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1 저작자표시 - 비영리 - 변경금지 2.0 대한민국 이용자는아래의조건을따르는경우에한하여자유롭게 이저작물을복제, 배포, 전송, 전시, 공연및방송할수있습니다. 다음과같은조건을따라야합니다 : 저작자표시. 귀하는원저작자를표시하여야합니다. 비영리. 귀하는이저작물을영리목적으로이용할수없습니다. 변경금지. 귀하는이저작물을개작, 변형또는가공할수없습니다. 귀하는, 이저작물의재이용이나배포의경우, 이저작물에적용된이용허락조건을명확하게나타내어야합니다. 저작권자로부터별도의허가를받으면이러한조건들은적용되지않습니다. 저작권법에따른이용자의권리는위의내용에의하여영향을받지않습니다. 이것은이용허락규약 (Legal Code) 을이해하기쉽게요약한것입니다. Disclaimer

2 push-pull Push-Pull boundary optimization problem of special steel industry to improve customer service level

3 (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

4 :,,, JRP, Power-of-Two : ii

5 כ ABC כ כ iii

6 כ iv

7 2.1 [ 1] [ 1] [ 2] [ 2] [ 3] כ (1) [ 3] כ (2) [ 3] כ ( : ) כ ( : ) כ ( : ) v

8 (ISM) ABC g/ v h(t ) g(v; T )/T Power-of-Two policy vi

9 (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

10 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

11 SSM,. SSM push.,,,. כ כ. SSM כ (1), (2), (3). ABC כ % A (921 ) 85% A. כ., [0 +10 mm]., % 20,. כ ( ) 3

12 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

13 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

14 ,. 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

15 , 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

16 JRP joint ,

17 2. כ,. כ כ ISM. 1 ( 2.1). 2,,,.. 2.1: 9

כ (1), (2), (3).. 95.., (drawing). כ ( ) ±0.

18 כ (1), (2), (3) , (drawing). כ ( ) ±0.04mm mm , 32., : 10

19 2.2 ABC. כ כ כ ABC. כ, כ Pareto כ A, B, C., כ 20% A, 30%, 50% B, C ABC 20% %. 2.3 pareto curve, כ. A. 2.3: ABC 11

20 2.3 כ כ (1), (2), (3). ISM,. כ...,.., כ. A [-5 +10mm]. A. 2.4 כ.. 32, 12

21 2.4. HD. SAIP. HD SAIP 18 כ.. 80%, 35%. 2.4:.., כ. 13

22 2.5 כ 2.3. [ mm]... 1 ( ).,., [ 1] כ. SKP 1 SA 2 L)AIP 2.1: [ 1] 14

23 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

24 3 [2 ].,, כ כ. [ 2] 41%, 8%, 0.4%.. SA. 11,., , 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

25 (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

26 11 - (SA) 2.5. A , % 20., כ. 6 כ 3.. A % 18 % 2.5: 1 18

27 3. 2. כ כ (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

28 lost sales כ., כ. lost sales. lot size, כ כ.., כ. כ.. כ 20% %. 20

29 3.3 (v) (T ). 3.1: כ כ.,. 21

30 3.2: כ. lost sales כ., כ. lost sales,,.,. - : 1. - : כ. H כ

31 - :. - :,. - כ :. - H 3 6 כ כ כ, ( 3.3). H 3.,.. 23

32 3.3: ( + ) ( 3.4).. 3.4: 24

33 3.5, כ ,.. c : p :, q :, f : h : 1 α : כ β : כ l : d : כ r : 25

34 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

35 (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

36 3.8 כ 3.4, 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

37 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

38 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

39 T v, 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

40 4.1: g/ v 4.2: h(t ) כ. כ 0 stationary point כ. T v 32

41 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

42 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

43 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

44 4.4: Power-of-Two policy 36

45 5. (enumeration) כ (d) 2 20 כ כ. (r),,,. כ (α) כ (β). 5%. poisson (λ)

46 %, 5% pull., %, כ. 38

47 39 표 5.1:

48 40 표 5.2: _ z q 6 x\ r3 É q& l h ÊÃ < º ( כ é ú A ß 0: ë " ß ) é

49 , 30 4., כ. 표 5.3: 고정 41

50 표 5.4: 고정 비 כ ( : ) 42

51 5.2.3 כ, כ כ. כ. 표 5.5: 경 כ ( : ) 43

52 6. pull.,., כ. כ. A A. B C.. 44

53 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

54 (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

55 [1] W. Alderson. Marketing Efficiency and the Principle of Postponement. Cost and Profit Outlook, [2] Esther Arkin, Dev Joneja, and Robin Roundy. Computational complexity of uncapacitated multi-echelon production planning problems. Operations Research Letters, 8(2):61 66, [3] Anantaram Balakrishnan and Stuart Brown. Process planning for aluminum tubes: An engineering-operations perspective. Operations Research, 44(1):7 20, [4] Anantaram Balakrishnan and Joseph Geunes. Production planning with flexible product specifications: an application to specialty steel manufacturing. Operations Research, 51(1):94 112, [5] Alexander O Brown, Hau L Lee, and Raja Petrakian. Xilinx improves its semiconductor supply chain using product and process postponement. Interfaces, 30(4):65 80, [6] Peter Dapiran. Benetton global logistics in action. International Journal of Physical Distribution & Logistics Management, 22(6):7 11, [7] Brian Denton, Diwakar Gupta, and Keith Jawahir. Managing increasing product variety at integrated steel mills. Interfaces, 33(2):41 53, [8] Amit Eynan and Dean H Kropp. Periodic review and joint replenishment in stochastic demand environments. IIE transactions, 30(11): ,

56 [9] Diwakar Gupta and Saif Benjaafar. Make-to-order, make-to-stock, or delay product differentiation? a common framework for modeling and analysis. IIE transactions, 36(6): , [10] Sung-Pil Hong and Yong-Hyuk Kim. A genetic algorithm for joint replenishment based on the exact inventory cost. Computers & Operations Research, 36(1): , [11] Peter Jackson, William Maxwell, and John Muckstadt. The joint replenishment problem with a powers-of-two restriction. IIE transactions, 17(1):25 32, [12] Fang-Chuan Lee and Ming-Jong Yao. A global optimum search algorithm for the joint replenishment problem under power-of-two policy. Computers & Operations Research, 30(9): , [13] Hau L Lee. Effective inventory and service management through product and process redesign. Operations Research, 44(1): , [14] Hau L Lee and Corey Billington. Designing products and processes for postponement. In Management of Design, pages Springer, [15] Hau L Lee and Christopher S Tang. Modelling the costs and benefits of delayed product differentiation. Management science, 43(1):40 53, [16] Steven Nahmias and Ye Cheng. Production and operations analysis, volume 2. Irwin Homewood, IL, [17] Uday S Rao. Properties of the periodic review (r, t) inventory control policy for stationary, stochastic demand. Manufacturing & Service Operations Management, 5(1):37 53,

57 [18] Robin Roundy. 98%-effective integer-ratio lot-sizing for one-warehouse multi-retailer systems. Management science, 31(11): , [19] Fernando F Suarez, Michael A Cusumano, and Charles H Fine. An empirical study of manufacturing flexibility in printed circuit board assembly. Operations research, 44(1): , [20] Jayashankar M Swaminathan and Sridhar R Tayur. Managing broader product lines through delayed differentiation using vanilla boxes. Management Science, 44(12-part-2):S161 S172, [21] Lixin Tang and Guoli Liu. A mathematical programming model and solution for scheduling production orders in shanghai baoshan iron and steel complex. European Journal of Operational Research, 182(3): , [22] Mark A Vonderembse. Selecting master slab width (s) for continuous steel casting. Journal of Operations Management, 4(3): , [23] Mark A Vonderembse and Robert W Haessler. A mathematical programming approach to schedule master slab casters in the steel industry. Management Science, 28(12): , [24] Walter Zinn. Should you assemble products before an order is received? Business Horizons, 33(2):70 73,

58 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

59 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 :

저작자표시 - 비영리 - 변경금지 2.0 대한민국 이용자는아래의조건을따르는경우에한하여자유롭게 이저작물을복제, 배포, 전송, 전시, 공연및방송할수있습니다. 다음과같은조건을따라야합니다 : 저작자표시. 귀하는원저작자를표시하여야합니다. 비영리. 귀하는이저작물을영리목적으로이용할

저작자표시 - 비영리 - 변경금지 2.0 대한민국 이용자는아래의조건을따르는경우에한하여자유롭게 이저작물을복제, 배포, 전송, 전시, 공연및방송할수있습니다. 다음과같은조건을따라야합니다 : 저작자표시. 귀하는원저작자를표시하여야합니다. 비영리. 귀하는이저작물을영리목적으로이용할수없습니다. 변경금지. 귀하는이저작물을개작, 변형또는가공할수없습니다. 귀하는, 이저작물의재이용이나배포의경우,