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Imperfection with inspection policy and variable demand under trade-credit: A deteriorating inventory model
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 |
A deteriorating inventory model with imperfect product and variable demand is formulated in this paper. A time-dependent deterioration factor is considered because the rate of deterioration is highly hinging on time. We introduce imperfect quality of production which leads to imperfect items in our proposed model. The retailer adopts inspection policy to pick over the perfect items from imperfect. Type Ⅰ and Type Ⅱ, both type of errors are included and the retailer invest some capital to improve the production process quality of the supplier. There is also a penalty cost for the retailer if they deliver some defective items by mistake. Sometime, there is a high amount of demand and, consequently, we assume shortages and partial backorder in our formulated model. The retailer adopts the trade-credit policy for his customers in order to promote market competition. The main objective of the paper is to show that the total cost is globally minimized and we have aimed at reducing the total cycle length, defectiveness of the system and the optimal order size by maximizing the total profit of the system. Then, we present three theorems and prove them to find an easy solution procedure to reduce the total cost of a system. The results are discussed with the help of numerical examples to approve the proposed model. A sensitivity analysis of the optimal solutions for the parameters is also provided. The paper ends with the conclusions and an outlook to 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. Google Scholar |
[2] |
M. Bakker, J. Riezebos and R. H. Teunter.,
Review of inventory systems with deterioration since 2001, European Journal of Operational Research, 221 (2012), 275-284.
doi: 10.1016/j.ejor.2012.03.004. |
[3] |
Z. T. Balkhi,
An optimal solution of a general lot size inventory model with deteriorated and imperfect products, taking into account inflation and time value of money, International Journal of Systems Science, 35 (2004), 87-96.
doi: 10.1016/S0377-2217(00)00133-8. |
[4] |
L. E. Cárdenas-Barrón, Economic production quantity with rework process at a single-stage manufacturing system with planned backorders, Computers and Industrial Engineering, 57 (2009), 1105-1113. Google Scholar |
[5] |
H. J. Chang and C. Y. Dye,
An inventory model for deteriorating items with partial back logging and permissible delay in payments, International Journal of Systems Science, 32 (2001), 345-352.
doi: 10.1080/002077201300029700. |
[6] |
K. Chung and P. Ting, An heuristic for replenishment of deteriorating items with a linear trend in demand, Journal of the Operational Research Society, 44 (1993), 1235-1241. Google Scholar |
[7] |
U. Dave and L. K. Patel,
$(T, S_j)$ policy inventory model for deteriorating items with time proportional demand, Journal of the Operational Research Society, 32 (1981), 137-142.
doi: 10.1016/0377-2217(80)90190-3. |
[8] |
W. A. Donaldson, Inventory replenishment policy for a linear trend in demand-an analytical solution, Operational Research Quaterly, 28 (1977), 663-670. Google Scholar |
[9] |
C. Y. Dye, The effect of preservation technology investment on a non-instantaneous deteriorating inventory model, Omega, 41 (2013), 872-880. Google Scholar |
[10] |
P. M. Ghare and G. P. Schrader, A model for an exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243. Google Scholar |
[11] |
S. K. Ghosh and K. S. Chaudhuri,
An order-level inventory model for a deteriorating item with Weibull distribution deterioration, time-quadratic demand and shortages, Advanced Modelling and Optimization, 6 (2004), 21-35.
|
[12] |
A. Goswami and K. S. Chaudhuri, An EOQ model for deteriorating items with shortages and a linear trend in demand, The Journal of the Operational Research Society, 42 (1991), 1105-1110. Google Scholar |
[13] |
S. K. Goyal, Economic order quantity under conditions of permissible delay in payments, The Journal of Operational Research Society, 36 (1985), 335-338. Google Scholar |
[14] |
S. K. Goyal and B. C. Giri,
Recents trends in modelling of deteriorating inventory, European Journal of Operational Research, 134 (2001), 1-16.
doi: 10.1016/S0377-2217(00)00248-4. |
[15] |
R. W. Hall, Zero Inventories, Illinois: Dow Jones-Irwin, Homewood. Google Scholar |
[16] |
M. A. Hargia and L. Benkherouf, Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand, European Journal of Operational Research, 79 (1994), 123-137. Google Scholar |
[17] |
A. K. Jalan, R. R. Giri and K. S. Chaudhuri, EOQ model for items with Weibull distribution deterioration, shortages and trended demand, International Journal of Systems Science, 27 (1996), 851-855. Google Scholar |
[18] |
M. Khan, M. Y. Jaber and A. R. Ahmad, An integrated supply chain model with errors in quality inspection and learning in production, Omega, 42 (2014), 16-24. Google Scholar |
[19] |
H. L. Lee and M. J. Rosenblatt, Simultaneous determination of production cycles and inspection schedules in a production system, Management Science, 33 (1987), 1125-1136. Google Scholar |
[20] |
J. J. Liao, An EOQ model with non instantaneous receipt and exponentially deteriorating items under two-level trade credit, International Journal of Production Economics, 113 (2008), 852-861. Google Scholar |
[21] |
T. Y. Lin and K. L. Hou,
An imperfect quality economic order quantity with advanced receiving, TOP, 23 (2015), 535-551.
doi: 10.1007/s11750-014-0352-x. |
[22] |
U. Mishra, L. E. Cárdenas-Barrón, S. Tiwari, A. A. Shaikh and G. Treviño-Garza,
An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment, Annals of Operations Research, 9 (2015), 351-365.
doi: 10.1007/s10479-017-2419-1. |
[23] |
L. Y. Ouyang, J. T. Teng and L. H. Chen,
Optimum ordering policy for deteriorating items with partial backlogging under permissible delay in payments, Journal of Global Optimization, 34 (2005), 245-271.
doi: 10.1007/s10898-005-2604-7. |
[24] |
L. Y. Ouyang, L. Y. Chen and C. T. Yang, Impacts of collaborative investment and inspection policies on the integrated inventory model with defective items, International Journal of Production Research, 51 (2013), 5789-5802. Google Scholar |
[25] |
G. Padmanabhan and P. Vrat, EOQ models for perishable items under stock dependent selling rate, European Journal of Operational Research, 86 (1995), 281-292. Google Scholar |
[26] |
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. Google Scholar |
[27] |
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. |
[28] |
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. |
[29] |
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. |
[30] |
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, 15 (2019), 1345-1373.
doi: 10.3934/jimo.2018098. |
[31] |
M. Pervin, S. K. Roy and G. W. Weber, Deteriorating inventory with preservation technology under price- and stock-sensitive demand, Journal of Industrial and Management Optimization, DOI: 10.3934/jimo.2019019.
doi: 10.3934/jimo.2019019. |
[32] |
E. L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction, Operations Research, 34 (1986), 137-144. Google Scholar |
[33] |
S. K. Roy, M. Pervin and G. W. Weber, A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy, Journal of Industrial and Management Optimization, DOI: 10.3934/jimo.2018167.
doi: 10.3934/jimo.2018167. |
[34] |
M. K. Salameh and M. Y. Jaber, Economic production quantity model for items with imperfect quality, International Journal of Production Economics, 64 (2000), 59-64. Google Scholar |
[35] |
S. S. Sana,
An economic production lot size model in an imperfect production system, European Journal of Operational Research, 201 (2010), 158-170.
doi: 10.1504/IJMOR.2010.033441. |
[36] |
S. S. Sana, S. K. Goyal and K. S. Chaudhuri,
A production inventory model for a deteriorating item with trended demand and shortages, European Journal of Operational Research, 157 (2004), 357-371.
doi: 10.1016/S0377-2217(03)00222-4. |
[37] |
B. Sarkar, S. Saren and L. E. Cárdenas-Barrón,
An inventory model with trade-credit policy and variable deterioration for fixed lifetime products, Annals of Operations Research, 229 (2015), 677-702.
doi: 10.1007/s10479-014-1745-9. |
[38] |
J. T. Teng, H. J. Chang, C. Y. Dye and C. H. Hung,
An optimal replenishment policy for deterioratng items with time-varying demand and partial backlogging, Operations Research Letters, 30 (2002), 387-393.
doi: 10.1016/S0167-6377(02)00150-5. |
[39] |
R. P. Tripathi, Inventory model with stock-level dependent demand rate and shortages under trade credits, International Journal of Modern Mathematical Sciences, 13 (2015), 122-136. Google Scholar |
[40] |
H. M. Wee, A deterministic lot-size inventory model for deteriorating items with shortages and a declining market, Computers and Operations Research, 22 (1995), 345-356. Google Scholar |
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. Google Scholar |
[2] |
M. Bakker, J. Riezebos and R. H. Teunter.,
Review of inventory systems with deterioration since 2001, European Journal of Operational Research, 221 (2012), 275-284.
doi: 10.1016/j.ejor.2012.03.004. |
[3] |
Z. T. Balkhi,
An optimal solution of a general lot size inventory model with deteriorated and imperfect products, taking into account inflation and time value of money, International Journal of Systems Science, 35 (2004), 87-96.
doi: 10.1016/S0377-2217(00)00133-8. |
[4] |
L. E. Cárdenas-Barrón, Economic production quantity with rework process at a single-stage manufacturing system with planned backorders, Computers and Industrial Engineering, 57 (2009), 1105-1113. Google Scholar |
[5] |
H. J. Chang and C. Y. Dye,
An inventory model for deteriorating items with partial back logging and permissible delay in payments, International Journal of Systems Science, 32 (2001), 345-352.
doi: 10.1080/002077201300029700. |
[6] |
K. Chung and P. Ting, An heuristic for replenishment of deteriorating items with a linear trend in demand, Journal of the Operational Research Society, 44 (1993), 1235-1241. Google Scholar |
[7] |
U. Dave and L. K. Patel,
$(T, S_j)$ policy inventory model for deteriorating items with time proportional demand, Journal of the Operational Research Society, 32 (1981), 137-142.
doi: 10.1016/0377-2217(80)90190-3. |
[8] |
W. A. Donaldson, Inventory replenishment policy for a linear trend in demand-an analytical solution, Operational Research Quaterly, 28 (1977), 663-670. Google Scholar |
[9] |
C. Y. Dye, The effect of preservation technology investment on a non-instantaneous deteriorating inventory model, Omega, 41 (2013), 872-880. Google Scholar |
[10] |
P. M. Ghare and G. P. Schrader, A model for an exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243. Google Scholar |
[11] |
S. K. Ghosh and K. S. Chaudhuri,
An order-level inventory model for a deteriorating item with Weibull distribution deterioration, time-quadratic demand and shortages, Advanced Modelling and Optimization, 6 (2004), 21-35.
|
[12] |
A. Goswami and K. S. Chaudhuri, An EOQ model for deteriorating items with shortages and a linear trend in demand, The Journal of the Operational Research Society, 42 (1991), 1105-1110. Google Scholar |
[13] |
S. K. Goyal, Economic order quantity under conditions of permissible delay in payments, The Journal of Operational Research Society, 36 (1985), 335-338. Google Scholar |
[14] |
S. K. Goyal and B. C. Giri,
Recents trends in modelling of deteriorating inventory, European Journal of Operational Research, 134 (2001), 1-16.
doi: 10.1016/S0377-2217(00)00248-4. |
[15] |
R. W. Hall, Zero Inventories, Illinois: Dow Jones-Irwin, Homewood. Google Scholar |
[16] |
M. A. Hargia and L. Benkherouf, Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand, European Journal of Operational Research, 79 (1994), 123-137. Google Scholar |
[17] |
A. K. Jalan, R. R. Giri and K. S. Chaudhuri, EOQ model for items with Weibull distribution deterioration, shortages and trended demand, International Journal of Systems Science, 27 (1996), 851-855. Google Scholar |
[18] |
M. Khan, M. Y. Jaber and A. R. Ahmad, An integrated supply chain model with errors in quality inspection and learning in production, Omega, 42 (2014), 16-24. Google Scholar |
[19] |
H. L. Lee and M. J. Rosenblatt, Simultaneous determination of production cycles and inspection schedules in a production system, Management Science, 33 (1987), 1125-1136. Google Scholar |
[20] |
J. J. Liao, An EOQ model with non instantaneous receipt and exponentially deteriorating items under two-level trade credit, International Journal of Production Economics, 113 (2008), 852-861. Google Scholar |
[21] |
T. Y. Lin and K. L. Hou,
An imperfect quality economic order quantity with advanced receiving, TOP, 23 (2015), 535-551.
doi: 10.1007/s11750-014-0352-x. |
[22] |
U. Mishra, L. E. Cárdenas-Barrón, S. Tiwari, A. A. Shaikh and G. Treviño-Garza,
An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment, Annals of Operations Research, 9 (2015), 351-365.
doi: 10.1007/s10479-017-2419-1. |
[23] |
L. Y. Ouyang, J. T. Teng and L. H. Chen,
Optimum ordering policy for deteriorating items with partial backlogging under permissible delay in payments, Journal of Global Optimization, 34 (2005), 245-271.
doi: 10.1007/s10898-005-2604-7. |
[24] |
L. Y. Ouyang, L. Y. Chen and C. T. Yang, Impacts of collaborative investment and inspection policies on the integrated inventory model with defective items, International Journal of Production Research, 51 (2013), 5789-5802. Google Scholar |
[25] |
G. Padmanabhan and P. Vrat, EOQ models for perishable items under stock dependent selling rate, European Journal of Operational Research, 86 (1995), 281-292. Google Scholar |
[26] |
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. Google Scholar |
[27] |
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. |
[28] |
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. |
[29] |
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. |
[30] |
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, 15 (2019), 1345-1373.
doi: 10.3934/jimo.2018098. |
[31] |
M. Pervin, S. K. Roy and G. W. Weber, Deteriorating inventory with preservation technology under price- and stock-sensitive demand, Journal of Industrial and Management Optimization, DOI: 10.3934/jimo.2019019.
doi: 10.3934/jimo.2019019. |
[32] |
E. L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction, Operations Research, 34 (1986), 137-144. Google Scholar |
[33] |
S. K. Roy, M. Pervin and G. W. Weber, A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy, Journal of Industrial and Management Optimization, DOI: 10.3934/jimo.2018167.
doi: 10.3934/jimo.2018167. |
[34] |
M. K. Salameh and M. Y. Jaber, Economic production quantity model for items with imperfect quality, International Journal of Production Economics, 64 (2000), 59-64. Google Scholar |
[35] |
S. S. Sana,
An economic production lot size model in an imperfect production system, European Journal of Operational Research, 201 (2010), 158-170.
doi: 10.1504/IJMOR.2010.033441. |
[36] |
S. S. Sana, S. K. Goyal and K. S. Chaudhuri,
A production inventory model for a deteriorating item with trended demand and shortages, European Journal of Operational Research, 157 (2004), 357-371.
doi: 10.1016/S0377-2217(03)00222-4. |
[37] |
B. Sarkar, S. Saren and L. E. Cárdenas-Barrón,
An inventory model with trade-credit policy and variable deterioration for fixed lifetime products, Annals of Operations Research, 229 (2015), 677-702.
doi: 10.1007/s10479-014-1745-9. |
[38] |
J. T. Teng, H. J. Chang, C. Y. Dye and C. H. Hung,
An optimal replenishment policy for deterioratng items with time-varying demand and partial backlogging, Operations Research Letters, 30 (2002), 387-393.
doi: 10.1016/S0167-6377(02)00150-5. |
[39] |
R. P. Tripathi, Inventory model with stock-level dependent demand rate and shortages under trade credits, International Journal of Modern Mathematical Sciences, 13 (2015), 122-136. Google Scholar |
[40] |
H. M. Wee, A deterministic lot-size inventory model for deteriorating items with shortages and a declining market, Computers and Operations Research, 22 (1995), 345-356. Google Scholar |




Author(s) | Imperfec tness | Variable demand | Deterio rations | Trade-credit policy | Short ages |
Sana et al. (2004) | |||||
Khan et al. (2014) | |||||
Lin and Hou (2015) | |||||
Teng et al. (2002) | |||||
Ghosh and Chaudhuri (2004) | |||||
Kumar et al. (2012) | |||||
Pervin et al. (2016, a) | |||||
Mahata (2012) | |||||
Goswami and Chaudhuri (1991) | |||||
Aggarwal and Jaggi (1995) | |||||
Ting (2015) | |||||
Ouyang et al. (2005) | |||||
Tripathi (2015) | |||||
Annadurai and Uthayakumar (2015) | |||||
Balkhi (2004) | |||||
Pervin et al. (2016, b) | |||||
Our paper |
Author(s) | Imperfec tness | Variable demand | Deterio rations | Trade-credit policy | Short ages |
Sana et al. (2004) | |||||
Khan et al. (2014) | |||||
Lin and Hou (2015) | |||||
Teng et al. (2002) | |||||
Ghosh and Chaudhuri (2004) | |||||
Kumar et al. (2012) | |||||
Pervin et al. (2016, a) | |||||
Mahata (2012) | |||||
Goswami and Chaudhuri (1991) | |||||
Aggarwal and Jaggi (1995) | |||||
Ting (2015) | |||||
Ouyang et al. (2005) | |||||
Tripathi (2015) | |||||
Annadurai and Uthayakumar (2015) | |||||
Balkhi (2004) | |||||
Pervin et al. (2016, b) | |||||
Our paper |
0.1077 | 1.235 | 1.302 | 1.187 | 3478.12 | 3599.45 | 3517.30 | |
0.1125 | 1.301 | 1.213 | 1.171 | 3560.82 | 3011.67 | 3069.57 | |
0.1092 | 1.420 | 1.387 | 1.432 | 3673.19 | 3095.07 | 3112.70 | |
0.1089 | 1.324 | 1.112 | 1.108 | 3488.22 | 2973.16 | 2844.93 | |
0.1107 | 1.403 | 1.274 | 1.392 | 3579.08 | 3077.45 | 3205.71 | |
0.1073 | 1.449 | 1.171 | 1.321 | 3678.99 | 3360.21 | 3119.54 | |
0.128 | 1.610 | 1.534 | 1.558 | 3879.04 | 3232.70 | 3374.56 | |
0.116 | 1.791 | 1.645 | 1.325 | 3927.34 | 3306.18 | 3317.84 | |
0.125 | 1.570 | 1.349 | 1.102 | 4012.57 | 3812.05 | 3518.38 | |
0.144 | 1.397 | 1.747 | 1.560 | 3939.55 | 3670.10 | 3575.68 |
0.1077 | 1.235 | 1.302 | 1.187 | 3478.12 | 3599.45 | 3517.30 | |
0.1125 | 1.301 | 1.213 | 1.171 | 3560.82 | 3011.67 | 3069.57 | |
0.1092 | 1.420 | 1.387 | 1.432 | 3673.19 | 3095.07 | 3112.70 | |
0.1089 | 1.324 | 1.112 | 1.108 | 3488.22 | 2973.16 | 2844.93 | |
0.1107 | 1.403 | 1.274 | 1.392 | 3579.08 | 3077.45 | 3205.71 | |
0.1073 | 1.449 | 1.171 | 1.321 | 3678.99 | 3360.21 | 3119.54 | |
0.128 | 1.610 | 1.534 | 1.558 | 3879.04 | 3232.70 | 3374.56 | |
0.116 | 1.791 | 1.645 | 1.325 | 3927.34 | 3306.18 | 3317.84 | |
0.125 | 1.570 | 1.349 | 1.102 | 4012.57 | 3812.05 | 3518.38 | |
0.144 | 1.397 | 1.747 | 1.560 | 3939.55 | 3670.10 | 3575.68 |
Para meter | value | Total Cost | Profit | |||||||
+50 | 1350 | 1.832 | 1.572 | 1.624 | 3122.05 | 2705.91 | 2812.83 | |||
+30 | 1170 | 1.510 | 1.480 | 1.613 | 2988.71 | 2633.61 | 2694.74 | |||
+10 | 990 | 1.257 | 1.437 | 1.589 | 2734.00 | 2482.09 | 2503.15 | |||
-10 | 810 | 0.941 | 1.428 | 1.541 | 2613.47 | 2290.41 | 2387.40 | |||
-30 | 630 | 0.703 | 1.410 | 1.516 | 2497.38 | 2100.16 | 2206.85 | |||
-50 | 450 | 0.627 | 1.377 | 1.487 | 2206.16 | 2000.00 | 2183.57 | |||
+50 | 600 | 0.904 | 0.867 | 0.880 | 3385.10 | 2834.61 | 2791.38 | |||
+30 | 520 | 0.760 | 0.843 | 0.861 | 3174.51 | 2690.42 | 2614.50 | |||
+10 | 440 | 0.601 | 0.829 | 0.847 | 2893.67 | 2517.83 | 2576.31 | |||
-10 | 360 | 0.472 | 0.820 | 0.831 | 2635.85 | 2385.76 | 2344.10 | |||
-30 | 280 | 0.275 | 0.816 | 0.822 | 2483.77 | 2189.02 | 2208.47 | |||
-50 | 200 | 0.064 | 0.803 | 0.815 | 2305.38 | 1985.47 | 2083.17 | |||
+50 | 150 | 1.966 | 1.973 | 1.989 | 3192.70 | 2911.56 | 2810.55 | |||
+30 | 130 | 1.728 | 1.854 | 1.910 | 2948.16 | 2738.64 | 2655.18 | |||
+10 | 110 | 1.601 | 1.779 | 1.878 | 2749.03 | 2500.53 | 2451.38 | |||
-10 | 90 | 1.486 | 1.611 | 1.763 | 2605.74 | 2374.95 | 2180.76 | |||
-30 | 70 | 1.310 | 1.572 | 1.683 | 2477.19 | 2285.31 | 2090.59 | |||
-50 | 50 | 1.173 | 1.489 | 1.557 | 2204.60 | 2069.73 | 1877.92 | |||
+50 | 300 | 2.765 | 2.581 | 2.593 | 3592.00 | 2746.31 | 2522.20 | |||
+30 | 260 | 2.303 | 2.505 | 2.512 | 3386.17 | 2506.57 | 2257.46 | |||
+10 | 220 | 2.007 | 2.488 | 2.502 | 3152.04 | 2344.10 | 2037.18 | |||
-10 | 180 | 1.841 | 2.394 | 2.581 | 2819.11 | 2183.51 | 1734.62 | |||
-30 | 140 | 1.573 | 2.353 | 2.473 | 2540.83 | 1982.86 | 1504.27 | |||
-50 | 100 | 1.250 | 2.279 | 2.371 | 2274.62 | 1710.27 | 1374.02 | |||
+50 | 22.5 | 2.791 | 2.880 | 2.898 | 2916.47 | 3721.40 | 2883.45 | |||
+30 | 19.5 | 2.675 | 2.741 | 2.805 | 2803.15 | 3569.00 | 2761.74 | |||
+10 | 16.5 | 2.533 | 2.689 | 2.775 | 2785.32 | 3477.54 | 2653.14 | |||
-10 | 13.5 | 2.412 | 2.537 | 2.643 | 2511.63 | 3307.11 | 2578.39 | |||
-30 | 10.5 | 2.370 | 2.481 | 2.550 | 2479.59 | 3258.46 | 2386.55 | |||
-50 | 7.5 | 2.264 | 2.372 | 2.445 | 2333.16 | 3117.35 | 2290.28 | |||
+50 | 30 | 2.672 | 2.503 | 2.475 | 3599.89 | 2800.00 | 2795.64 | |||
+30 | 26 | 2.538 | 2.484 | 2.449 | 3512.04 | 2715.35 | 2683.05 | |||
+10 | 22 | 2.460 | 2.336 | 2.429 | 3475.68 | 2610.97 | 2500.34 | |||
-10 | 18 | 2.397 | 2.260 | 2.405 | 3381.62 | 2573.61 | 2435.65 | |||
-30 | 14 | 2.200 | 2.175 | 2.391 | 3260.91 | 2483.29 | 2362.41 | |||
-50 | 10 | 2.822 | 2.124 | 2.364 | 3129.56 | 2321.79 | 2155.20 | |||
+50 | 0.60 | 1.754 | 2.134 | 2.431 | 3529.87 | 3138.56 | 2490.18 | |||
+30 | 0.52 | 1.694 | 2.089 | 2.379 | 3348.72 | 2763.79 | 2317.93 | |||
+10 | 0.44 | 1.504 | 1.905 | 2.248 | 3095.23 | 2480.58 | 2188.37 | |||
-10 | 0.36 | 1.438 | 1.881 | 2.179 | 2860.93 | 2201.49 | 2020.99 | |||
-30 | 0.28 | 1.215 | 1.753 | 2.098 | 2547.65 | 1973.10 | 1845.73 | |||
-50 | 0.20 | 1.093 | 1.668 | 1.979 | 2196.37 | 1748.53 | 1549.27 | |||
+50 | 75 | 2.402 | 1.402 | 1.657 | 3891.57 | 3124.51 | 3054.36 | |||
+30 | 65 | 2.763 | 1.435 | 1.661 | 3522.56 | 2910.28 | 2839.17 | |||
+10 | 55 | 2.911 | 1.492 | 1.704 | 3205.84 | 2764.33 | 2780.10 | |||
-10 | 45 | 3.250 | 1.555 | 1.783 | 2935.27 | 2459.37 | 2638.61 | |||
-30 | 35 | 3.619 | 1.784 | 2.044 | 2789.42 | 2218.06 | 2529.50 | |||
-50 | 25 | 3.873 | 1.976 | 2.423 | 2642.17 | 2049.62 | 2485.73 |
Para meter | value | Total Cost | Profit | |||||||
+50 | 1350 | 1.832 | 1.572 | 1.624 | 3122.05 | 2705.91 | 2812.83 | |||
+30 | 1170 | 1.510 | 1.480 | 1.613 | 2988.71 | 2633.61 | 2694.74 | |||
+10 | 990 | 1.257 | 1.437 | 1.589 | 2734.00 | 2482.09 | 2503.15 | |||
-10 | 810 | 0.941 | 1.428 | 1.541 | 2613.47 | 2290.41 | 2387.40 | |||
-30 | 630 | 0.703 | 1.410 | 1.516 | 2497.38 | 2100.16 | 2206.85 | |||
-50 | 450 | 0.627 | 1.377 | 1.487 | 2206.16 | 2000.00 | 2183.57 | |||
+50 | 600 | 0.904 | 0.867 | 0.880 | 3385.10 | 2834.61 | 2791.38 | |||
+30 | 520 | 0.760 | 0.843 | 0.861 | 3174.51 | 2690.42 | 2614.50 | |||
+10 | 440 | 0.601 | 0.829 | 0.847 | 2893.67 | 2517.83 | 2576.31 | |||
-10 | 360 | 0.472 | 0.820 | 0.831 | 2635.85 | 2385.76 | 2344.10 | |||
-30 | 280 | 0.275 | 0.816 | 0.822 | 2483.77 | 2189.02 | 2208.47 | |||
-50 | 200 | 0.064 | 0.803 | 0.815 | 2305.38 | 1985.47 | 2083.17 | |||
+50 | 150 | 1.966 | 1.973 | 1.989 | 3192.70 | 2911.56 | 2810.55 | |||
+30 | 130 | 1.728 | 1.854 | 1.910 | 2948.16 | 2738.64 | 2655.18 | |||
+10 | 110 | 1.601 | 1.779 | 1.878 | 2749.03 | 2500.53 | 2451.38 | |||
-10 | 90 | 1.486 | 1.611 | 1.763 | 2605.74 | 2374.95 | 2180.76 | |||
-30 | 70 | 1.310 | 1.572 | 1.683 | 2477.19 | 2285.31 | 2090.59 | |||
-50 | 50 | 1.173 | 1.489 | 1.557 | 2204.60 | 2069.73 | 1877.92 | |||
+50 | 300 | 2.765 | 2.581 | 2.593 | 3592.00 | 2746.31 | 2522.20 | |||
+30 | 260 | 2.303 | 2.505 | 2.512 | 3386.17 | 2506.57 | 2257.46 | |||
+10 | 220 | 2.007 | 2.488 | 2.502 | 3152.04 | 2344.10 | 2037.18 | |||
-10 | 180 | 1.841 | 2.394 | 2.581 | 2819.11 | 2183.51 | 1734.62 | |||
-30 | 140 | 1.573 | 2.353 | 2.473 | 2540.83 | 1982.86 | 1504.27 | |||
-50 | 100 | 1.250 | 2.279 | 2.371 | 2274.62 | 1710.27 | 1374.02 | |||
+50 | 22.5 | 2.791 | 2.880 | 2.898 | 2916.47 | 3721.40 | 2883.45 | |||
+30 | 19.5 | 2.675 | 2.741 | 2.805 | 2803.15 | 3569.00 | 2761.74 | |||
+10 | 16.5 | 2.533 | 2.689 | 2.775 | 2785.32 | 3477.54 | 2653.14 | |||
-10 | 13.5 | 2.412 | 2.537 | 2.643 | 2511.63 | 3307.11 | 2578.39 | |||
-30 | 10.5 | 2.370 | 2.481 | 2.550 | 2479.59 | 3258.46 | 2386.55 | |||
-50 | 7.5 | 2.264 | 2.372 | 2.445 | 2333.16 | 3117.35 | 2290.28 | |||
+50 | 30 | 2.672 | 2.503 | 2.475 | 3599.89 | 2800.00 | 2795.64 | |||
+30 | 26 | 2.538 | 2.484 | 2.449 | 3512.04 | 2715.35 | 2683.05 | |||
+10 | 22 | 2.460 | 2.336 | 2.429 | 3475.68 | 2610.97 | 2500.34 | |||
-10 | 18 | 2.397 | 2.260 | 2.405 | 3381.62 | 2573.61 | 2435.65 | |||
-30 | 14 | 2.200 | 2.175 | 2.391 | 3260.91 | 2483.29 | 2362.41 | |||
-50 | 10 | 2.822 | 2.124 | 2.364 | 3129.56 | 2321.79 | 2155.20 | |||
+50 | 0.60 | 1.754 | 2.134 | 2.431 | 3529.87 | 3138.56 | 2490.18 | |||
+30 | 0.52 | 1.694 | 2.089 | 2.379 | 3348.72 | 2763.79 | 2317.93 | |||
+10 | 0.44 | 1.504 | 1.905 | 2.248 | 3095.23 | 2480.58 | 2188.37 | |||
-10 | 0.36 | 1.438 | 1.881 | 2.179 | 2860.93 | 2201.49 | 2020.99 | |||
-30 | 0.28 | 1.215 | 1.753 | 2.098 | 2547.65 | 1973.10 | 1845.73 | |||
-50 | 0.20 | 1.093 | 1.668 | 1.979 | 2196.37 | 1748.53 | 1549.27 | |||
+50 | 75 | 2.402 | 1.402 | 1.657 | 3891.57 | 3124.51 | 3054.36 | |||
+30 | 65 | 2.763 | 1.435 | 1.661 | 3522.56 | 2910.28 | 2839.17 | |||
+10 | 55 | 2.911 | 1.492 | 1.704 | 3205.84 | 2764.33 | 2780.10 | |||
-10 | 45 | 3.250 | 1.555 | 1.783 | 2935.27 | 2459.37 | 2638.61 | |||
-30 | 35 | 3.619 | 1.784 | 2.044 | 2789.42 | 2218.06 | 2529.50 | |||
-50 | 25 | 3.873 | 1.976 | 2.423 | 2642.17 | 2049.62 | 2485.73 |
Para meter | value | Total Cost | Profit | |||||||
+50 | 60 | 2.402 | 2.265 | 1.875 | 3891.57 | 3124.51 | 3054.36 | |||
+30 | 52 | 2.257 | 2.203 | 1.713 | 3522.56 | 2910.28 | 2839.17 | |||
+10 | 44 | 2.105 | 2.165 | 1.681 | 3205.84 | 2764.33 | 2780.10 | |||
-10 | 36 | 1.943 | 2.081 | 1.578 | 2935.27 | 2459.37 | 2638.61 | |||
-30 | 28 | 1.870 | 1.863 | 1.475 | 2789.42 | 2218.06 | 2529.50 | |||
-50 | 20 | 1.655 | 1.756 | 1.409 | 2642.17 | 2049.62 | 2485.73 | |||
+50 | 15 | 2.795 | 2.531 | 2.320 | 3891.57 | 3124.51 | 3054.36 | |||
+30 | 13 | 2.661 | 2.457 | 2.259 | 3522.56 | 2910.28 | 2839.17 | |||
+10 | 11 | 2.573 | 2.347 | 2.188 | 3205.84 | 2764.33 | 2780.10 | |||
-10 | 9 | 2.412 | 2.201 | 2.096 | 2935.27 | 2459.37 | 2638.61 | |||
-30 | 7 | 2.345 | 2.179 | 2.016 | 2789.42 | 2218.06 | 2529.50 | |||
-50 | 5 | 2.235 | 2.153 | 1.875 | 2642.17 | 2049.62 | 2485.73 | |||
+50 | 60 | 1.987 | 1.853 | 1.760 | 3891.57 | 3124.51 | 3054.36 | |||
+30 | 52 | 1.664 | 1.571 | 1.483 | 3522.56 | 2910.28 | 2839.17 | |||
+10 | 44 | 1.370 | 1.356 | 1.338 | 3205.84 | 2764.33 | 2780.10 | |||
-10 | 36 | 1.297 | 1.283 | 1.275 | 2935.27 | 2459.37 | 2638.61 | |||
-30 | 28 | 1.264 | 1.257 | 1.241 | 2789.42 | 2218.06 | 2529.50 | |||
-50 | 20 | 1.239 | 1.221 | 1.195 | 2642.17 | 2049.62 | 2485.73 | |||
+50 | 45 | 2.354 | 2.279 | 2.165 | 3567.10 | 3049.31 | 3098.21 | |||
+30 | 39 | 2.170 | 2.086 | 1.952 | 3417.05 | 2994.22 | 2947.18 | |||
+10 | 33 | 1.941 | 1.876 | 1.740 | 3307.53 | 2885.31 | 2856.37 | |||
-10 | 27 | 1.769 | 1.635 | 1.509 | 3268.37 | 2765.42 | 2664.00 | |||
-30 | 21 | 1.526 | 1.470 | 1.358 | 3191.30 | 2670.51 | 2509.11 | |||
-50 | 15 | 1.391 | 1.258 | 1.174 | 3034.67 | 2500.00 | 2481.03 | |||
+50 | 0.45 | 1.310 | 1.465 | 1.589 | 2473.11 | 1730.22 | 2017.27 | |||
+30 | 0.39 | 1.574 | 1.640 | 1.736 | 2705.43 | 1918.47 | 2384.53 | |||
+10 | 0.33 | 1.812 | 1.922 | 1.989 | 3058.24 | 2164.38 | 2673.40 | |||
-10 | 0.27 | 2.123 | 2.070 | 2.145 | 3347.80 | 2351.06 | 2945.82 | |||
-30 | 0.21 | 2.492 | 2.195 | 2.287 | 3692.47 | 2537.64 | 3255.70 | |||
-50 | 0.15 | 2.760 | 2.358 | 2.460 | 3903.12 | 2799.00 | 3509.35 | |||
+50 | 30 | 2.385 | 2.072 | 2.110 | 3392.46 | 2918.36 | 2840.79 | |||
+30 | 26 | 2.200 | 1.915 | 2.048 | 3175.13 | 2875.42 | 2711.54 | |||
+10 | 22 | 2.071 | 1.854 | 1.991 | 2917.00 | 2704.60 | 2657.18 | |||
-10 | 18 | 1.848 | 1.774 | 1.867 | 2739.26 | 2538.11 | 2302.63 | |||
-30 | 14 | 1.639 | 1.640 | 1.790 | 2543.35 | 2326.83 | 2199.29 | |||
-50 | 10 | 1.325 | 1.573 | 1.615 | 2319.67 | 2100.00 | 1978.63 | |||
+50 | 1.8 | 1.367 | 1.470 | 1.585 | 3141.47 | 2758.10 | 2890.05 | |||
+30 | 1.56 | 1.532 | 1.609 | 1.779 | 3250.26 | 2893.55 | 2918.62 | |||
+10 | 1.32 | 1.727 | 1.826 | 1.963 | 3319.51 | 2964.28 | 3022.37 | |||
-10 | 1.08 | 1.904 | 1.995 | 2.057 | 3471.43 | 3027.83 | 3126.29 | |||
-30 | 0.84 | 2.157 | 2.257 | 2.376 | 3520.79 | 3119.44 | 3257.81 | |||
-50 | 0.6 | 2.370 | 2.450 | 2.538 | 3752.00 | 3348.63 | 3486.90 | |||
+50 | 0.6 | 2.752 | 2.568 | 2.330 | 4180.57 | 3042.78 | 3506.79 | |||
+30 | 0.52 | 2.695 | 2.418 | 2.257 | 3912.36 | 2965.03 | 3481.20 | |||
+10 | 0.44 | 2.516 | 2.343 | 2.194 | 3764.25 | 2860.24 | 3358.18 | |||
-10 | 0.36 | 2.404 | 2.267 | 2.210 | 3580.19 | 2725.57 | 3293.49 | |||
-30 | 0.28 | 2.279 | 2.001 | 1.935 | 3318.38 | 2530.29 | 3167.16 | |||
-50 | 0.20 | 2.011 | 1.883 | 1.520 | 3127.93 | 2350.03 | 2948.57 |
Para meter | value | Total Cost | Profit | |||||||
+50 | 60 | 2.402 | 2.265 | 1.875 | 3891.57 | 3124.51 | 3054.36 | |||
+30 | 52 | 2.257 | 2.203 | 1.713 | 3522.56 | 2910.28 | 2839.17 | |||
+10 | 44 | 2.105 | 2.165 | 1.681 | 3205.84 | 2764.33 | 2780.10 | |||
-10 | 36 | 1.943 | 2.081 | 1.578 | 2935.27 | 2459.37 | 2638.61 | |||
-30 | 28 | 1.870 | 1.863 | 1.475 | 2789.42 | 2218.06 | 2529.50 | |||
-50 | 20 | 1.655 | 1.756 | 1.409 | 2642.17 | 2049.62 | 2485.73 | |||
+50 | 15 | 2.795 | 2.531 | 2.320 | 3891.57 | 3124.51 | 3054.36 | |||
+30 | 13 | 2.661 | 2.457 | 2.259 | 3522.56 | 2910.28 | 2839.17 | |||
+10 | 11 | 2.573 | 2.347 | 2.188 | 3205.84 | 2764.33 | 2780.10 | |||
-10 | 9 | 2.412 | 2.201 | 2.096 | 2935.27 | 2459.37 | 2638.61 | |||
-30 | 7 | 2.345 | 2.179 | 2.016 | 2789.42 | 2218.06 | 2529.50 | |||
-50 | 5 | 2.235 | 2.153 | 1.875 | 2642.17 | 2049.62 | 2485.73 | |||
+50 | 60 | 1.987 | 1.853 | 1.760 | 3891.57 | 3124.51 | 3054.36 | |||
+30 | 52 | 1.664 | 1.571 | 1.483 | 3522.56 | 2910.28 | 2839.17 | |||
+10 | 44 | 1.370 | 1.356 | 1.338 | 3205.84 | 2764.33 | 2780.10 | |||
-10 | 36 | 1.297 | 1.283 | 1.275 | 2935.27 | 2459.37 | 2638.61 | |||
-30 | 28 | 1.264 | 1.257 | 1.241 | 2789.42 | 2218.06 | 2529.50 | |||
-50 | 20 | 1.239 | 1.221 | 1.195 | 2642.17 | 2049.62 | 2485.73 | |||
+50 | 45 | 2.354 | 2.279 | 2.165 | 3567.10 | 3049.31 | 3098.21 | |||
+30 | 39 | 2.170 | 2.086 | 1.952 | 3417.05 | 2994.22 | 2947.18 | |||
+10 | 33 | 1.941 | 1.876 | 1.740 | 3307.53 | 2885.31 | 2856.37 | |||
-10 | 27 | 1.769 | 1.635 | 1.509 | 3268.37 | 2765.42 | 2664.00 | |||
-30 | 21 | 1.526 | 1.470 | 1.358 | 3191.30 | 2670.51 | 2509.11 | |||
-50 | 15 | 1.391 | 1.258 | 1.174 | 3034.67 | 2500.00 | 2481.03 | |||
+50 | 0.45 | 1.310 | 1.465 | 1.589 | 2473.11 | 1730.22 | 2017.27 | |||
+30 | 0.39 | 1.574 | 1.640 | 1.736 | 2705.43 | 1918.47 | 2384.53 | |||
+10 | 0.33 | 1.812 | 1.922 | 1.989 | 3058.24 | 2164.38 | 2673.40 | |||
-10 | 0.27 | 2.123 | 2.070 | 2.145 | 3347.80 | 2351.06 | 2945.82 | |||
-30 | 0.21 | 2.492 | 2.195 | 2.287 | 3692.47 | 2537.64 | 3255.70 | |||
-50 | 0.15 | 2.760 | 2.358 | 2.460 | 3903.12 | 2799.00 | 3509.35 | |||
+50 | 30 | 2.385 | 2.072 | 2.110 | 3392.46 | 2918.36 | 2840.79 | |||
+30 | 26 | 2.200 | 1.915 | 2.048 | 3175.13 | 2875.42 | 2711.54 | |||
+10 | 22 | 2.071 | 1.854 | 1.991 | 2917.00 | 2704.60 | 2657.18 | |||
-10 | 18 | 1.848 | 1.774 | 1.867 | 2739.26 | 2538.11 | 2302.63 | |||
-30 | 14 | 1.639 | 1.640 | 1.790 | 2543.35 | 2326.83 | 2199.29 | |||
-50 | 10 | 1.325 | 1.573 | 1.615 | 2319.67 | 2100.00 | 1978.63 | |||
+50 | 1.8 | 1.367 | 1.470 | 1.585 | 3141.47 | 2758.10 | 2890.05 | |||
+30 | 1.56 | 1.532 | 1.609 | 1.779 | 3250.26 | 2893.55 | 2918.62 | |||
+10 | 1.32 | 1.727 | 1.826 | 1.963 | 3319.51 | 2964.28 | 3022.37 | |||
-10 | 1.08 | 1.904 | 1.995 | 2.057 | 3471.43 | 3027.83 | 3126.29 | |||
-30 | 0.84 | 2.157 | 2.257 | 2.376 | 3520.79 | 3119.44 | 3257.81 | |||
-50 | 0.6 | 2.370 | 2.450 | 2.538 | 3752.00 | 3348.63 | 3486.90 | |||
+50 | 0.6 | 2.752 | 2.568 | 2.330 | 4180.57 | 3042.78 | 3506.79 | |||
+30 | 0.52 | 2.695 | 2.418 | 2.257 | 3912.36 | 2965.03 | 3481.20 | |||
+10 | 0.44 | 2.516 | 2.343 | 2.194 | 3764.25 | 2860.24 | 3358.18 | |||
-10 | 0.36 | 2.404 | 2.267 | 2.210 | 3580.19 | 2725.57 | 3293.49 | |||
-30 | 0.28 | 2.279 | 2.001 | 1.935 | 3318.38 | 2530.29 | 3167.16 | |||
-50 | 0.20 | 2.011 | 1.883 | 1.520 | 3127.93 | 2350.03 | 2948.57 |
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