An application of Genetic Algorithm and PSO in an inventory model for single deteriorating item with variable demand dependent on marketing strategy and displayed stock level

Document Type : Article

Authors

1 Department of Mathematics, The University of Burdwan, Burdwan-713104, India

2 School of Engineering and Sciences, Tecnológico de Monterrey, Ave. E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, Nuevo León, México

3 Department of Mathematics & Statistics, Banasthali University, Banathali, India

Abstract

This paper deals with an inventory model for single deteriorated item considering the impact of marketing decisions and the displaced stock level on the demand. Partial backlogged shortages are allowed. Analyzing the storage capacity of the shop and demand parameters, different scenarios have been investigated. For each scenario, the corresponding problem has been formulated as a nonlinear mixed integer optimization problem and solved by real coded genetic algorithm and particle swarm optimization technique.  To illustrate the inventory model, a numerical example has been solved and sensitivity analyses have been done numerically to study the effect of changes of different parameters on the optimal policies.

Keywords

Main Subjects


References
1. Mandal, B.N. and Phaujdar, S. An inventory model
for deteriorating items and stock-dependent consumption
rate", Journal of Operational Research Society,
40(5), pp. 483-488 (1989).
2. Pakkala, T.P.M. and Achary, K.K. A deterministic
inventory model for deteriorating items with two
warehouse and nite replenishment rate", European
Journal of Operational Research, 57(1), pp. 71-76
(1992).
3. Goyal, S.K. and Gunasekaran, A. An integrated
production-inventory-marketing model for deteriorating
items", Computers & Industrial Engineering,
28(4), pp. 755-762 (1995).
4. Giri, B.C., Pal, S., Goswami, A., and Chaudhuri,
K.S. An inventory model for deteriorating items with
stock-dependent demand rate", European Journal of
Operational Research, 95(3), pp. 604-610 (1996).
A.K. Bhunia et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 1641{1655 1653
5. Bhunia, A.K. and Maiti, M. An inventory model
for decaying items with selling price, frequency of
advertisement and linearly time-dependent demand
with shortages", IAPQR Transactions, 22, pp. 41-49
(1997).
6. Bhunia, A.K. and Maiti, M. A two warehouses inventory
model for deteriorating items with linear trend
in demand and shortages", Journal of Operational
Research Society, 49(3), pp. 287-292 (1997).
7. Luo, W. An integrated inventory system for perishable
goods with backordering", Computers & Industrial
Engineering, 34(3), pp. 685-693 (1998).
8. Chang, J. and Dye, C.Y. An EOQ model for deteriorating
items with time varying and partial backlogging",
Journal of the Operational Research Society,
50(11), pp. 1176 -1182 (1999).
9. Abad, P.L. Optimal lot size for a perishable good
under conditions of nite production and partial
backordering and lost sale", Computers & Industrial
Engineering, 38(4), pp. 457-468 (2000).
10. Pal, A.K., Bhunia, A.K., and Mukherjee, R.N. Optimal
lot size model for deteriorating items with demand
rate dependent on displayed stock level (DSL) and partial
backordering", European Journal of Operational
Research, 175(2), pp. 977-991 (2006).
11. Dye, C.Y., Ouyang, L.Y., and Hsieh, T.P. Deterministic
inventory model for deteriorating items with the
capability constraint and time-proportional backlogging
rate", European Journal of Operational Research,
178(3), pp. 789-807 (2007).
12. Pal, P., Bhunia, A.K., and Goyal, S.K. On optimal
partially integrated production and marketing policy
with variable demand under
exibility and reliability
considerations via genetic algorithm", Applied Mathematics
and Computation, 188(1), pp. 525-537 (2007).
13. Taleizadeh, A.A., Niaki, S.T., Sha i, N.,
Ghavamizadeh, Meibodi, R., and Jabbarzadeh,
A. A particle swarm optimization approach for
constraint joint single buyer single vendor inventory
problem with changeable lead-time and (r;Q) policy
in supply chain", International Journal of Advanced
Manufacturing Technology, 51(9), pp. 1209-1223
(2010).
14. Bhunia, A.K., Pal, P., Chattopadhyay, S., and Medya,
B.K. An inventory model of two-warehouse system
with variable demand dependent on instantaneous
displayed stock and marketing decision via hybrid
RCGA", International Journal of Industrial Engineering
Computations, 2(2), pp. 351-368 (2011).
15. Bhunia, A.K. and Shaikh, A.A. A two warehouse
inventory model for deteriorating items with time
dependent partial backlogging and variable demand
dependent on marketing strategy and time", International
Journal of Inventory Control and Management,
1, pp. 95-110 (2011).
16. Bhunia, A.K. and Shaikh, A.A. A deterministic model
for deteriorating items with displayed inventory level
dependent demand rate incorporating marketing decisions
with transportation cost", International Journal
of Industrial Engineering Computations, 2, pp. 547-
562 (2011).
17. Liang, Y. and Zhou, F. A two-warehouse inventory
model for deteriorating items under conditionally
permissible delay in payment", Applied Mathematical
Modelling, 35(5), pp. 2221-2231 (2011).
18. Yang, H.L. Two-warehouse partial backlogging inventory
models with three-parameter Weibull distribution
deterioration under in
ation", International Journal of
Production Economics, 138(1), pp. 107-116 (2012).
19. Taleizadeh, A.A., Pentico, D.W., Aryanezhad, M.B.,
and Ghoreyshi, M. An economic order quantity model
with partial backordering and a special sale price",
European Journal of Operational Research, 221(3), pp.
571-583 (2012).
20. Taleizadeh, A.A., Niaki, S.T.A., and Makui, A.
Multi-product multi-chance constraint multi-buyer
single-vendor supply chain problem with stochastic
demand and variable lead time", Expert Systems with
Applications, 39, pp. 5338-5348 (2012).
21. Bhunia, A.K., Shaikh, A.A., Maiti, A.K., and Maiti,
M. A two warehouse deterministic inventory model
for deteriorating items with a linear trend in time
dependent demand over nite time horizon by elitist
real-coded genetic algorithm", International Journal
Industrial Engineering and Computations, 4(2), pp.
241-258 (2013).
22. Yang, H.L. and Chang, C.T. A two-warehouse partial
backlogging inventory model for deteriorating items
with permissible delay in payment under in
ation",
Applied Mathematical Modelling, 37(5), pp. 2717-2726
(2013).
23. Taleizadeh, A.A., Pentico, D.W., Jabalameli, M.S.,
and Aryanezhad, M.B. An economic order quantity
model with multiple partial prepayments and
partial backordering", Mathematical and Computer
Modelling, 57(3-4), pp. 311-323 (2013).
24. Taleizadeh, A.A., Pentico, D.W., Jabalameli, M.S. and
Aryanezhad, M.B. An EOQ problem under partial
delayed payment and partial backordering", Omega,
41(2), pp. 354-368 (2013).
25. Taleizadeh, A.A., Wee, H.M., and Jolai, F. Revisiting
fuzzy rough economic order quantity model for
deteriorating items considering quantity discount and
prepayment", Mathematical and Computer Modeling,
57(5-6), pp. 1466-1479 (2013).
26. Bhunia, A.K. and Shaikh, A.A. A deterministic
inventory model for deteriorating items with selling
price dependent demand and three-parameter Weibull
distributed deterioration", International Journal of
Industrial Engineering Computations, 5(3), pp. 497-
510 (2014).
27. Bhunia, A.K., Mahato, S.K., Shaikh, A.A., and
Jaggi, C.K. A deteriorating inventory model with
displayed stock-level-dependent demand and partially
1654 A.K. Bhunia et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 1641{1655
backlogged shortages with all unit discount facilities
via particle swarm optimization", International Journal
of System Science Operations and Logistic, 1(3),
pp. 164-180 (2015).
28. Bhunia, A.K., Shaikh, A.A., and Gupta, R.K. A
study on two-warehouse partially backlogged deteriorating
inventory models under in
ation via particle
swarm optimization", International Journal of System
Science, 46(6), pp. 1036-1050 (2015).
29. Bhunia, A.K., Shaikh, A.A., Sharma, G., and Pareek,
S. A two storage inventory model for deteriorating
items with variable demand and partial backlogging",
Journal of Industrial and Production Engineering,
32(4), pp. 263-272 (2015).
30. Mondal, B., Bhunia, A.K., and Maiti, M. A model of
two storage inventory system under stock dependent
selling rate incorporating marketing decisions and
transportation cost with optimum release rule", Tamsui
Oxford Journal of Mathematical Sciences, 23(3),
pp. 243-267 (2007).
31. Baker, R.C. and Urban, T.L. A deterministic inventory
system with an inventory-level-dependent demand
rate", Journal of Operational Research Society, 39(9),
pp. 1823-1831 (1988).
32. Datta, T.K., and Pal, A.K. A note on an inventory
model with inventory-level-dependent demand rate",
Journal of the Operational Research Society, 41(10),
pp. 971 -975 (1990).
33. Urban, T.L. An inventory model with an inventorylevel-
dependent rate and relaxed terminal conditions",
Journal of Operational Research Society, 43(7), pp.
721-724 (1992).
34. Paul, K., Datta, T.K., Chaudhuri, K.S., and Pal, A.K.
An inventory model with two component demand rate
and shortages", Journal of the Operational Research
Society, 47(8), pp. 1029-1036 (1996).
35. Urban, T.L. Deterministic inventory models incorporating
marketing decisions", Computers & Industrial
Engineering, 22(1), pp. 85-93 (1992).
36. Abad, P.L. Optimal pricing and lot-sizing when the
supplier o ers a temporary price reduction over an
interval", Computers & Industrial Engineering, 30(1),
pp. 63-74 (2003).
37. Pal, A.K., Bhunia, A.K. and Mukherjee, R.N.
A marketing-oriented inventory model with threecomponent
demand rate dependent on displayed stock
level (DSL)", Journal of the Operational Research
Society, 56, pp. 113-118 (2004).
38. Sarkar, B. An EOQ model with delay-in-payments
and time-varying deterioration rate", Mathematical
and Computer Modelling, 55(3-4), pp. 367-377 (2012).
39. Sarkar, B. A production-inventory model with probabilistic
deterioration in two-echelon supply chain management",
Applied Mathematical Modelling, 37(5), pp.
3138-3151 (2013).
40. Sarkar, B. Supply chain coordination with variable
backorder, inspections, and discount policy for xed
lifetime products", Mathematical Problem in Engineering,
Article ID 6318737, 14 pages (2016).
41. Sarkar, B., Saren, S., and Cardenas-Barron, L.E. An
inventory model with trade-credit policy and variable
deterioration for xed lifetime products", Annals of
Operations Research, 229(1), pp. 677-702 (2015).
42. Sarkar, B., Mandal, P., and Sarkar, S. An EMQ model
with price and time dependent demand under the e ect
of reliability and in
ation", Applied Mathematics and
Computation, 231, pp. 414-421 (2014).
43. Sarkar, B. and Sarkar, S. An improved inventory
model with partial backlogging, time varying deterioration
and stock-dependent demand", Economic
Modelling, 30, pp. 924-932 (2013).
44. Sarkar, B. and Sarkar, S. Variable deterioration and
demand-An inventory model", Economic Modelling,
31, pp. 548-556 (2013).
45. Goldberg, D.E., Genetic Algorithms: Search, Optimization
and Machine Learning, Addison Wesley,
Reading, MA (1989).
46. Holland, J.H., Adaptation of Natural and Arti cial
System, University of Michigan Press, Ann Arbor
(1975).
47. Michalawicz, Z., Genetic Algorithms + Data structure
= Evolution Programs, Springer-Verlag, Berlin (1992).
48. Deb, K., Optimization for Engineering Design -
Algorithms and Examples, Prentice-Hall of India, New
Delhi (1995).
49. Sakawa, M., Genetic Algorithms and Fuzzy Multi-
Objective Optimization, Kluwer Academic Publishers
(2002).
50. Bhunia, A.K., Sahoo, L., and Roy, D. Reliability
stochastic optimization for a series system with interval
component reliability via genetic algorithm",
Applied Mathematics and Computation, 216(3), pp.
929-939 (2010).
51. Eberhart, R.C. and Kennedy, J.F. A new optimizer
using particle swarm theory", In Proceeding of the
Sixth International Symposium on Micro Machine and
Human Science, Nagoya, Japan, pp. 39-43 (1995).
52. Kennedy, J.F. and Eberhart, R.C. Particle swarm
optimization", In Proceeding of the IEEE International
Conference on Neural Network, IV, Perth, Australia,
pp. 1942-1948 (1995).
53. Clerc, M. The swarm and queen: towards a deterministic
and adaptive particle swarm optimization",
In Proceedings of IEEE Congress on Evolutionary
Computation, Washington, DC, USA, pp. 1951-1957
(1999).
54. Clerc, M. and Kennedy, J.F. The particle swarm:
explosion, stability, and Convergence in a multidimensional
complex space", IEEE Trans Evol Comput.,
6(1), pp. 58-73 (2002).
A.K. Bhunia et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 1641{1655 1655