Inventory of complementary products with stock-dependent demand under vendor-managed inventory with consignment policy

Document Type : Article

Authors

Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez avenue, 1591634311, Tehran, Iran

Abstract

This paper proposes an integrated two-stage model, which consists of one vendor and one buyer for two complementary products. The vendor produces two types of products and delivers them to the buyer in distinct batches. Buyer stocks items in the warehouse and on the shelf. The demand for each product is sensitive to stock levels of both products. A vendor managed inventory with consignment stock policy is considered. The number of shipments and replenishment lot sizes are jointly determined as decision variables in such a way that total profit is maximized. The numerical study shows that as complementary rate increases, the quantity of transfers and demand of both products increase. Hence, ignoring the complementation between products leads to some customers lost.

Keywords

Main Subjects


References
1. Modak, N.M., Panda, S., and Sana, S.S. \Pricing
policy and coordination for a two-layer supply chain
of duopolistic retailers and socially responsible manufacturer",
International Journal of Logistics Research
and Applications, 19(6), pp. 487-508 (2016).
2. Roy, M.D., Sana, S.S., and Chaudhuri, K. \An integrated
producer-buyer relationship in the environment
of EMQ and JIT production systems", International
Journal of Production Research, 50(19), pp. 5597-5614
(2012).
3. Goyal, S.K. \An integrated inventory model for a
single supplier-single customer problem", International
Journal of Production Research, 15(1), pp. 107-111
(1977).
M. Hemmati et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2347{2360 2357
4. Banerjee, A. \A joint economic-lot-size model for
purchaser and vendor", Decision Sciences, 17(3), pp.
292-311 (1986).
5. Goyal, S.K. \A joint economic-lot-size model for purchaser
and vendor: A comment", Decision Sciences,
19(1), pp. 236-241 (1988).
6. Jokar, M.R.A. and Sajadieh, M.S. \Optimizing a
joint economic lot sizing problem with price-sensitive
demand", Scientia Iranica. Transactions E, Industrial
Engineering, 16(2), pp. 159-164 (2009).
7. Kim, T., Hong, Y., and Chang, S.Y. \Joint economic
procurement-production-delivery policy for multiple
items in a single-manufacturer, multiple-retailer system",
International Journal of Production Economics,
103(1), pp. 199-208 (2006).
8. Sajadieh, M.S., Jokar, M.R.A., and Modarres, M.
\Developing a coordinated vendor-buyer model in
two-stage supply chains with stochastic lead-times",
Computers and Operations Research, 36(8), pp. 2484-
2489 (2009).
9. Ben-Daya, M., Darwish, M., and Ertogral, K. \The
joint economic lot sizing problem: Review and extensions",
European Journal of Operational Research,
185(2), pp. 726-742 (2008).
10. Glock, C.H. \The joint economic lot size problem:
A review", International Journal of Production Economics,
135(2), pp. 671-686 (2012).
11. Sajadieh, M.S., Thorstenson, A., and Akbari Jokar,
M.R. \An integrated vendor-buyer model with stockdependent
demand", Transportation Research Part E:
Logistics and Transportation Review, 46(6), pp. 963-
974 (2010).
12. Pal, B., Sana, S.S., and Chaudhuri, K. \Joint pricing
and ordering policy for two echelon imperfect production
inventory model with two cycles", International
Journal of Production Economics, 155, pp. 229-238
(2014).
13. Sana, S.S. \Optimal production lot size and reorder
point of a two-stage supply chain while random demand
is sensitive with sales teams' initiatives", International
Journal of Systems Science, 47(2), pp. 450-
465 (2014).
14. Sana, S.S. and Panda, S. \Optimal sales team's
initiatives and pricing of pharmaceutical products",
International Journal of Systems Science: Operations
& Logistics, 2(3), pp. 168-176 (2015).
15. Ma, P.,Wang, H., and Shang, J. \Supply chain channel
strategies with quality and marketing e ort-dependent
demand", International Journal of Production Economics,
144(2), pp. 572-581 (2013).
16. Teng, J.T. and Chang, C.T. \Economic production
quantity models for deteriorating items with price
and stock dependent demand", Computer & Operation
Research, 32(2), pp. 297-308 (2005).
17. Goyal, S.K. and Chang, C.T. \Optimal ordering and
transfer policy for an inventory with stock dependent
demand", European Journal of Operational Research,
196(1), pp. 177-185 (2009).
18. Duan, Y., Li, G., Tien, J.M., and Huo, J. \Inventory
models for perishable items with inventory level dependent
demand rate", Applied Mathematical Modelling,
36(10), pp. 5015-5028 (2012).
19. Yang, S., Hong, K.S., and Lee, C. \Supply chain
coordination with stock-dependent demand rate and
credit incentives", International Journal of Production
Economics, 157(1), pp. 105-111 (2014).
20. Braglia, M. and Zavanella, L. \Modelling an industrial
strategy for inventory management in supply chains:
the 'Consignment Stock' case", International Journal
of Production Research, 41(16), pp. 3793-3808 (2003).
21. Yi, H. and Sarker, B.R. \An operational policy for
an integrated inventory system under consignment
stock policy with controllable lead time and buyers'
space limitation", Computers and Operations Research,
40(11), pp. 2632-2645 (2013).
22. Zanoni, S. and Jaber, M.Y. \A two-level supply
chain with consignment stock agreement and stockdependent
demand", International Journal of Production
Research, 53(12), pp. 3561-3572 (2015).
23. Wang, S.P. and Lee, W. \A note on \A two-level
supply chain with consignment stock agreement and
stock-dependent demand", International Journal of
Production Research, 54(9), pp. 2750-2756 (2016).
24. Giri, B.C. and Bardhan, S. \A vendor-buyer JELS
model with stock-dependent demand and consigned
inventory under buyer's space constraint", Operational
Research, 15(1), pp. 79-93 (2015).
25. Hariga, M.A. and Al-Ahmari, A. \An integrated retail
space allocation and lot sizing models under vendor
managed inventory and consignment stock arrangements",
Computers and Industrial Engineering, 64(1),
pp. 45-55 (2013).
26. Giri, B.C., Bhattachaarjee, R., and Chakraborty, A.
\A vendor-buyer integrated inventory system with
vendor's capacity constraint", International Journal of
Logistics Systems and Management, 21(3), pp. 284-303
(2015).
27. Cardenas-Barron, L.E. and Sana, S.S. \Multi-item
EOQ inventory model in a two-layer supply chain
while demand varies with promotional e ort", Applied
Mathematical Modelling, 39(21), pp. 6725-6737 (2015).
28. Ghosh, S.K., Sarkar, T., and Chaudhuri, K. \A
multi-item inventory model for deteriorating items in
limited storage space with stock-dependent demand",
American Journal of Mathematical and Management
Sciences, 34(2), pp. 147-161 (2015).
29. Yue, X., Samar K., Mukhopadhyay, S.K., and Zhu, X.
\A Bertrand model of pricing of complementary goods
under information asymmetry", Journal of Business
Research, 59(10), pp. 1182-1192 (2006).
30. Yan, R. and Bandyopadhyay, S. \The pro t bene ts of
bundle pricing of complementary products", Journal of
Retailing and Consumer Services, 18(4), pp. 355-361
(2011).
2358 M. Hemmati et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2347{2360
31. Wei, J., Zhao, J., and Li, Y. \Pricing decisions for
complementary products with rms' di erent market
powers", European Journal of Operational Research,
224(3), pp. 507-519 (2013).
32. Taleizadeh, A.A. and Charmchi, M. \Optimal advertising
and pricing decisions for complementary products",
Journal of Industrial Engineering International, 11(1),
pp. 111-117 (2015).
33. Maity, K. and Maiti, M. \Inventory of deteriorating
complementary and substitute items with stock dependent
demand", American Journal of Mathematical and
Management Sciences, 25(1-2), pp. 83-96 (2005).
34. Sana, S.S. \An EOQ model for salesmen's initiatives,
stock and price sensitive demand of similar products
- A dynamical system", Applied Mathematics and
Computation, 218(7), pp. 3277-3288 (2011).
35. Stavrulaki, E. \Inventory decisions for substitutable
products with stock-dependent demand", International
Journal of Production Economics, 129(1), pp.
65-78 (2011).
36. Maity, K. and Maiti, M. \Optimal inventory policies
for deteriorating complementary and substitute
items", International Journal of Systems Science,
40(3), pp. 267-276 (2009).