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An inventory model with imperfect item, inspection errors, preventive maintenance and partial backlogging in uncertainty environment
Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy
1. | Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, India |
2. | Faculty of Engineering Management, Chair of Marketing and Economic Engineering, Poznan University of Technology, Ul. Strzelecka 11, 60-965 Poznan, Poland |
This article is concerned with a multi-item inventory model for deteriorating items. The model is formed on the basis of a two-level supply chain policy, i.e., based on manufacturer's and retailer's perspective. The deterioration rate is considered as constant. The demand factor of any items suffer from a large amount of stock level; so, we consider stock-dependent demand function. The demand of any item is also dependent on its selling price; thus, a price-dependent demand function is introduced here. The retailer adopts the trade-credit policy for his customers in order to promote market competitiveness. He can earn revenue and interest after the customer pays the amount of purchasing cost to the retailer until the end of the trade-credit period, offered by the supplier. Shortages are allowed in the retailer's model as it is a very realistic item, too. A price discount on backordered commodities is offered for those customers who are willing to backorder their demand. Thereafter, we present an easy analytical solution procedure to find the total profit for both manufacturer and retailer. We also use the classical game theory and Nash equilibrium approach to find an optimal solution of the joint profit. The results are discussed with several numerical examples to illustrate our model and to provide some managerial insights related to the model. Furthermore, a parametric sensitivity analysis of the optimal solutions is provided and a concavity figure of our profit function is supplied to stabilize our model. The paper ends with a conclusion and an outlook to future research projects.
References:
[1] |
S. P. Aggarwal and C. K. Jaggi,
Ordering policies of deteriorating items under permissible delay in payments, The Journal of the Operational Research Society, 46 (1995), 658-662.
|
[2] |
M. Ben-daya and A. Raouf,
On the constrained multi-item single period inventory problem, International Journal of Production Management, 13 (1993), 104-112.
doi: 10.1108/01443579310046472. |
[3] |
L. Benkherouf and M. Omar,
Optimal integrated policies for a single-vendor single-buyer time-varying demand model, Computers and Mathematics with Applications, 60 (2010), 2066-2077.
doi: 10.1016/j.camwa.2010.07.047. |
[4] |
D. K. Bhattacharya,
Production, manufacturing and logistics on multi-item inventory, European Journal of Operational Research, 162 (2005), 786-791.
doi: 10.1016/j.ejor.2003.02.004. |
[5] |
J. Chen and P. C. Bell,
Coordinating a decentralized supply chain with customer returns and price-dependent stochastic demand using a buyback policy, European Journal of Operational Research, 212 (2011), 293-300.
doi: 10.1016/j.ejor.2011.01.036. |
[6] |
V. Choudri, M. Venkatachalam and S. Panayappan,
Production inventory model with deteriorating items, two rates of production cost and taking account of time value of money, Journal of Industrial and Management Optimization, 12 (2016), 1153-1172.
doi: 10.3934/jimo.2016.12.1153. |
[7] |
T. K. Datta and K. Paul,
An inventory system with stock-dependent, price-sensitive demand rate, Production Planning and Control, 12 (2001), 13-20.
doi: 10.1080/09537280150203933. |
[8] |
P. M. Ghare and G. P. Schrader,
A model for an exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243.
|
[9] |
A. Goswami and K. S. Chaudhuri,
An EOQ model for deteriorating items with shortages and a linear trend in demand, Journal of the Operational Research Society, 42 (1991), 1105-1110.
|
[10] |
S. K. Goyal,
Economic order quantity under conditions of permissible delay in payments, Journal of Operational Research Society, 36 (1985), 335-338.
|
[11] |
S. Kar, T. Roy and M. Maiti,
Multi-item inventory model with probabilistic price dependent damand and imprecise goal and constraints, Yugoslav Journal of Operations Research, 11 (2001), 93-103.
|
[12] |
N. A. Kurdhi, J. Prasetyo and S. S. Handajani,
An inventory model involving back-order price discount when the amount received is uncertain, International Journal of Systems Science, 47 (2016), 662-671.
doi: 10.1080/00207721.2014.900136. |
[13] |
R. I. Levin, C. P. McLaughlin, R. P. Lamone and J. F. Kottas,
Productions Operations Management: Contemporary Policy for Managing Operating System, McGraw-Hill Series in Management, New York, 1972. |
[14] |
T. Y. Lin, M. T. Chen and K. L. Hou,
An inventory model for items with imperfect quality and quantity discounts under adjusted screening rate and earned interest, Journal of Industrial and Management Optimization, 12 (2016), 1333-1347.
doi: 10.3934/jimo.2016.12.1333. |
[15] |
M. Mohammadzadeh, A. A. Khamseh and M. Mohammadi,
A multi-objective integrated model for closed-loop supply chain configuration and supplier selection considering uncertain demand and different performance levels, Journal of Industrial and Management Optimization, 13 (2017), 1041-1064.
doi: 10.3934/jimo.2016061. |
[16] |
L. Y. Ouyang, B. R. Chuang and Y. J. Lin,
Impact of backorder discounts on periodic review inventory model, International Journal of Information and Management Sciences, 14 (2003), 1-13.
|
[17] |
S. Pal, G. S. Mahapatra and G. P. Samanta,
An inventory model of price and stock dependent demand rate with deterioration under inflation and delay in payment, International Journal of System Assurance Engineering and Management, 5 (2014), 591-601.
doi: 10.1007/s13198-013-0209-y. |
[18] |
M. Pervin, G. C. Mahata and S. K. Roy,
An inventory model with demand declining market for deteriorating items under trade credit policy, International Journal of Management Science and Engineering Management, 11 (2016), 243-251.
doi: 10.1080/17509653.2015.1081082. |
[19] |
M. Pervin, S. K. Roy and G. W. Weber,
Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 260 (2018), 437-460.
doi: 10.1007/s10479-016-2355-5. |
[20] |
M. Pervin, S. K. Roy and G. W. Weber,
A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items, Numerical Algebra, Control and Optimization, 7 (2017), 21-50.
doi: 10.3934/naco.2017002. |
[21] |
M. Pervin, S. K. Roy and G. W. Weber,
An integrated inventory model with variable holding cost under two levels of trade-credit policy, Numerical Algebra, Control and Optimization, 8 (2018), 169-191.
|
[22] |
M. J. Rosenblatt,
Multi-item inventory system with budgetary constraint: A comparison between the Lagrangian and fixed cycle approach, International Journal of Production Research, 19 (1981), 331-339.
doi: 10.1080/00207548108956661. |
[23] |
B. Sarkar, B. Mandal and S. Sarkar,
Quality improvement and backorder price discount under controllable lead time in an inventory model, Journal of Manufacturing Systems, 35 (2015), 26-36.
doi: 10.1016/j.jmsy.2014.11.012. |
[24] |
B. Sarkar, B. Mandal and S. Sarkar,
Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages, Journal of Industrial and Management Optimization, 13 (2017), 187-206.
doi: 10.3934/jimo.2016011. |
[25] |
B. Sarkar, A. Majumder, M. Sarkar, B. K. Dey and G. Roy,
Two-echelon supply chain model with manufacturing quality improvement and setup cost reduction, Journal of Industrial and Management Optimization, 13 (2017), 1085-1104.
doi: 10.3934/jimo.2016063. |
[26] |
J. T. Teng and C. T. Chang,
Economic production quantity models for deteriorating items with price- and stock-dependent demand, Computers and Operations Research, 32 (2005), 297-308.
doi: 10.1016/S0305-0548(03)00237-5. |
[27] |
A. Thangam and R. Uthayakumar,
Two echelon trade credits financing for perishable items in a supply chain when demands on both selling price and credit period, Computers and Industrial Engineering, 57 (2009), 773-786.
doi: 10.1016/j.cie.2009.02.005. |
[28] |
Y. C. Tsao,
Ordering policy for non-instantaneously deteriorating products under price adjustment and trade credits, Journal of Industrial and Management Optimization, 13 (2017), 327-345.
doi: 10.3934/jimo.2016020. |
[29] |
Q. Wang and M. Parlar,
A three-person game theory model arising in stochastic inventory control theory, European Journal of Operational Research, 76 (1994), 83-97.
doi: 10.1016/0377-2217(94)90008-6. |
[30] |
J. Wu, L. Y. Ouyang, L. E. Cárdenas-Barrón and S. K. Goyal,
Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing, European Journal of Operational Research, 237 (2014), 898-908.
doi: 10.1016/j.ejor.2014.03.009. |
show all references
References:
[1] |
S. P. Aggarwal and C. K. Jaggi,
Ordering policies of deteriorating items under permissible delay in payments, The Journal of the Operational Research Society, 46 (1995), 658-662.
|
[2] |
M. Ben-daya and A. Raouf,
On the constrained multi-item single period inventory problem, International Journal of Production Management, 13 (1993), 104-112.
doi: 10.1108/01443579310046472. |
[3] |
L. Benkherouf and M. Omar,
Optimal integrated policies for a single-vendor single-buyer time-varying demand model, Computers and Mathematics with Applications, 60 (2010), 2066-2077.
doi: 10.1016/j.camwa.2010.07.047. |
[4] |
D. K. Bhattacharya,
Production, manufacturing and logistics on multi-item inventory, European Journal of Operational Research, 162 (2005), 786-791.
doi: 10.1016/j.ejor.2003.02.004. |
[5] |
J. Chen and P. C. Bell,
Coordinating a decentralized supply chain with customer returns and price-dependent stochastic demand using a buyback policy, European Journal of Operational Research, 212 (2011), 293-300.
doi: 10.1016/j.ejor.2011.01.036. |
[6] |
V. Choudri, M. Venkatachalam and S. Panayappan,
Production inventory model with deteriorating items, two rates of production cost and taking account of time value of money, Journal of Industrial and Management Optimization, 12 (2016), 1153-1172.
doi: 10.3934/jimo.2016.12.1153. |
[7] |
T. K. Datta and K. Paul,
An inventory system with stock-dependent, price-sensitive demand rate, Production Planning and Control, 12 (2001), 13-20.
doi: 10.1080/09537280150203933. |
[8] |
P. M. Ghare and G. P. Schrader,
A model for an exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243.
|
[9] |
A. Goswami and K. S. Chaudhuri,
An EOQ model for deteriorating items with shortages and a linear trend in demand, Journal of the Operational Research Society, 42 (1991), 1105-1110.
|
[10] |
S. K. Goyal,
Economic order quantity under conditions of permissible delay in payments, Journal of Operational Research Society, 36 (1985), 335-338.
|
[11] |
S. Kar, T. Roy and M. Maiti,
Multi-item inventory model with probabilistic price dependent damand and imprecise goal and constraints, Yugoslav Journal of Operations Research, 11 (2001), 93-103.
|
[12] |
N. A. Kurdhi, J. Prasetyo and S. S. Handajani,
An inventory model involving back-order price discount when the amount received is uncertain, International Journal of Systems Science, 47 (2016), 662-671.
doi: 10.1080/00207721.2014.900136. |
[13] |
R. I. Levin, C. P. McLaughlin, R. P. Lamone and J. F. Kottas,
Productions Operations Management: Contemporary Policy for Managing Operating System, McGraw-Hill Series in Management, New York, 1972. |
[14] |
T. Y. Lin, M. T. Chen and K. L. Hou,
An inventory model for items with imperfect quality and quantity discounts under adjusted screening rate and earned interest, Journal of Industrial and Management Optimization, 12 (2016), 1333-1347.
doi: 10.3934/jimo.2016.12.1333. |
[15] |
M. Mohammadzadeh, A. A. Khamseh and M. Mohammadi,
A multi-objective integrated model for closed-loop supply chain configuration and supplier selection considering uncertain demand and different performance levels, Journal of Industrial and Management Optimization, 13 (2017), 1041-1064.
doi: 10.3934/jimo.2016061. |
[16] |
L. Y. Ouyang, B. R. Chuang and Y. J. Lin,
Impact of backorder discounts on periodic review inventory model, International Journal of Information and Management Sciences, 14 (2003), 1-13.
|
[17] |
S. Pal, G. S. Mahapatra and G. P. Samanta,
An inventory model of price and stock dependent demand rate with deterioration under inflation and delay in payment, International Journal of System Assurance Engineering and Management, 5 (2014), 591-601.
doi: 10.1007/s13198-013-0209-y. |
[18] |
M. Pervin, G. C. Mahata and S. K. Roy,
An inventory model with demand declining market for deteriorating items under trade credit policy, International Journal of Management Science and Engineering Management, 11 (2016), 243-251.
doi: 10.1080/17509653.2015.1081082. |
[19] |
M. Pervin, S. K. Roy and G. W. Weber,
Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 260 (2018), 437-460.
doi: 10.1007/s10479-016-2355-5. |
[20] |
M. Pervin, S. K. Roy and G. W. Weber,
A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items, Numerical Algebra, Control and Optimization, 7 (2017), 21-50.
doi: 10.3934/naco.2017002. |
[21] |
M. Pervin, S. K. Roy and G. W. Weber,
An integrated inventory model with variable holding cost under two levels of trade-credit policy, Numerical Algebra, Control and Optimization, 8 (2018), 169-191.
|
[22] |
M. J. Rosenblatt,
Multi-item inventory system with budgetary constraint: A comparison between the Lagrangian and fixed cycle approach, International Journal of Production Research, 19 (1981), 331-339.
doi: 10.1080/00207548108956661. |
[23] |
B. Sarkar, B. Mandal and S. Sarkar,
Quality improvement and backorder price discount under controllable lead time in an inventory model, Journal of Manufacturing Systems, 35 (2015), 26-36.
doi: 10.1016/j.jmsy.2014.11.012. |
[24] |
B. Sarkar, B. Mandal and S. Sarkar,
Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages, Journal of Industrial and Management Optimization, 13 (2017), 187-206.
doi: 10.3934/jimo.2016011. |
[25] |
B. Sarkar, A. Majumder, M. Sarkar, B. K. Dey and G. Roy,
Two-echelon supply chain model with manufacturing quality improvement and setup cost reduction, Journal of Industrial and Management Optimization, 13 (2017), 1085-1104.
doi: 10.3934/jimo.2016063. |
[26] |
J. T. Teng and C. T. Chang,
Economic production quantity models for deteriorating items with price- and stock-dependent demand, Computers and Operations Research, 32 (2005), 297-308.
doi: 10.1016/S0305-0548(03)00237-5. |
[27] |
A. Thangam and R. Uthayakumar,
Two echelon trade credits financing for perishable items in a supply chain when demands on both selling price and credit period, Computers and Industrial Engineering, 57 (2009), 773-786.
doi: 10.1016/j.cie.2009.02.005. |
[28] |
Y. C. Tsao,
Ordering policy for non-instantaneously deteriorating products under price adjustment and trade credits, Journal of Industrial and Management Optimization, 13 (2017), 327-345.
doi: 10.3934/jimo.2016020. |
[29] |
Q. Wang and M. Parlar,
A three-person game theory model arising in stochastic inventory control theory, European Journal of Operational Research, 76 (1994), 83-97.
doi: 10.1016/0377-2217(94)90008-6. |
[30] |
J. Wu, L. Y. Ouyang, L. E. Cárdenas-Barrón and S. K. Goyal,
Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing, European Journal of Operational Research, 237 (2014), 898-908.
doi: 10.1016/j.ejor.2014.03.009. |




Authors | Multi items | Two-echelon model | Stock- and Price- dependent demand | Deterio- rations | Trade-credit policy | Price discount on backorders |
Lenard and Roy (1995) | √ | |||||
Kar et al. (2001) | √ | √ | ||||
Ben-daya and Raouf (1993) | √ | |||||
Chen and Bell (2011) | √ | |||||
Datta and Paul (2001) | √ | |||||
Pal et al. (2014) | √ | √ | ||||
Teng and Chang (2005) | √ | √ | ||||
Thangam and Uthayakumar (2009) | √ | √ | √ | |||
Pervin et al. (2016) | √ | √ | √ | |||
Goswami and Chaudhuri (1991) | √ | √ | ||||
Wu et al. (2014) | √ | √ | ||||
Sarkar et al. (2017) | √ | √ | ||||
Pervin et al. (2017) | √ | √ | ||||
Ouyang et al. (2015) | √ | |||||
This paper | √ | √ | √ | √ | √ | √ |
Authors | Multi items | Two-echelon model | Stock- and Price- dependent demand | Deterio- rations | Trade-credit policy | Price discount on backorders |
Lenard and Roy (1995) | √ | |||||
Kar et al. (2001) | √ | √ | ||||
Ben-daya and Raouf (1993) | √ | |||||
Chen and Bell (2011) | √ | |||||
Datta and Paul (2001) | √ | |||||
Pal et al. (2014) | √ | √ | ||||
Teng and Chang (2005) | √ | √ | ||||
Thangam and Uthayakumar (2009) | √ | √ | √ | |||
Pervin et al. (2016) | √ | √ | √ | |||
Goswami and Chaudhuri (1991) | √ | √ | ||||
Wu et al. (2014) | √ | √ | ||||
Sarkar et al. (2017) | √ | √ | ||||
Pervin et al. (2017) | √ | √ | ||||
Ouyang et al. (2015) | √ | |||||
This paper | √ | √ | √ | √ | √ | √ |
Parameters | i=1 | i=2 | i=3 | Joint effects of all 3 items |
|
30 | 35 | 40 | 105 |
|
10 | 15 | 20 | 45 |
|
500 | 600 | 700 | 1800 |
|
0.05 | 0.07 | 0.09 | 0.21 |
|
10 | 14 | 18 | 42 |
|
5 | 10 | 15 | 30 |
|
0.12 | 0.18 | 0.23 | 0.53 |
|
0.20 | 0.25 | 0.30 | 0.75 |
|
0.50 | 0.55 | 0.60 | 1.65 |
|
0.30 | 0.35 | 0.40 | 1.05 |
|
0.7 | 0.8 | 0.9 | 2.4 |
|
0.2 | 0.3 | 0.4 | 0.9 |
|
0.5 | 0.6 | 0.7 | 1.8 |
|
0.4 | 0.6 | 0.8 | 1.8 |
|
1.2 | 1.6 | 2.0 | 4.8 |
|
0.8 | 1.0 | 1.2 | 3.0 |
|
0.5 | 0.7 | 0.9 | 2.1 |
|
10.62 | 17.55 | 29.37 | 32.76 |
|
9.20 | 15.72 | 22.18 | 29.18 |
|
15.11 | 19.83 | 26.07 | 36.30 |
|
13.57 | 22.15 | 34.49 | 35.02 |
|
26.6214 | 42.1753 | 63.8068 | 91.4128 |
|
95.1506 | 117.3394 | 182.7139 | 220.6210 |
|
165.3726 | 199.5379 | 274.2680 | 326.1660 |
Parameters | i=1 | i=2 | i=3 | Joint effects of all 3 items |
|
30 | 35 | 40 | 105 |
|
10 | 15 | 20 | 45 |
|
500 | 600 | 700 | 1800 |
|
0.05 | 0.07 | 0.09 | 0.21 |
|
10 | 14 | 18 | 42 |
|
5 | 10 | 15 | 30 |
|
0.12 | 0.18 | 0.23 | 0.53 |
|
0.20 | 0.25 | 0.30 | 0.75 |
|
0.50 | 0.55 | 0.60 | 1.65 |
|
0.30 | 0.35 | 0.40 | 1.05 |
|
0.7 | 0.8 | 0.9 | 2.4 |
|
0.2 | 0.3 | 0.4 | 0.9 |
|
0.5 | 0.6 | 0.7 | 1.8 |
|
0.4 | 0.6 | 0.8 | 1.8 |
|
1.2 | 1.6 | 2.0 | 4.8 |
|
0.8 | 1.0 | 1.2 | 3.0 |
|
0.5 | 0.7 | 0.9 | 2.1 |
|
10.62 | 17.55 | 29.37 | 32.76 |
|
9.20 | 15.72 | 22.18 | 29.18 |
|
15.11 | 19.83 | 26.07 | 36.30 |
|
13.57 | 22.15 | 34.49 | 35.02 |
|
26.6214 | 42.1753 | 63.8068 | 91.4128 |
|
95.1506 | 117.3394 | 182.7139 | 220.6210 |
|
165.3726 | 199.5379 | 274.2680 | 326.1660 |
Parameter | ||||||
|
0.035 | 0.04 | 0.045 | 0.055 | 0.06 | 0.065 |
|
28.6725 | 28.4218 | 28.2240 | 27.9031 | 27.7633 | 27.5502 |
|
96.1162 | 95.9631 | 95.8812 | 95.7243 | 95.5708 | 95.3276 |
|
166.502 | 166.372 | 166.127 | 165.872 | 165.609 | 165.421 |
|
0.049 | 0.056 | 0.063 | 0.077 | 0.084 | 0.091 |
|
43.3213 | 43.1045 | 42.8871 | 42.7490 | 42.5289 | 42.3407 |
|
118.6731 | 118.4830 | 118.2571 | 117.9013 | 117.7856 | 117.5126 |
|
199.410 | 199.107 | 198.884 | 198.619 | 198.470 | 198.159 |
|
0.063 | 0.072 | 0.081 | 0.099 | 0.108 | 0.117 |
|
65.1173 | 64.8243 | 64.5740 | 64.2581 | 63.8056 | 63.5731 |
|
183.9920 | 183.7526 | 183.4911 | 183.2354 | 182.8744 | 182.8530 |
|
273.576 | 273.291 | 272.876 | 272.651 | 272.304 | 272.118 |
|
324.13 | 307.47 | 299.53 | 271.84 | 256.77 | 231.64 |
|
573.38 | 529.13 | 478.46 | 431.47 | 390.52 | 358.30 |
|
642.10 | 618.34 | 583.57 | 549.73 | 499.05 | 452.17 |
Parameter | ||||||
|
0.035 | 0.04 | 0.045 | 0.055 | 0.06 | 0.065 |
|
28.6725 | 28.4218 | 28.2240 | 27.9031 | 27.7633 | 27.5502 |
|
96.1162 | 95.9631 | 95.8812 | 95.7243 | 95.5708 | 95.3276 |
|
166.502 | 166.372 | 166.127 | 165.872 | 165.609 | 165.421 |
|
0.049 | 0.056 | 0.063 | 0.077 | 0.084 | 0.091 |
|
43.3213 | 43.1045 | 42.8871 | 42.7490 | 42.5289 | 42.3407 |
|
118.6731 | 118.4830 | 118.2571 | 117.9013 | 117.7856 | 117.5126 |
|
199.410 | 199.107 | 198.884 | 198.619 | 198.470 | 198.159 |
|
0.063 | 0.072 | 0.081 | 0.099 | 0.108 | 0.117 |
|
65.1173 | 64.8243 | 64.5740 | 64.2581 | 63.8056 | 63.5731 |
|
183.9920 | 183.7526 | 183.4911 | 183.2354 | 182.8744 | 182.8530 |
|
273.576 | 273.291 | 272.876 | 272.651 | 272.304 | 272.118 |
|
324.13 | 307.47 | 299.53 | 271.84 | 256.77 | 231.64 |
|
573.38 | 529.13 | 478.46 | 431.47 | 390.52 | 358.30 |
|
642.10 | 618.34 | 583.57 | 549.73 | 499.05 | 452.17 |
Parameter | ||||||
|
0.21 | 0.24 | 0.27 | 0.33 | 0.36 | 0.39 |
|
27.6820 | 27.8921 | 28.1675 | 28.4691 | 28.8722 | 29.3225 |
|
96.3546 | 96.6704 | 96.9124 | 97.3510 | 97.6021 | 97.9146 |
|
165.318 | 165.702 | 165.993 | 166.247 | 166.583 | 166.875 |
|
0.245 | 0.28 | 0.315 | 0.385 | 0.420 | 0.455 |
|
42.6813 | 42.8904 | 43.3612 | 43.6675 | 43.9130 | 44.4362 |
|
117.1325 | 117.4076 | 117.7451 | 118.2169 | 118.5306 | 118.8539 |
|
198.478 | 198.825 | 199.350 | 199.718 | 199.958 | 237.574 |
|
0.28 | 0.32 | 0.36 | 0.44 | 0.48 | 0.52 |
|
66.3753 | 66.5206 | 66.8347 | 67.2541 | 67.6088 | 67.9346 |
|
182.7090 | 182.9364 | 183.2674 | 183.5104 | 183.7984 | 184.2576 |
|
273.157 | 273.409 | 273.749 | 273.986 | 274.370 | 274.875 |
|
142.39 | 187.52 | 224.78 | 279.70 | 330.87 | 367.42 |
|
413.49 | 437.61 | 475.23 | 493.27 | 534.17 | 562.19 |
|
650.14 | 688.07 | 723.47 | 767.33 | 784.35 | 820.69 |
Parameter | ||||||
|
0.21 | 0.24 | 0.27 | 0.33 | 0.36 | 0.39 |
|
27.6820 | 27.8921 | 28.1675 | 28.4691 | 28.8722 | 29.3225 |
|
96.3546 | 96.6704 | 96.9124 | 97.3510 | 97.6021 | 97.9146 |
|
165.318 | 165.702 | 165.993 | 166.247 | 166.583 | 166.875 |
|
0.245 | 0.28 | 0.315 | 0.385 | 0.420 | 0.455 |
|
42.6813 | 42.8904 | 43.3612 | 43.6675 | 43.9130 | 44.4362 |
|
117.1325 | 117.4076 | 117.7451 | 118.2169 | 118.5306 | 118.8539 |
|
198.478 | 198.825 | 199.350 | 199.718 | 199.958 | 237.574 |
|
0.28 | 0.32 | 0.36 | 0.44 | 0.48 | 0.52 |
|
66.3753 | 66.5206 | 66.8347 | 67.2541 | 67.6088 | 67.9346 |
|
182.7090 | 182.9364 | 183.2674 | 183.5104 | 183.7984 | 184.2576 |
|
273.157 | 273.409 | 273.749 | 273.986 | 274.370 | 274.875 |
|
142.39 | 187.52 | 224.78 | 279.70 | 330.87 | 367.42 |
|
413.49 | 437.61 | 475.23 | 493.27 | 534.17 | 562.19 |
|
650.14 | 688.07 | 723.47 | 767.33 | 784.35 | 820.69 |
Parameter | ||||||
|
0.35 | 0.40 | 0.45 | 0.55 | 0.60 | 0.65 |
|
30.2670 | 30.8305 | 31.4758 | 32.0165 | 32.7736 | 33.3814 |
|
98.4236 | 98.9470 | 99.5024 | 100.0631 | 100.5861 | 101.1425 |
|
167.264 | 167.752 | 168.369 | 168.804 | 169.362 | 169.972 |
|
0.42 | 0.48 | 0.54 | 0.66 | 0.72 | 0.78 |
|
45.6149 | 46.1543 | 46.5783 | 47.1462 | 47.6388 | 48.3592 |
|
118.4268 | 118.9005 | 119.2457 | 119.8319 | 120.3670 | 120.7591 |
|
210.375 | 210.763 | 211.136 | 211.545 | 211.987 | 212.307 |
|
0.49 | 0.56 | 0.63 | 0.77 | 0.84 | 0.91 |
|
68.3871 | 68.8414 | 69.4206 | 70.9126 | 70.4756 | 70.8225 |
|
185.2477 | 185.6470 | 186.0853 | 186.4800 | 186.8175 | 187.2052 |
|
275.8145 | 276.335 | 276.857 | 277.3670 | 277.8950 | 277.4352 |
|
150.26 | 163.73 | 175.44 | 189.71 | 213.46 | 252.04 |
|
409.24 | 422.19 | 435.07 | 442.86 | 453.20 | 467.15 |
|
660.14 | 671.42 | 684.35 | 697.23 | 713.75 | 729.06 |
Parameter | ||||||
|
0.35 | 0.40 | 0.45 | 0.55 | 0.60 | 0.65 |
|
30.2670 | 30.8305 | 31.4758 | 32.0165 | 32.7736 | 33.3814 |
|
98.4236 | 98.9470 | 99.5024 | 100.0631 | 100.5861 | 101.1425 |
|
167.264 | 167.752 | 168.369 | 168.804 | 169.362 | 169.972 |
|
0.42 | 0.48 | 0.54 | 0.66 | 0.72 | 0.78 |
|
45.6149 | 46.1543 | 46.5783 | 47.1462 | 47.6388 | 48.3592 |
|
118.4268 | 118.9005 | 119.2457 | 119.8319 | 120.3670 | 120.7591 |
|
210.375 | 210.763 | 211.136 | 211.545 | 211.987 | 212.307 |
|
0.49 | 0.56 | 0.63 | 0.77 | 0.84 | 0.91 |
|
68.3871 | 68.8414 | 69.4206 | 70.9126 | 70.4756 | 70.8225 |
|
185.2477 | 185.6470 | 186.0853 | 186.4800 | 186.8175 | 187.2052 |
|
275.8145 | 276.335 | 276.857 | 277.3670 | 277.8950 | 277.4352 |
|
150.26 | 163.73 | 175.44 | 189.71 | 213.46 | 252.04 |
|
409.24 | 422.19 | 435.07 | 442.86 | 453.20 | 467.15 |
|
660.14 | 671.42 | 684.35 | 697.23 | 713.75 | 729.06 |
Parameter | ||||||
|
0.28 | 0.32 | 0.36 | 0.44 | 0.48 | 0.52 |
|
28.2743 | 28.6183 | 29.0179 | 29.3746 | 29.6524 | 29.9032 |
|
97.3176 | 97.6480 | 97.9208 | 98.4635 | 98.7705 | 99.1432 |
|
165.418 | 165.727 | 166.284 | 166.546 | 166.920 | 167.335 |
|
0.42 | 0.48 | 0.54 | 0.66 | 0.72 | 0.78 |
|
44.1267 | 44.4725 | 44.8213 | 45.2018 | 45.5537 | 45.8715 |
|
116.4503 | 116.6931 | 116.9917 | 117.4361 | 117.8543 | 118.5174 |
|
206.421 | 206.885 | 207.367 | 207.753 | 208.290 | 208.668 |
|
0.56 | 0.64 | 0.72 | 0.88 | 0.96 | 1.04 |
|
67.3417 | 67.8864 | 68.4011 | 68.9172 | 79.5140 | 79.8711 |
|
189.1106 | 189.6587 | 190.2275 | 190.6340 | 191.3719 | 191.5603 |
|
279.9902 | 280.4275 | 280.8670 | 281.2552 | 282.7732 | 283.5112 |
|
140.31 | 153.10 | 161.49 | 175.25 | 183.39 | 199.37 |
|
408.72 | 417.28 | 425.01 | 437.26 | 445.49 | 467.00 |
|
657.29 | 669.81 | 672.31 | 685.01 | 693.33 | 707.46 |
Parameter | ||||||
|
0.28 | 0.32 | 0.36 | 0.44 | 0.48 | 0.52 |
|
28.2743 | 28.6183 | 29.0179 | 29.3746 | 29.6524 | 29.9032 |
|
97.3176 | 97.6480 | 97.9208 | 98.4635 | 98.7705 | 99.1432 |
|
165.418 | 165.727 | 166.284 | 166.546 | 166.920 | 167.335 |
|
0.42 | 0.48 | 0.54 | 0.66 | 0.72 | 0.78 |
|
44.1267 | 44.4725 | 44.8213 | 45.2018 | 45.5537 | 45.8715 |
|
116.4503 | 116.6931 | 116.9917 | 117.4361 | 117.8543 | 118.5174 |
|
206.421 | 206.885 | 207.367 | 207.753 | 208.290 | 208.668 |
|
0.56 | 0.64 | 0.72 | 0.88 | 0.96 | 1.04 |
|
67.3417 | 67.8864 | 68.4011 | 68.9172 | 79.5140 | 79.8711 |
|
189.1106 | 189.6587 | 190.2275 | 190.6340 | 191.3719 | 191.5603 |
|
279.9902 | 280.4275 | 280.8670 | 281.2552 | 282.7732 | 283.5112 |
|
140.31 | 153.10 | 161.49 | 175.25 | 183.39 | 199.37 |
|
408.72 | 417.28 | 425.01 | 437.26 | 445.49 | 467.00 |
|
657.29 | 669.81 | 672.31 | 685.01 | 693.33 | 707.46 |
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