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Continuous-time mean-variance portfolio selection with no-shorting constraints and regime-switching
A two-warehouse probabilistic model with price discount on backorders under two levels of 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 |
It is impossible in this competitive era to assess the demand for items in advance. So, it is essential to refer to a stochastic demand function. In this paper, a probabilistic inventory model for deteriorating items is unfolded. Here, the supplier as well as the retailer adopt the trade-credit policy for their customers with the aim of promoting the market competition. Shortages are included into the model, and when stock on hand is zero, the retailer offers a price discount to those customers who are willing to back-order their demands. We consider two different warehouses in which the first one is an Own Warehouse (OW) where the deterioration is constant over time and the other is a Rented Warehouse (RW), and where the deterioration rate follows a Weibull distribution. An algorithm is provided for finding the solutions of the formulated model.Global convexity of the cost function is established which shows that our proposed model is very helpful for any supplier or retailer to finalize the optimal ordering policy. Beside of this, we target to increase the total profit for retailer by reducing the corresponding total inventory cost. The theoretical concept is justified with the help of some numerical examples. A sensitivity analysis of the optimal solution with respect to the major parameters is also provided in order to stabilize our model. We finalize the paper through a conclusion and a preview onto possible future studies.
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] |
B. Bank, J. Guddat, B. Kummer and K. Tammer,
Non-Linear Parametric Optimization, Birkhäuser, Basel, 2014.
doi: 10.1007/978-3-0348-6328-5. |
[3] |
L. Benkherouf,
A deterministic order level inventory model for deteriorating items with two storage facilities, International Journal of Production Economics, 48 (1997), 167-175.
doi: 10.1016/S0925-5273(96)00070-9. |
[4] |
A. K. Bhunia, C. K. Jaggi, A. Sharma and R. Sharma,
A two-warehouse inventory model for deteriorating items under permissible delay in payment with partial backlogging, Applied Mathematics and Computation, 232 (2014), 1125-1137.
doi: 10.1016/j.amc.2014.01.115. |
[5] |
A. K. Bhunia and M. Maiti,
A two-warehouse inventory model for a linear trend in demand, Opsearch, 31 (1994), 318-329.
|
[6] |
T. Chakrabarty, B. C. Giri and K. S. Chaudhuri,
An EOQ model for items with Weibull distribution deterioration, shortages and trended demand: An extension of Philip's model, Computers & Operations Research, 25 (1998), 649-657.
doi: 10.1016/S0305-0548(97)00081-6. |
[7] |
K. Chung and T. Huang,
The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing, International Journal of Production Economics, 106 (2007), 127-145.
doi: 10.1016/j.ijpe.2006.05.008. |
[8] |
K. J. Chung and J. J. Liao,
Lot-sizing decisions under trade credit depending on the ordering quantity, Computers and Operations Research, 31 (2004), 909-928.
doi: 10.1016/S0305-0548(03)00043-1. |
[9] |
R. P. Covert and G. S. Philip,
An EOQ model for items with Weibull distribution deterioration, AIIE Transactions, 5 (1973), 323-326.
doi: 10.1080/05695557308974918. |
[10] |
D. Das, M. B. Kar, A. Roy and S. Kar,
Two-warehouse production model for deteriorating inventory items with stock-dependent demand under inflation over a random planning horizon, Central European Journal of Operations Research, 20 (2012), 251-280.
doi: 10.1007/s10100-010-0165-4. |
[11] |
T. K. Datta and A. K. Pal,
Order level inventory system with power demand pattern for items with variable rate of deterioration, Indian Journal of Pure and Applied Mathematics, 19 (1988), 1043-1053.
|
[12] |
L. N. De and A. Goswami,
Probabilistic EOQ model for deteriorating items under trade credit financing, International Journal of System Science, 40 (2009), 335-346.
doi: 10.1080/00207720802435663. |
[13] |
P. M. Ghare and G. P. Schrader,
A model for an exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243.
|
[14] |
M. Ghoreishi, G. W. Weber and A. Mirzazadeh,
An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation and selling price-dependent demand and customer returns, Annals of Operations Research, 226 (2015), 221-238.
doi: 10.1007/s10479-014-1739-7. |
[15] |
A. Goswami and K. S. Chaudhuri,
An economic order quantity model for items with two levels of storage for a linear trend in demand, Journal of the Operational Research Society, 43 (1992), 157-167.
|
[16] |
S. K. Goyal,
Economic order quantity under conditions of permissible delay in payments, Journal of Operational Research Society, 36 (1985), 335-338.
|
[17] |
V. R. Hartely,
Operations Research - A Managerial Emphasis, Chapter 12, Good Year, Santa Monica, CA, (1976), 315-317.
|
[18] |
C. K. Jaggi, L. E. Cárdenas-Barrón, S. Tiwari and A. A. Shafi,
Two-warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments, Scientia Iranica E, 24 (2017), 390-412.
doi: 10.24200/sci.2017.4042. |
[19] |
H. Th. Jongen and G. W. Weber,
On parametric nonlinear programming, Annals of Operations Research, 27 (1990), 253-284.
doi: 10.1007/BF02055198. |
[20] |
N. K. Kaliraman, R. Raj, S. Chandra and H. Chaudhary,
Two warehouse inventory model for deteriorating item with exponential demand rate and permissible delay in payment, Yugoslav Journal of Operations Research, 27 (2017), 109-124.
doi: 10.2298/YJOR150404007K. |
[21] |
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. |
[22] |
M. Lashgari, A. A. Taleizadeh and A. Ahmadi,
Partial up-stream advanced payment and partial down-stream delayed payment in a three-level supply chain, Annals of Operations Research, 238 (2016), 329-354.
doi: 10.1007/s10479-015-2100-5. |
[23] |
L. Y. Ouyang, C. T. Chang and P. Shum,
The inter-dependent reductions of lead time and ordering cost in periodic review inventory model with backorder price discount, International
Journal of Information and Management Sciences(3), 18 (2007), 195-208.
|
[24] |
M. Palanivel, R. Sundararajan and R. Uthayakumar,
Two-warehouse inventory model with non-instantaneously deteriorating items, stock-dependent demand, shortages and inflation, Journal of Management Analytics, 3 (2016), 152-173.
doi: 10.1080/23270012.2016.1145078. |
[25] |
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. |
[26] |
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. |
[27] |
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.
doi: 10.3934/naco.2018010. |
[28] |
M. Pervin, S. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy,
Journal of Industrial and Management Optimization, (2018).
doi: 10.3934/jimo.2018098. |
[29] |
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. |
[30] |
J. Ray and K. S. Chaudhuri,
An EOQ model with stock-dependent demand, shortage, inflation and time discounting, International Journal of Production Economics, 53 (1997), 171-180.
doi: 10.1016/S0925-5273(97)00112-6. |
[31] |
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. |
[32] |
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. |
[33] |
K. V. S. Sarma,
A deterministic inventory model with two level of storage and an optimum release rule, Opsearch, 20 (1983), 175-180.
|
[34] |
S. Shabani, A. Mirzazadeh and E. Sharifi,
A two-warehouse inventory model with fuzzy deterioratinn rate and fuzzy demand rate under conditionally permissible delay in payment, Journal of Industrial and Production Engineering(2), 33 (2016), 134-142.
|
[35] |
N. H. Shah,
Probabilistic order level system with lead time when delay in payments are permissible, TOP, 5 (1997), 297-305.
doi: 10.1007/BF02568555. |
[36] |
N. H. Shah and Y. K. Shah,
A discrete-in-time probabilistic inventory model for deteriorating items under conditions of permissible delay in payments, International Journal of System Science, 29 (1998), 121-125.
doi: 10.1080/00207729808929504. |
[37] |
S. Singh, J. Sharma and S. Singh,
Profit maximizing probabilistic inventory model under the effect of permissible delay, International Multi Conference of Engineers and Computer Scientists, 3 (2010), 17-19.
|
[38] |
A. A. Taleizadeh and M. Noori-daryan,
Pricing, manufacturing and inventory policies for raw material in a three-level supply chain, International Journal of Systems Science, 47 (2016), 919-931.
doi: 10.1080/00207721.2014.909544. |
[39] |
G. W. Weber,
On the topology of parametric optimal control, Journal of the Australian Mathematical Society, Series B, 39 (1997), 1-35.
doi: 10.1017/S033427000000775X. |
[40] |
H. Yang,
Two-warehouse inventory models for deteriorating items with shortages under inflation, European Journal of Operational Research, 157 (2006), 344-356.
doi: 10.1016/S0377-2217(03)00221-2. |
[41] |
H. L. Yang and C. T. Chang,
A two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation, Applied Mathematical Modelling, 37 (2013), 2717-2726.
doi: 10.1016/j.apm.2012.05.008. |
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] |
B. Bank, J. Guddat, B. Kummer and K. Tammer,
Non-Linear Parametric Optimization, Birkhäuser, Basel, 2014.
doi: 10.1007/978-3-0348-6328-5. |
[3] |
L. Benkherouf,
A deterministic order level inventory model for deteriorating items with two storage facilities, International Journal of Production Economics, 48 (1997), 167-175.
doi: 10.1016/S0925-5273(96)00070-9. |
[4] |
A. K. Bhunia, C. K. Jaggi, A. Sharma and R. Sharma,
A two-warehouse inventory model for deteriorating items under permissible delay in payment with partial backlogging, Applied Mathematics and Computation, 232 (2014), 1125-1137.
doi: 10.1016/j.amc.2014.01.115. |
[5] |
A. K. Bhunia and M. Maiti,
A two-warehouse inventory model for a linear trend in demand, Opsearch, 31 (1994), 318-329.
|
[6] |
T. Chakrabarty, B. C. Giri and K. S. Chaudhuri,
An EOQ model for items with Weibull distribution deterioration, shortages and trended demand: An extension of Philip's model, Computers & Operations Research, 25 (1998), 649-657.
doi: 10.1016/S0305-0548(97)00081-6. |
[7] |
K. Chung and T. Huang,
The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing, International Journal of Production Economics, 106 (2007), 127-145.
doi: 10.1016/j.ijpe.2006.05.008. |
[8] |
K. J. Chung and J. J. Liao,
Lot-sizing decisions under trade credit depending on the ordering quantity, Computers and Operations Research, 31 (2004), 909-928.
doi: 10.1016/S0305-0548(03)00043-1. |
[9] |
R. P. Covert and G. S. Philip,
An EOQ model for items with Weibull distribution deterioration, AIIE Transactions, 5 (1973), 323-326.
doi: 10.1080/05695557308974918. |
[10] |
D. Das, M. B. Kar, A. Roy and S. Kar,
Two-warehouse production model for deteriorating inventory items with stock-dependent demand under inflation over a random planning horizon, Central European Journal of Operations Research, 20 (2012), 251-280.
doi: 10.1007/s10100-010-0165-4. |
[11] |
T. K. Datta and A. K. Pal,
Order level inventory system with power demand pattern for items with variable rate of deterioration, Indian Journal of Pure and Applied Mathematics, 19 (1988), 1043-1053.
|
[12] |
L. N. De and A. Goswami,
Probabilistic EOQ model for deteriorating items under trade credit financing, International Journal of System Science, 40 (2009), 335-346.
doi: 10.1080/00207720802435663. |
[13] |
P. M. Ghare and G. P. Schrader,
A model for an exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243.
|
[14] |
M. Ghoreishi, G. W. Weber and A. Mirzazadeh,
An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation and selling price-dependent demand and customer returns, Annals of Operations Research, 226 (2015), 221-238.
doi: 10.1007/s10479-014-1739-7. |
[15] |
A. Goswami and K. S. Chaudhuri,
An economic order quantity model for items with two levels of storage for a linear trend in demand, Journal of the Operational Research Society, 43 (1992), 157-167.
|
[16] |
S. K. Goyal,
Economic order quantity under conditions of permissible delay in payments, Journal of Operational Research Society, 36 (1985), 335-338.
|
[17] |
V. R. Hartely,
Operations Research - A Managerial Emphasis, Chapter 12, Good Year, Santa Monica, CA, (1976), 315-317.
|
[18] |
C. K. Jaggi, L. E. Cárdenas-Barrón, S. Tiwari and A. A. Shafi,
Two-warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments, Scientia Iranica E, 24 (2017), 390-412.
doi: 10.24200/sci.2017.4042. |
[19] |
H. Th. Jongen and G. W. Weber,
On parametric nonlinear programming, Annals of Operations Research, 27 (1990), 253-284.
doi: 10.1007/BF02055198. |
[20] |
N. K. Kaliraman, R. Raj, S. Chandra and H. Chaudhary,
Two warehouse inventory model for deteriorating item with exponential demand rate and permissible delay in payment, Yugoslav Journal of Operations Research, 27 (2017), 109-124.
doi: 10.2298/YJOR150404007K. |
[21] |
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. |
[22] |
M. Lashgari, A. A. Taleizadeh and A. Ahmadi,
Partial up-stream advanced payment and partial down-stream delayed payment in a three-level supply chain, Annals of Operations Research, 238 (2016), 329-354.
doi: 10.1007/s10479-015-2100-5. |
[23] |
L. Y. Ouyang, C. T. Chang and P. Shum,
The inter-dependent reductions of lead time and ordering cost in periodic review inventory model with backorder price discount, International
Journal of Information and Management Sciences(3), 18 (2007), 195-208.
|
[24] |
M. Palanivel, R. Sundararajan and R. Uthayakumar,
Two-warehouse inventory model with non-instantaneously deteriorating items, stock-dependent demand, shortages and inflation, Journal of Management Analytics, 3 (2016), 152-173.
doi: 10.1080/23270012.2016.1145078. |
[25] |
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. |
[26] |
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. |
[27] |
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.
doi: 10.3934/naco.2018010. |
[28] |
M. Pervin, S. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy,
Journal of Industrial and Management Optimization, (2018).
doi: 10.3934/jimo.2018098. |
[29] |
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. |
[30] |
J. Ray and K. S. Chaudhuri,
An EOQ model with stock-dependent demand, shortage, inflation and time discounting, International Journal of Production Economics, 53 (1997), 171-180.
doi: 10.1016/S0925-5273(97)00112-6. |
[31] |
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. |
[32] |
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. |
[33] |
K. V. S. Sarma,
A deterministic inventory model with two level of storage and an optimum release rule, Opsearch, 20 (1983), 175-180.
|
[34] |
S. Shabani, A. Mirzazadeh and E. Sharifi,
A two-warehouse inventory model with fuzzy deterioratinn rate and fuzzy demand rate under conditionally permissible delay in payment, Journal of Industrial and Production Engineering(2), 33 (2016), 134-142.
|
[35] |
N. H. Shah,
Probabilistic order level system with lead time when delay in payments are permissible, TOP, 5 (1997), 297-305.
doi: 10.1007/BF02568555. |
[36] |
N. H. Shah and Y. K. Shah,
A discrete-in-time probabilistic inventory model for deteriorating items under conditions of permissible delay in payments, International Journal of System Science, 29 (1998), 121-125.
doi: 10.1080/00207729808929504. |
[37] |
S. Singh, J. Sharma and S. Singh,
Profit maximizing probabilistic inventory model under the effect of permissible delay, International Multi Conference of Engineers and Computer Scientists, 3 (2010), 17-19.
|
[38] |
A. A. Taleizadeh and M. Noori-daryan,
Pricing, manufacturing and inventory policies for raw material in a three-level supply chain, International Journal of Systems Science, 47 (2016), 919-931.
doi: 10.1080/00207721.2014.909544. |
[39] |
G. W. Weber,
On the topology of parametric optimal control, Journal of the Australian Mathematical Society, Series B, 39 (1997), 1-35.
doi: 10.1017/S033427000000775X. |
[40] |
H. Yang,
Two-warehouse inventory models for deteriorating items with shortages under inflation, European Journal of Operational Research, 157 (2006), 344-356.
doi: 10.1016/S0377-2217(03)00221-2. |
[41] |
H. L. Yang and C. T. Chang,
A two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation, Applied Mathematical Modelling, 37 (2013), 2717-2726.
doi: 10.1016/j.apm.2012.05.008. |





Author(s) | Two warehouse | Probabilistic demand | Trade credit | Deterio-rations | Shortage | Price discount |
Datta and Pal (1988) | ||||||
Bhunia and Maiti (1994) | ||||||
Shah and Shah (1998) | ||||||
Shah (1997) | ||||||
Palanivel et al. (2016) | ||||||
Jaggi et al. (2017) | ||||||
Benkherouf (1997) | ||||||
Singh et al. (2010) | ||||||
Kaliraman et al. (2017) | ||||||
Bhunia et al. (2014) | ||||||
Chung and Liao (2004) | ||||||
Yang (2006) | ||||||
De and Goswami (2009) | ||||||
Chung and Huang (2007) | ||||||
Kurdhi et al. (2015) | ||||||
Pervin et al. (2018) | ||||||
Pervin et al. (2017) | ||||||
Goyal (1985) | ||||||
Yang and Chang (2013) | ||||||
Sarkar et al. (2015) | ||||||
Ray and Chaudhuri (1997) | ||||||
Hariga (1995) | ||||||
Our paper |
Author(s) | Two warehouse | Probabilistic demand | Trade credit | Deterio-rations | Shortage | Price discount |
Datta and Pal (1988) | ||||||
Bhunia and Maiti (1994) | ||||||
Shah and Shah (1998) | ||||||
Shah (1997) | ||||||
Palanivel et al. (2016) | ||||||
Jaggi et al. (2017) | ||||||
Benkherouf (1997) | ||||||
Singh et al. (2010) | ||||||
Kaliraman et al. (2017) | ||||||
Bhunia et al. (2014) | ||||||
Chung and Liao (2004) | ||||||
Yang (2006) | ||||||
De and Goswami (2009) | ||||||
Chung and Huang (2007) | ||||||
Kurdhi et al. (2015) | ||||||
Pervin et al. (2018) | ||||||
Pervin et al. (2017) | ||||||
Goyal (1985) | ||||||
Yang and Chang (2013) | ||||||
Sarkar et al. (2015) | ||||||
Ray and Chaudhuri (1997) | ||||||
Hariga (1995) | ||||||
Our paper |
Case | ||||||
0.5 | 0.4 | 0.088 | 521 | 1923.41 | ||
800 | 0.9 | 0.8 | 0.097 | 560 | 1979.05 | |
0.6 | 0.9 | 0.109 | 582 | 1992.16 | ||
0.5 | 0.4 | 0.0896 | 559 | 2075.04 | ||
1000 | 0.9 | 0.8 | 0.0927 | 570 | 2152.00 | |
0.6 | 0.9 | 0.0989 | 590 | 2203.12 | ||
0.5 | 0.4 | 0.0735 | 601 | 2214.07 | ||
1500 | 0.9 | 0.8 | 0.0857 | 647 | 2539.11 | |
0.6 | 0.9 | 0.0875 | 685 | 2886.00 |
Case | ||||||
0.5 | 0.4 | 0.088 | 521 | 1923.41 | ||
800 | 0.9 | 0.8 | 0.097 | 560 | 1979.05 | |
0.6 | 0.9 | 0.109 | 582 | 1992.16 | ||
0.5 | 0.4 | 0.0896 | 559 | 2075.04 | ||
1000 | 0.9 | 0.8 | 0.0927 | 570 | 2152.00 | |
0.6 | 0.9 | 0.0989 | 590 | 2203.12 | ||
0.5 | 0.4 | 0.0735 | 601 | 2214.07 | ||
1500 | 0.9 | 0.8 | 0.0857 | 647 | 2539.11 | |
0.6 | 0.9 | 0.0875 | 685 | 2886.00 |
Parameter | value | ||||||||||
+50 | 600 | 1 | 1.5 | ... | ... | ... | 0.274 | 594 | 2284.24 | +36.64 | |
+20 | 480 | 1 | 1.5 | 2 | ... | ... | 0.240 | 573 | 2170.33 | +28.41 | |
-20 | 320 | 1 | 1.5 | 2 | 2.5 | ... | 0.208 | 557 | 2001.16 | +9.71 | |
-50 | 200 | 1 | 1.5 | 2 | 2.3 | 3 | 0.173 | 529 | 1981.07 | -0.85 | |
+50 | 90 | 1 | 1.5 | ... | ... | ... | 0.198 | 468 | 2478.21 | +27.53 | |
+20 | 72 | 1 | 1.5 | 2 | ... | ... | 0.183 | 450 | 2356.34 | +21.23 | |
-20 | 48 | 1 | 1.5 | 2 | 2.5 | ... | 0.175 | 438 | 2213.08 | +18.73 | |
-50 | 30 | 1 | 1.5 | 2 | 2.5 | 3 | 0.166 | 426 | 2087.60 | +9.39 | |
+50 | 105 | 1 | 1.5 | ... | ... | ... | 0.098 | 537 | 3798.26 | +47.07 | |
+20 | 84 | 1 | 1.5 | 2 | ... | ... | 0.082 | 522 | 3523.65 | +31.67 | |
-20 | 56 | 1 | 1.5 | 2 | 2.5 | ... | 0.076 | 517 | 3247.43 | +23.81 | |
-50 | 35 | 1 | 1.5 | 2 | 2.5 | 3 | 0.680 | 510 | 3068.11 | -1.27 | |
+50 | 1.2 | 1 | 1.5 | ... | ... | ... | 0.176 | 526 | 2109.87 | +28.45 | |
+20 | 0.96 | 1 | 1.5 | 2 | ... | ... | 0.248 | 538 | 2084.21 | +17.39 | |
-20 | 0.64 | 1 | 1.5 | 2 | 2.5 | ... | 0.273 | 559 | 1985.06 | -1.87 | |
-50 | 0.4 | 1 | 1.5 | 2 | 2.5 | 3 | 0.296 | 570 | 1867.30 | -2.64 | |
+50 | 0.075 | 1 | 1.5 | ... | ... | ... | 0.211 | 523 | 2075.32 | +12.37 | |
+20 | 0.06 | 1 | 1.5 | 2 | ... | ... | 0.250 | 538 | 1924.00 | +10.22 | |
-20 | 0.04 | 1 | 1.5 | 2 | 2.5 | ... | 0.310 | 550 | 1775.71 | -0.79 | |
-50 | 0.025 | 1 | 1.5 | 2 | 2.5 | 3 | 0.352 | 567 | 1528.66 | -2.85 | |
+50 | 4.5 | 1 | 1.5 | ... | ... | ... | 0.560 | 413 | 1968.20 | +25.75 | |
+20 | 3.6 | 1 | 1.5 | 2 | ... | ... | 0.581 | 399 | 1876.11 | +10.29 | |
-20 | 2.4 | 1 | 1.5 | 2 | 2.5 | ... | 0.615 | 307 | 1718.53 | -2.20 | |
-50 | 1.5 | 1 | 1.5 | 2 | 2.5 | 3 | 0.672 | 279 | 1528.04 | -5.43 | |
+50 | 0.12 | 1 | 1.5 | ... | ... | ... | 0.736 | 578 | 1727.34 | +24.74 | |
+20 | 0.096 | 1 | 1.5 | 2 | ... | ... | 0.703 | 530 | 1783.05 | +18.42 | |
-20 | 0.064 | 1 | 1.5 | 2 | 2.5 | ... | 0.682 | 492 | 1816.11 | +10.53 | |
-50 | 0.04 | 1 | 1.5 | 2 | 2.5 | 3 | 0.644 | 454 | 1874.20 | -8.64 | |
+50 | 0.725 | 1 | 1.5 | ... | ... | ... | 0.675 | 649 | 2665.93 | +43.25 | |
+20 | 0.6 | 1 | 1.5 | 2 | ... | ... | 0.510 | 687 | 2682.75 | +21.36 | |
-20 | 0.4 | 1 | 1.5 | 2 | 2.5 | ... | 0.509 | 760 | 2789.77 | +13.85 | |
-50 | 0.25 | 1 | 1.5 | 2 | 2.5 | 3 | 0.588 | 781 | 2895.34 | +7.04 | |
+50 | 0.6 | 1 | 1.5 | ... | ... | ... | 0.322 | 300 | 2541.11 | +40.52 | |
+20 | 0.48 | 1 | 1.5 | 2 | ... | ... | 0.379 | 349 | 2562.47 | +37.06 | |
-20 | 0.32 | 1 | 1.5 | 2 | 2.5 | ... | 0.401 | 373 | 2580.63 | -7.43 | |
-50 | 0.2 | 1 | 1.5 | 2 | 2.5 | 3 | 0.419 | 388 | 2558.47 | -8.65 | |
+50 | 15 | 1 | 1.5 | ... | ... | ... | 0.411 | 644 | 1563.72 | +15.27 | |
+20 | 12 | 1 | 1.5 | 2 | ... | ... | 0.458 | 541 | 1571.08 | +9.04 | |
-20 | 8 | 1 | 1.5 | 2 | 2.5 | ... | 0.392 | 520 | 1584.60 | -10.11 | |
-50 | 5 | 1 | 1.5 | 2 | 2.5 | 3 | 0.450 | 501 | 1599.01 | -5.14 | |
+50 | 75 | 1 | 1.5 | ... | ... | ... | 0.749 | 385 | 1932.84 | +29.27 | |
+20 | 60 | 1 | 1.5 | 2 | ... | ... | 0.755 | 337 | 1920.03 | +21.43 | |
-20 | 40 | 1 | 1.5 | 2 | 2.5 | ... | 0.759 | 249 | 1907.32 | +37.19 | |
-50 | 25 | 1 | 1.5 | 2 | 2.5 | 3 | 0.780 | 277 | 1871.92 | +22.48 | |
+50 | 15 | 1 | 1.5 | ... | ... | ... | 0.753 | 495 | 1884.67 | +23.42 | |
+20 | 12 | 1 | 1.5 | 2 | ... | ... | 0.734 | 327 | 1940.59 | +17.99 | |
-20 | 8 | 1 | 1.5 | 2 | 2.5 | ... | 0.690 | 224 | 1982.47 | -2.33 | |
-50 | 5 | 1 | 1.5 | 2 | 2.5 | 3 | 0.638 | 200 | 2027.59 | -7.21 | |
+50 | 1200 | 1 | 1.5 | ... | ... | ... | 0.922 | 540 | 1825.49 | +29.36 | |
+20 | 960 | 1 | 1.5 | 2 | ... | ... | 0.870 | 511 | 1871.52 | +22.15 | |
-20 | 640 | 1 | 1.5 | 2 | 2.5 | ... | 0.761 | 487 | 1905.14 | -5.22 | |
-50 | 400 | 1 | 1.5 | 2 | 2.5 | 3 | 0.739 | 475 | 1917.26 | -9.46 | |
+50 | 75 | 1 | 1.5 | ... | ... | ... | 0.875 | 610 | 1932.34 | +31.06 | |
+20 | 60 | 1 | 1.5 | 2 | ... | ... | 0.852 | 587 | 1956.07 | +26.17 | |
-20 | 40 | 1 | 1.5 | 2 | 2.5 | ... | 0.830 | 551 | 1988.23 | +13.50 | |
-50 | 25 | 1 | 1.5 | 2 | 2.5 | 3 | 0.781 | 513 | 2130.54 | +4.21 |
Parameter | value | ||||||||||
+50 | 600 | 1 | 1.5 | ... | ... | ... | 0.274 | 594 | 2284.24 | +36.64 | |
+20 | 480 | 1 | 1.5 | 2 | ... | ... | 0.240 | 573 | 2170.33 | +28.41 | |
-20 | 320 | 1 | 1.5 | 2 | 2.5 | ... | 0.208 | 557 | 2001.16 | +9.71 | |
-50 | 200 | 1 | 1.5 | 2 | 2.3 | 3 | 0.173 | 529 | 1981.07 | -0.85 | |
+50 | 90 | 1 | 1.5 | ... | ... | ... | 0.198 | 468 | 2478.21 | +27.53 | |
+20 | 72 | 1 | 1.5 | 2 | ... | ... | 0.183 | 450 | 2356.34 | +21.23 | |
-20 | 48 | 1 | 1.5 | 2 | 2.5 | ... | 0.175 | 438 | 2213.08 | +18.73 | |
-50 | 30 | 1 | 1.5 | 2 | 2.5 | 3 | 0.166 | 426 | 2087.60 | +9.39 | |
+50 | 105 | 1 | 1.5 | ... | ... | ... | 0.098 | 537 | 3798.26 | +47.07 | |
+20 | 84 | 1 | 1.5 | 2 | ... | ... | 0.082 | 522 | 3523.65 | +31.67 | |
-20 | 56 | 1 | 1.5 | 2 | 2.5 | ... | 0.076 | 517 | 3247.43 | +23.81 | |
-50 | 35 | 1 | 1.5 | 2 | 2.5 | 3 | 0.680 | 510 | 3068.11 | -1.27 | |
+50 | 1.2 | 1 | 1.5 | ... | ... | ... | 0.176 | 526 | 2109.87 | +28.45 | |
+20 | 0.96 | 1 | 1.5 | 2 | ... | ... | 0.248 | 538 | 2084.21 | +17.39 | |
-20 | 0.64 | 1 | 1.5 | 2 | 2.5 | ... | 0.273 | 559 | 1985.06 | -1.87 | |
-50 | 0.4 | 1 | 1.5 | 2 | 2.5 | 3 | 0.296 | 570 | 1867.30 | -2.64 | |
+50 | 0.075 | 1 | 1.5 | ... | ... | ... | 0.211 | 523 | 2075.32 | +12.37 | |
+20 | 0.06 | 1 | 1.5 | 2 | ... | ... | 0.250 | 538 | 1924.00 | +10.22 | |
-20 | 0.04 | 1 | 1.5 | 2 | 2.5 | ... | 0.310 | 550 | 1775.71 | -0.79 | |
-50 | 0.025 | 1 | 1.5 | 2 | 2.5 | 3 | 0.352 | 567 | 1528.66 | -2.85 | |
+50 | 4.5 | 1 | 1.5 | ... | ... | ... | 0.560 | 413 | 1968.20 | +25.75 | |
+20 | 3.6 | 1 | 1.5 | 2 | ... | ... | 0.581 | 399 | 1876.11 | +10.29 | |
-20 | 2.4 | 1 | 1.5 | 2 | 2.5 | ... | 0.615 | 307 | 1718.53 | -2.20 | |
-50 | 1.5 | 1 | 1.5 | 2 | 2.5 | 3 | 0.672 | 279 | 1528.04 | -5.43 | |
+50 | 0.12 | 1 | 1.5 | ... | ... | ... | 0.736 | 578 | 1727.34 | +24.74 | |
+20 | 0.096 | 1 | 1.5 | 2 | ... | ... | 0.703 | 530 | 1783.05 | +18.42 | |
-20 | 0.064 | 1 | 1.5 | 2 | 2.5 | ... | 0.682 | 492 | 1816.11 | +10.53 | |
-50 | 0.04 | 1 | 1.5 | 2 | 2.5 | 3 | 0.644 | 454 | 1874.20 | -8.64 | |
+50 | 0.725 | 1 | 1.5 | ... | ... | ... | 0.675 | 649 | 2665.93 | +43.25 | |
+20 | 0.6 | 1 | 1.5 | 2 | ... | ... | 0.510 | 687 | 2682.75 | +21.36 | |
-20 | 0.4 | 1 | 1.5 | 2 | 2.5 | ... | 0.509 | 760 | 2789.77 | +13.85 | |
-50 | 0.25 | 1 | 1.5 | 2 | 2.5 | 3 | 0.588 | 781 | 2895.34 | +7.04 | |
+50 | 0.6 | 1 | 1.5 | ... | ... | ... | 0.322 | 300 | 2541.11 | +40.52 | |
+20 | 0.48 | 1 | 1.5 | 2 | ... | ... | 0.379 | 349 | 2562.47 | +37.06 | |
-20 | 0.32 | 1 | 1.5 | 2 | 2.5 | ... | 0.401 | 373 | 2580.63 | -7.43 | |
-50 | 0.2 | 1 | 1.5 | 2 | 2.5 | 3 | 0.419 | 388 | 2558.47 | -8.65 | |
+50 | 15 | 1 | 1.5 | ... | ... | ... | 0.411 | 644 | 1563.72 | +15.27 | |
+20 | 12 | 1 | 1.5 | 2 | ... | ... | 0.458 | 541 | 1571.08 | +9.04 | |
-20 | 8 | 1 | 1.5 | 2 | 2.5 | ... | 0.392 | 520 | 1584.60 | -10.11 | |
-50 | 5 | 1 | 1.5 | 2 | 2.5 | 3 | 0.450 | 501 | 1599.01 | -5.14 | |
+50 | 75 | 1 | 1.5 | ... | ... | ... | 0.749 | 385 | 1932.84 | +29.27 | |
+20 | 60 | 1 | 1.5 | 2 | ... | ... | 0.755 | 337 | 1920.03 | +21.43 | |
-20 | 40 | 1 | 1.5 | 2 | 2.5 | ... | 0.759 | 249 | 1907.32 | +37.19 | |
-50 | 25 | 1 | 1.5 | 2 | 2.5 | 3 | 0.780 | 277 | 1871.92 | +22.48 | |
+50 | 15 | 1 | 1.5 | ... | ... | ... | 0.753 | 495 | 1884.67 | +23.42 | |
+20 | 12 | 1 | 1.5 | 2 | ... | ... | 0.734 | 327 | 1940.59 | +17.99 | |
-20 | 8 | 1 | 1.5 | 2 | 2.5 | ... | 0.690 | 224 | 1982.47 | -2.33 | |
-50 | 5 | 1 | 1.5 | 2 | 2.5 | 3 | 0.638 | 200 | 2027.59 | -7.21 | |
+50 | 1200 | 1 | 1.5 | ... | ... | ... | 0.922 | 540 | 1825.49 | +29.36 | |
+20 | 960 | 1 | 1.5 | 2 | ... | ... | 0.870 | 511 | 1871.52 | +22.15 | |
-20 | 640 | 1 | 1.5 | 2 | 2.5 | ... | 0.761 | 487 | 1905.14 | -5.22 | |
-50 | 400 | 1 | 1.5 | 2 | 2.5 | 3 | 0.739 | 475 | 1917.26 | -9.46 | |
+50 | 75 | 1 | 1.5 | ... | ... | ... | 0.875 | 610 | 1932.34 | +31.06 | |
+20 | 60 | 1 | 1.5 | 2 | ... | ... | 0.852 | 587 | 1956.07 | +26.17 | |
-20 | 40 | 1 | 1.5 | 2 | 2.5 | ... | 0.830 | 551 | 1988.23 | +13.50 | |
-50 | 25 | 1 | 1.5 | 2 | 2.5 | 3 | 0.781 | 513 | 2130.54 | +4.21 |
+50 | 75 | 0.725 | 0.6 | 0.12 | 0.165 | 610 | 2685.00 | +25.16 |
+40 | 70 | 0.70 | 0.56 | 0.112 | 0.137 | 589 | 2576.27 | +32.00 |
+30 | 65 | 0.65 | 0.52 | 0.104 | 0.114 | 576 | 2450.08 | +23.76 |
+20 | 60 | 0.6 | 0.48 | 0.096 | 0.105 | 558 | 2329.18 | +21.34 |
+10 | 55 | 0.55 | 0.44 | 0.088 | 0.098 | 543 | 2249.71 | +19.47 |
0 | 50 | 0.5 | 0.4 | 0.08 | 0.089 | 522 | 1923.46 | ... |
-10 | 45 | 0.45 | 0.36 | 0.072 | 0.068 | 516 | 1879.34 | +13.32 |
-20 | 40 | 0.4 | 0.32 | 0.064 | 0.062 | 511 | 1794.11 | -11.06 |
-30 | 35 | 0.35 | 0.28 | 0.056 | 0.058 | 504 | 1720.57 | +5.48 |
-40 | 30 | 0.30 | 0.24 | 0.048 | 0.051 | 497 | 1685.00 | -2.21 |
-50 | 25 | 0.25 | 0.2 | 0.04 | 0.048 | 483 | 1649.27 | -0.23 |
+50 | 75 | 0.725 | 0.6 | 0.12 | 0.165 | 610 | 2685.00 | +25.16 |
+40 | 70 | 0.70 | 0.56 | 0.112 | 0.137 | 589 | 2576.27 | +32.00 |
+30 | 65 | 0.65 | 0.52 | 0.104 | 0.114 | 576 | 2450.08 | +23.76 |
+20 | 60 | 0.6 | 0.48 | 0.096 | 0.105 | 558 | 2329.18 | +21.34 |
+10 | 55 | 0.55 | 0.44 | 0.088 | 0.098 | 543 | 2249.71 | +19.47 |
0 | 50 | 0.5 | 0.4 | 0.08 | 0.089 | 522 | 1923.46 | ... |
-10 | 45 | 0.45 | 0.36 | 0.072 | 0.068 | 516 | 1879.34 | +13.32 |
-20 | 40 | 0.4 | 0.32 | 0.064 | 0.062 | 511 | 1794.11 | -11.06 |
-30 | 35 | 0.35 | 0.28 | 0.056 | 0.058 | 504 | 1720.57 | +5.48 |
-40 | 30 | 0.30 | 0.24 | 0.048 | 0.051 | 497 | 1685.00 | -2.21 |
-50 | 25 | 0.25 | 0.2 | 0.04 | 0.048 | 483 | 1649.27 | -0.23 |
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