A Study of an EOQ Model of Growing Items with Parabolic Dense Fuzzy Lock Demand Rate
Abstract
:1. Introduction
1.1. Literature Review on Dense Fuzzy Sets
1.2. Literature Review on Inventory Models
1.3. Motivation and Specific Study
2. Preliminaries
3. Arithmetic Operation over Parabolic Dense Fuzzy Numbers
- (i)
- Addition of Two Parabolic Dense Fuzzy Numbers
- (ii)
- Subtraction of Two Parabolic Dense Fuzzy Numbers
- (iii)
- Scalar multiplication of Parabolic Dense Fuzzy Numbers
- (iv)
- Multiplication of Two Parabolic Dense Fuzzy Numbers
- (v)
- Inverse of a Parabolic Dense Fuzzy Number
4. Formulation of Crisp Model
- (i)
- We considered an additional cost for feeding the growing items.
- (ii)
- Feeding cost depended on the weight of the items.
- (iii)
- The growth function was approximated by a linear function.
- (iv)
- We considered an idle cost for the growth period and cleaning period.
5. Fuzzy Mathematical Model
5.1. Rules of Finding Key Values of the Fuzzy Locks
5.2. Solution Algorithm
6. A Real Case Study
Sensitivity Analysis
7. Graphical Illustration
8. Managerial Insights
- (i)
- Learning experience is a crucial part of any inventory problem to optimize the inventory cost.
- (ii)
- The decision maker can optimize the inventory cost by utilizing proper key values.
- (iii)
- The less qualified decision maker can also minimize the cost using the PDFLS approach.
- (iv)
- The PDFLS approach gives a finer optimum than the parabolic dense set approach.
9. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Notations
Demand rate per unit time (g/year) | |
Growing rate per fish per unit time | |
Approximated weight of a fingerling (g) | |
Approximated weight of a fish at the time of selling (g) | |
Total weight of inventory at time t (g) | |
The time required to clean the pond for starting a new cycle (years) | |
Growing period (years) (decision variable) | |
Selling period (years) (decision variable) | |
Cycle length (years) | |
Total number of fish bought in each period (decision variable) | |
Feeding cost per unit item per unit time ( ) | |
Holding cost per unit time ($/year) | |
Setup cost, cost for preparing the environment per period ($) | |
Price of fingerlings per gram ($/g) | |
Natural idle cost per unit time ($/year); this cost is considered when the retailer cannot fulfill the customer’s demand | |
B | Operational cost per cycle ($) |
Fuzzy deviation parameters |
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Authors | Product | Demand | Matter of Growing Items | Solution Approach | |
---|---|---|---|---|---|
Conventional Items | Growing Items | ||||
Harris [14] | ✓ | Crisp | Not included | Convex Optimization | |
Salameh and Jaber [32] | ✓ | Crisp | Not included | Statistical method | |
Rezaei [28] | ✓ | Crisp | Non-specific | Convex Optimization | |
Zhang et al. [29] | ✓ | Crisp | Non-specific | Convex Optimization | |
Nobil et al. [27] | ✓ | Crisp | Poultry | Convex Optimization | |
Sebatjane and Adetunji [33] | ✓ | Crisp | Non-specific | Convex Optimization | |
Wee et al. [34] | ✓ | Crisp | Non-specific | Convex Optimization | |
Alfares and Afzal [35] | ✓ | Crisp | Non-specific | Convex Optimization | |
Rana et al. [36] | ✓ | Crisp | Non-specific | Convex Optimization | |
This Paper | ✓ | Fuzzy (PDFS and PDFLS) | Fishery | New solution algorithm via new defuzzification methods |
Approach | ||||||
---|---|---|---|---|---|---|
Crisp | - | 0.5479 | 0.4330 | 2887 | 319,476.8 | - |
General Fuzzy | - | 0.5479 | 0.4330 | 2790 | 308,834.3 | −3.33 |
Parabolic dense fuzzy | 1 | 0.5479 | 0.4327 | 2838 | 314,155.5 | −1.66 |
2 | 0.5479 | 0.4321 | 2846 | 315,042.4 | −1.39 | |
3 | 0.5479 | 0.4318 | 2852 | 315,633.7 | −1.20 | |
PDFLS | 1 | 05479 | 0.4330 | 2740 | 303,233.0 | −5.08 |
2 | 0.5479 | 0.4331 | 2724 | 301,459.3 | −5.64 | |
3 | 0.5479 | 0.4330 | 2713 | 300,276.8 | −6.00 |
Parameter | % Change | |||||
---|---|---|---|---|---|---|
+30 | 0.5151 | 0.4659 | 2919 | 286,691.8 | −10.26 | |
+10 | 0.5369 | 0.4440 | 2782 | 296,074.7 | −7.32 | |
−10 | 0.5589 | 0.4220 | 2644 | 304,128.4 | −4.80 | |
−30 | 0.5808 | 0.4002 | 2507 | 310,708.3 | −2.74 | |
+30 | 0.7452 | 0.2358 | 1136 | 231,708.0 | −27.47 | |
+10 | 0.6137 | 0.3673 | 2092 | 289,909.2 | −9.25 | |
−10 | 0.4822 | 0.4988 | 3472 | 298,384.2 | −6.60 | |
−30 | 0.3507 | 0.6303 | 5642 | 259,093.1 | −18.90 | |
+30 | 0.5479 | 0.4330 | 2713 | 301,090.8 | −5.75 | |
+10 | 0.5479 | 0.4330 | 2713 | 300,548.1 | −5.92 | |
−10 | 0.5479 | 0.4330 | 2713 | 300,005.4 | −6.09 | |
−30 | 0.5479 | 0.4330 | 2713 | 299,462.7 | −6.26 | |
+30 | 0.5479 | 0.4330 | 2713 | 389,485.0 | +21.91 | |
+10 | 0.5479 | 0.4330 | 2713 | 330,012.8 | +3.29 | |
−10 | 0.5479 | 0.4330 | 2713 | 270,540.7 | −15.31 | |
−30 | 0.5479 | 0.4330 | 2713 | 211,068.6 | −33.93 | |
+30 | 0.5479 | 0.4330 | 2713 | 300,306.8 | −6.00 | |
+10 | 0.5479 | 0.4330 | 2713 | 300,286.3 | −6.00 | |
−10 | 0.5479 | 0.4330 | 2713 | 300,266.8 | −6.01 | |
−30 | 0.5479 | 0.4330 | 2713 | 300,246.8 | −6.01 | |
+30 | 0.5479 | 0.4330 | 2713 | 300,283.6 | −6.00 | |
+10 | 0.5479 | 0.4330 | 2713 | 300,279.0 | −6.00 | |
−10 | 0.5479 | 0.4330 | 2713 | 300,274.5 | −6.01 | |
−30 | 0.5479 | 0.4330 | 2713 | 300,270.0 | −6.01 | |
+30 | 0.5479 | 0.4330 | 2451 | 271,280.7 | −15.08 | |
+10 | 0.5479 | 0.4330 | 2626 | 290,611.4 | −9.03 | |
−10 | 0.5479 | 0.4330 | 2800 | 309,942.1 | −2.98 | |
−30 | 0.5479 | 0.4330 | 2975 | 329,272.8 | +3.06 | |
+30 | 0.5479 | 0.4330 | 2923 | 323,512.8 | +1.26 | |
+10 | 0.5479 | 0.4330 | 2783 | 308,022.1 | −3.58 | |
−10 | 0.5479 | 0.4330 | 2643 | 292,531.4 | −8.43 | |
−30 | 0.5479 | 0.4330 | 2503 | 277,040.7 | −13.28 |
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Maity, S.; De, S.K.; Pal, M.; Mondal, S.P. A Study of an EOQ Model of Growing Items with Parabolic Dense Fuzzy Lock Demand Rate. Appl. Syst. Innov. 2021, 4, 81. https://doi.org/10.3390/asi4040081
Maity S, De SK, Pal M, Mondal SP. A Study of an EOQ Model of Growing Items with Parabolic Dense Fuzzy Lock Demand Rate. Applied System Innovation. 2021; 4(4):81. https://doi.org/10.3390/asi4040081
Chicago/Turabian StyleMaity, Suman, Sujit Kumar De, Madhumangal Pal, and Sankar Prasad Mondal. 2021. "A Study of an EOQ Model of Growing Items with Parabolic Dense Fuzzy Lock Demand Rate" Applied System Innovation 4, no. 4: 81. https://doi.org/10.3390/asi4040081