O(gn) , where gn = w5/2 n τ−1/q′ n + w1/2n−1/2τ−1/2−4/q′ n + w−1 + τn , (4.4) γn = τn + w/n, q′ [...] n−⌈nbn⌉ )⊤ (4.6) of the vector Z̃σ j in (4.2), where Ẑ σ̂ i,l = Ẑ σ̂ i ( l n ) = (Ẑ σ̂ i,l,1, . . . Ẑ σ̂ i,l,p) ⊤ . Theorem 4.2. Assume that the conditions of Theorem 3.3(ii), Proposition 4.1 and Theorem …

Microsoft Word - IJTTC160305 KOPP_226162

optimisation, waste and error minimisation and cost reductions. 3.3 Industry 4.0 and Logistics 4.0 in need for MST and WPI The Industry 4.0 and technological change in many sectors, such as the logistics sector [...] experiences in Sociotechnical perspectives on digitalisation and Industry 4.0 291 logistics and process industry and in context of Industry 4.0, this article discusses firstly the model of classical STS approach [...] currently coordinating two international projects on work in advanced manufacturing (SBO Paradigms4.0; H2020 Beyond4.0). He is an advisor of the European Commission on the next research programme 2021–2029 Horizon …