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push-pull Push-Pull boundary optimization problem of special steel industry to improve customer service level 2017 8
(Integrated Steel Mill Industry, ISM) (Special Steel Mill Industry, SSM). ISM push-pull SSM pull. SSM. כ כ.,, push-pull. כ כ. Joint Replenishment Problem(JRP), כ.. NP hard JRP כ, 2 כ Power-of-Two policy.. i
:,,, JRP, Power-of-Two : 2015 21157 ii
1 1 1.1..................... 1 1.2............................. 5 1.3............................. 8 2 כ 9 2.1....................... 9 2.2 ABC............................. 11 2.3............................. 12 2.4.......................... 12 2.5...................... 14 3 19 3.1 כ................................ 19 3.2................................ 19 3.3............................. 21 3.4............................. 21 3.4.1................ 21 3.4.2................ 22 3.4.3...................... 23 3.4.4......................... 24 3.5 כ................................ 25 3.6................................ 25 iii
3.7....................... 26 3.8...................... 28 3.9...................... 29 4 31 4.1............. 31 4.2 כ............................. 32 4.3............................. 34 5 37 5.1............................. 37 5.2................................ 38 5.2.1............... 38 5.2.2.................. 41 5.2.3............ 43 6 44 7 45 47 50 iv
2.1 [ 1].......................... 14 2.2 [ 1].......................... 15 2.3 [ 2].......................... 15 2.4 [ 2].......................... 15 2.5 [ 3].......................... 17 2.6 כ (1) [ 3]................... 17 2.7 כ (2) [ 3]................... 17 5.1............... 39 5.2 כ ( : ).......... 40 5.3................... 41 5.4 כ ( : )............. 42 5.5 כ ( : )...... 43 v
1.1......................... 1 1.2 (ISM).................... 2 2.1..................... 9 2.2.................... 10 2.3 ABC.......................... 11 2.4.................... 13 2.5 1.................. 18 3.1 1.................. 21 3.2 1.................. 22 3.3................. 24 3.4................. 24 4.1 g/ v........................... 32 4.2 h(t )............................ 32 4.3 g(v; T )/T......................... 34 4.4 Power-of-Two policy.............. 36 vi
1. 1.1 (Integrated Steel Mill Industry, ISM) (Special Steel Mill Industry). ISM push-pull SSM pull. (Post-ponement Strategy) (Alderson, 1950) כ. 1.1 כ (push), כ כ (pull). 1.1: (risk pooling) (customer lead time) (Lee and Tang, 1997; Denton et al., 2003). ISM 1
כ. ISM (slab)., כ כ כ ( 1.2). כ (reheat) (Denton et al., 2003). ISM (Balakrishnan and Geunes, 2003), (Vonderembse, 1984; Balakrishnan and Brown, 1996) (Vonderembse and Haessler, 1982). 1.2: (ISM) 2
SSM,. SSM push.,,,. כ כ. SSM כ (1), (2), (3). ABC כ. 4600 20% A (921 ) 85% A. כ., [0 +10 mm].,.. 122 20% 20,. כ ( ) 3
כ. כ. כ כ,. Joint Replenishment Problem(JRP) NP hard (Arkin et al., 1989). כ כ JRP כ. (Jackson et al., 1985) כ (Eynan and Kropp, 1998). JRP Economic Order Quantity(EOQ), EOQ insensitivity כ, כ. כ.,. T v., v (n) T n v n., n T n כ, T n insensitivity 4
כ. T n Power-of-Two policy JRP כ כ 2 כ (Jackson et al., 1985). (suboptimal). כ 2 כ כ. 1.2 Alerson (1950). כ. Zinn (1990) כ כ., כ כ כ. Dapiran (1992) Benetton. Benetton כ, כ. Benetton, כ. (1), (2), (3), (4). Swaminathan and Tayur (1998). 5
,. IBM. (Brown et al., 2000). (Lee and Billington, 1994).. Denton et al. (2003) Balakrishnan and Geunes (2003) ISM.,.., (i) (j). ISM ISM ( ) (Vonderembse, 1984; Balakrishnan and Brown, 1996)..,, כ.,., כ ( ).. JRP. Arkin et al. (1989) JRP NP hard 6
, כ, כ. JRP EOQ EOQ כ sensitivity, JRP. Jackson et al. (1985) Power-of-Two Policy. כ. joint (i) (T i ). T i כ T i 2 כ. Eynan and Kropp (1998) כ (i) (Q i ) (T i )., כ. כ. Rao (2003) Eynan and Kropp (1998) כ,.. JRP. JRP. כ כ כ. joint 7
JRP joint. 1.3. 2. 3, 4 3. 5 6. 8
2. כ,. כ כ. 2.1. ISM. 1 ( 2.1). 2,,,.. 2.1: 9
כ (1), (2), (3).. 95.., (drawing). כ ( ) ±0.04mm. 2 55 mm. 2.2 8., 32., 2 4600. 2.2: 10
2.2 ABC. כ כ כ ABC. כ, כ Pareto כ A, B, C., כ 20% A, 30%, 50% B, C. 4600 ABC 20% 921 85%. 2.3 pareto curve, כ. A. 2.3: ABC 11
2.3 כ כ (1), (2), (3). ISM,. כ...,.., כ. A [-5 +10mm]. A. 2.4 כ.. 32, 12
2.4. HD. SAIP. HD SAIP 18 כ.. 80%, 35%. 2.4:.., כ. 13
2.5 כ 2.3. [-5 +10 mm]... 1 ( ).,.,. 2.1 2.2 [ 1] כ. SKP 1 SA 2 L)AIP 2.1: [ 1] 14
SKP 1 SA 2 L)AIP 2.2: [ 1] 2 [1 ]. ( ),.,. Spheroidized Annealing (SA), Low Temperature Annealing (LA), Regular Annealing (RA).. (RA) (SA) 1 RAPC 2 SAPC 2.3: [ 2] (RA) (SA) 1 RAPC 2 SAPC 2.4: [ 2] 15
3 [2 ].,, כ כ. [ 2] 41%, 8%, 0.4%.. SA. 11,.,. 2.5 1 2 - -, 1, 2, 3 -.,. כ (1) 1, 2 A, 1, 2, 3 B. A 10 % 3 A 3 B. כ (2). A 20%, 3 10%. A 3 A. 2.5 כ 2.6 2.7. 16
(SA) SKP כ (1) כ (2) 1 S)AIP 5% 5% 2 PSALAF 5% 15 % 3 PSASAIP 20% 10 % 2.5: [ 3] (SA) SKP 1 S)AIP 1 PSALAF 1 PSASAIP 2.6: כ (1) [ 3] (SA) SKP 1 S)AIP 1 PSALAF 2 PSASAIP 2.7: כ (2) [ 3] 17
11 - (SA) 2.5. A 11 122, 122. 20% 20., כ. 6 כ 3.. A 4600 921 424 162 20 % 18 % 2.5: 1 18
3. 2. כ כ.. 3.1 1 20 (v) (T )., כ (1), (2), (3), (4). lost sales,. 3.2 כ. כ כ כ, כ. כ כ. כ כ,. כ כ כ poisson arrival. 19
lost sales כ., כ. lost sales. lot size, כ כ.., כ. כ.. כ 20%. 20 20%. 20
3.3 (v) (T ). 3.1: 1 3.4 3.4.1 כ כ.,. 21
3.2: 1 3.4.2 כ. lost sales כ., כ. lost sales,,.,. - : 1. - : כ. H כ 1. 1. 22
- :. - :,. - כ :. - H 3 6 כ.. 3.4.3. כ כ, ( 3.3). H 3.,.. 23
3.3: 3.4.4... ( + ) ( 3.4).. 3.4: 24
3.5, כ... 3.6.,.. c : p :, q :, f : h : 1 α : כ β : כ l : d : כ r : 25
λ : v : T : 3.7 כ. } - min v,t {g(v, T )/T g(v, T ), g(v, T ) (1) (8). g(v, T ) (1) cv : T (λt) k e λt (2) cr (v kd) + dt 0 k! : T (λt ) k e λt (3) pα (v (v kd) + ) k! : T (λt ) k e λt (4) c (v kd) + k! : T 26
(λt ) k e λt (5) qβ (kd v + (v kd) + ) 1 k! : T (λt ) k e λt (6) l(β α) (kd v + (v kd) + ) k! : T כ (7) f (λt ) k e λt kd v + (v kd)+ ( ) k! h כ : (8) f : 1 kd v + (v dk) + = (kd v) + 27
3.8 כ 3.4,. 3.8.1 min v,t g(v, T )/T sub.to v 0, T 0 T, g(v, T ) = cv + cr 0 +pα c (λt) k e λt (v kd) + dt k! (λt ) k e λt (v (v kd) + ) k! (λt ) k e λt (v kd) + k! +(qβ + l(β α)) +f (λt ) k e λt (kd v + (v kd) + ) k! (λt ) k e λt kd v + (v kd)+ ( ) + f k! h 28
3.9 כ 3.3. n :, n = 1,, N j :, j = 1,, J d n : n כ w j : j v n : n T n : n (n),.. 29
3.9.1 min vn,t n sub.to N n=1 N n=1 v 0, T 0 g(v n, T n ) T n lcm(t 1, T 2,, T n ) T n v n lcm(t 1, T 2,, T n ) T n w j, j n n T, g(v n, T n )/T n = cv n + cr 0 +pα c (λt) k e λt (v n kd n ) + dt k! (λt ) k e λt (v n (v n kd n ) + ) k! (λt ) k e λt (v n kd n ) + k! +(qβ + l(β α)) +f (λt ) k e λt k! (λt ) k e λt (kd n v n + (v n kd n ) + ) k! ( kd n v n + (v n kd n ) + ) + f h 30
4. 3 3.8.1 T v, 3.9.1. 3.9.1. 4.1 כ. (v, T ),. { g(v,t ) min v,t T = min T g(v;t ) inf v T, T (1 T M) min v } g(v; T )/T T (h(t )). h(t ) T. T (1 T M) v g(v; T )/T.,. 4.1 T g(v; T )/T v כ,. כ v כ, כ. 4.2 T g(v; T )/T כ. T g(v; T )/T v... 31
4.1: g/ v 4.2: h(t ) 4.2 3. 4.1 כ. כ 0 stationary point כ. T v 32
כ d stationary point. T (1 T M) g(v; T )/T v v כ.? כ (n) v n T n כ. JRP. JRP. EOQ. JRP NP hard (Arkin et al., 1989).,. T n כ, T n כ. T n כ JRP, Power-of-Two policy. Power-of-Two Policy Jackson et al., (1985), T n 2 כ כ, 6% כ. 2% (Roundy, 1985). T n כ JRP EOQ. EOQ senstivitiy. כ כ. EOQ. 33
sensitivity. 4.3 T כ v כ כ g(v; T )/T. 4.3: g(v; T )/T sensitivity. Tn T n, כ., Tn T n Power-of-Two Policy. 4.3 T 1, T 2,, T n כ, N g(v n,t n) T n v 1, v 2,, v n. n=1 v.. 34
g(v 1. n = 1, 2,, N min n,t n) vn T n Tn. 2. T n 2 ρn ρ n. 3. T n = 2 ρn, n v 1, v 2,, v N. Tn כ v n T n כ. EOQ sensitivity. JRP NP hard, subgradient. senstivity כ כ כ כ. 4.4 Power-of-Two policy.. 35
4.4: Power-of-Two policy 36
5. (enumeration).. 5.1. כ (d) 2 20 כ כ. (r),,,. כ (α) כ (β). 5%. poisson (λ) 20. 37
5.2.. 5.2.1 0%, 5%. 100. pull.,. 10 30%, כ. 38
39 표 5.1:
40 표 5.2: _ z q 6 x\ r3 É q& l h ÊÃ < º ( כ é ú A ß 0: ë " ß ) é
5.2.2.. 20 114, 30 4., כ. 표 5.3: 고정 41
표 5.4: 고정 비 כ ( : ) 42
5.2.3 כ, כ כ. כ. 표 5.5: 경 כ ( : ) 43
6. pull.,., כ. כ. A A. B C.. 44
7. T g(v; T )/T v. g(v; T )/T v, 1., T g(v; T ) כ.,. g(v, T )/T = { 1 T 0 (c + pα qβ l(β α) f d )v + cr T (λt) k e λt (v kd) + dt k! +( pα + qβ + l(β α) c + f d ) (λt ) k e λt (v kd) + k! } +(qβ + l(β α) + f d ) (λt ) k e λt (dk) + f. k! i) f 1 (v) = (c + pα qβ l(β α) f d )v, f 1(v) v 1. (λt) k e λt ii) f 2 (v) = w 1 (v kd) +, v 1, v 2 domf 2 (v), µ : 0 k! µ 1. (, w 1 = ( c pα + qβ + l(β α) + f d )) (λt) k e λt w 1 (µv 1 + (1 µ)v 2 kd) + k! (λt) k e λt = w 1 (µ(v 1 kd) + (1 µ)(v 2 kd)) + k! 45
(λt) k e λt w 1 (µ(v 1 kd) + + (1 µ)(v 2 kd) + ) k! (λt) k e λt = w 1 µ (v 1 kd) + (λt) k e λt + w 1 (1 µ) (v 2 kd) +. k! k! f 2 (v). T (λt) k e λt iii) f 3 (v) = cr (v kd) + dt, v 1, v 2 domf 3 (v), ν : 0 k! 0 ν 1. T (λt) k e λt cr (νv 1 + (1 ν)v 2 kd) + dt 0 k! T (λt) k e λt = cr (ν(v 1 kd) + (1 ν)(v 2 kd)) + dt 0 k! T (λt) k e λt cr (ν(v 1 kd) + + (1 ν)(v 2 kd) + )dt 0 k! T (λt) k e λt T = crν (v 1 kd) + (λt) k e λt dt+cr(1 ν) (v 2 kd) + dt. 0 k! 0 k! f 3 (v).,, T g(v; T )/T v. 46
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ABSTRACT Hyeon-Ji Hwang Department of Industrial Engineering The Graduate School Seoul National University The steel industry is divided into the Integrated Steel Mill Industry(ISM) and Special Steel Mill Industry(SSM). ISM is easy to apply push-pull hybrid strategy, whereas forr the SSM only the Pull strategy has been considered. In this paper, we consider pushpull boundary optimization problem to reduce costs and improve customer service level. As a representative hybrid strategy, the delayed differentiation strategy is based on inventory of common semi-finished products. It means that if the actual demand arrives, it will be supplied through the remaining processes. In this study, first, we derived semi-finished products through the analysis of product, raw material, product processes, and define the problem of inventory management of semi-finished products to achieve push-pull border optimization. Specifically, the problem of semi-finished goods inventory management is deciding target inventory and the replenishment cycle. This problem is similar with the Joint Replenishment Problem (JRP), where both problems are finding multiple cycle makes the problem difficult. Therefore, Solve problems through heuristics. 50
JRP, known as NP hard, fixes the problem by fixing the period to a constant value. In this model, similarly, the period is fixed by multiplier of 2, power-of-two policy. Introduction of semi-finished products through experiments, the cost was reduced compared to before. Keywords : Postponement strategy, Special steel industry, production planning problem, JRP Student number : 2015-21157 51