owned warehouse/show-room (OW) and rented warehouse (RW) is developed. The proposed
model of this paper also considers a realistic assumption regarding the storage capacity of the
rented warehouse. Demand is a function of selling price, advertisement of an item and
displayed inventory level in OW. The stocks of RW are shipped to OW under bulk release
pattern where shortages are not allowed. We discuss different scenarios of the proposed model
to address relative size of stock dependency parameters and the capacity of owned warehouse.
For each scenario, the corresponding problem is formulated as a constrained mixed integer
nonlinear programming problem with three integer and two non-integer variables and a real
coded genetic algorithm (RCGA) is developed to solve the resulted problem. The proposed
model of the paper is also examined using some numerical examples and sensitivity analysis is
performed.
How to cite this paper
Bhunia, A., Pal, P., Chattopadhyay, S & Medya, B. (2011). An inventory model of two-warehouse system with variable demand dependent on instantaneous displayed stock and marketing decisions via hybrid RCGA.International Journal of Industrial Engineering Computations , 2(2), 351-368.
Refrences
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Anily, S. & Federgruen, A. (1990). One warehouse multiple retailer systems with vehicle routing costs. Management Sciences ,36, 92- 114.
Baker, R. C., & Urban, T. L. (1985). A deterministic inventory system with an inventory-level-dependent demand rate. Journal of Operational Research Society, 39, 823-831.
Baumol, W. J., & Vinod, H.C. (1970). An inventory theoretic model of freight transport demand. Management Science 16, 413-421.
Benkherouf, L. (1997). A deterministic order level inventory model for deteriorating items with two storage facilities, International Journal of Production Economics ,48, 167-175.
Bhunia, A. K. & Maiti, M. (1994). A two warehouse inventory model for a linear trend in demand. Opsearch ,31, 318-329.
Bhunia, A. K. & Maiti, M. (1995). A deterministic two storage inventory model for variable production and inventory level dependent demand rate. Cashiers du Cero,37,17-24.
Bhunia, A.K. & Maiti, M. (1998). A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages. Journal of Operational Research Society ,49, 289-292.
Buffa, F., & Munn, J. (1989). A recursive algorithm for order cycle time that minimizes logistics cost. Journal of Operational Research Society, 40, 367-377.
Constable, G. K., & Whybark, D. C. (1978). Interactions of transportation and inventory decisions, Decision Sciences, 9, 688-699.
Das, B., Maity, K., & Maiti, M. (2007). A two warehouse supply chain model under possibility/ necessity/ credibility measures. Mathematical and Computer Modeling, 46, 398-409.
Datta, T. K., & Pal, A. K. (1990). A note on an inventory model with inventory level-dependent demand rate. Journal of Operational Research Society, 41, 971-975.
Dave, U. (1988). On the EOQ models with two levels of storage, Opsearch, 25, 190-196.
Dey, J. K., Mondal, S. K., & Maiti, M. (2008). Two storage inventory problem with dynamic demand and interval valued lead-time over finite time horizon under inflation and time-value of money, European Journal of Operational Research, 185, 170-194.
Dye, C.Y., Ouyang, L. Y., & Hsieh, T. P. (2007). Deterministic inventory model for deteriorating items with the capability constraint and time-proportional backlogging rate. European Journal of Operational Research, 178, 789-807.
Gen, M. & Cheng, R. (2000). Genetic Algorithms and Engineering Optimization. John Wiley & Sons Inc.
Giri, B. C., & Chaudhuri, K. S. (1998). Deterministic models for perishable inventory with stock –dependent demand rate and non-dependent holding cost. European Journal of Operational Research, 105, 467-474.
Giri, B. C., Pal, S., Goswami, A & Chaudhuri, K. S. (1996). An inventory model for deteriorating items and stock-dependent demand rate. European Journal of Operational Research, 95, 604-610.
Goldberg, D. E. (1989). Genetic Algorithms: Search, Optimization and Machine Learning; Addison Wesley.
Goswami, A. & Chaudhuri, K. S. (1992). An economic order quantity model for items with two level of storage for a linear trend in demand. Journal of Operational Research Society, 43, 157-167.
Goyal, S. K., & Gunasekaran, A. (1995). An integrated production – inventory marketing model for deteriorating items. Computers and Industrial Engineering, 28, 755-762.
Hartely, R.V. (1976). Operations Research- A Managerial Emphasis., Good Year Publishing Company, California, 315-317.
Holland, J. H. (1975). Adaptation of Natural and Artificial system, University of Michigan Press, Ann Arbor.
Jaggi, C. K. & Arneja, N. (2011). Stochastic integrated vendor–buyer model with unstable lead time and setup cost. International Journal of Industrial Engineering Computations, 2(1), 123-140.
Kar, S., Bhunia, A. K., & Maiti, M, (2001). Deterministic inventory model with levels of storage, a linear trend in demand and a fixed time horizon. Computer and Operations Research, 28, 1315-1331.
Kotler, P. (1971). Marketing Decision Making: A Model Building Approach. Holt. Rinehart, Winston, New York .
Ladany, S., & Sternleib, A. (1974). The intersection of economic ordering quantities and marketing policies, AIIE Transactions, 6, 35-40.
Luo, W. (1998). An integrated inventory system for perishable goods with backordering. Computers and Industrial Engineering, 34, 685-693.
Mandal, B.N., & Phaujdar, S. (1989). An inventory model for deteriorating items and stock-dependent consumption rate. Journal of Operational Research Society, 4, 483-488.
Michalawicz, Z. (1996). Genetic Algorithms + Data structure= Evaluation Programs. Springer Verlog, Berlin.
Mondal, B., Bhunia, A. K., & Maiti, M. (2007). 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), 243-267.
Niu, B., & Xie, J. (2008). A note on Two-warehouse inventory model with deterioration under FIFO dispatch policy. European Journal of Operational Research, 190, 571-577.
Padmanabhan, G., & Vrat, P., (1995). EOQ models for perishable items under stock-dependent selling rate. European Journal of Operational Research, 86, 281-292.
Pakkala, T. P. M., & Achary, K. K. (1992-a). A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate. European Journal of Operational Research , 57, 71-76.
Pakkala, T. P. M., & Achary, K. K. (1992-b). Discrete time inventory model for deterministic inventory model for deteriorating items with two warehouses, Opsearch, 29 (1992-b), 90-103.
Pal, A. K., Bhunia, A.K., & Mukherjee, R.N. (2004). A marketing-oriented inventory model with three-component demand rate dependent on displayed stock level (DSL). Journal of the Operational Research Society, 56, 113-118.
Pal, A. K., Bhunia, A. K., & Mukherjee, R. N. (2006). 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, 977-991.
Pal, P., Das, B., Panda, A. & Bhunia, A. K. (2005). An application of real-coded genetic algorithm for mixed integer non-linear programming in an optimal two-warehouse inventory policy for deteriorating items with a linear trend in demand and a fixed planning horizon. International Journal of Computer Mathematics, 82(2), 167-175.
Pal, S., Goswami, A. & Chaudhuri, K. S., (1993). A deterministic inventory model for deteriorating items and stock-dependent demand rate. International Journal of Production Economics, 32, 291-299.
Rong, M., Mahapatra, N. K., & Maiti, M. (2008). A two warehouse inventory model for a deteriorating item with partially/ full backlogged shortage and fuzzy lead time. European Journal of Operational Research, 189, 69-75.
Sarkar, B. R., Mukherjee, S., & Balan, C. V., (1997). An order-level lot-size inventory model with inventory-level dependent demand and deterioration. International Journal of Production Economics, 48, 227-236.
Sarma, K. V. S. (1983). A deterministic inventory model with two levels storage and an optimum release rule. Opsearch, 20, 175-180.
Sarma, K. V. S. (1983). A deterministic order-level inventory model for deteriorating items with two storage facilities. European Journal of Operational Research ,29, 70-72.
Subramanyam, S., & Kumaraswamy, S. (1981). EOQ formula under varying marketing policies and conditions. AIIE Transtions ,13, 312-314.
Urban, T. C. (1992). Deterministic inventory models incorporating marketing decisions. Computers & Industrial Engineering, 22, 85-93.
Urban, T. L. (1995). Inventory models with the demand rate dependent on stock and shortage levels. International Journal of Production Economics ,40, 21-28.
Yang, H. L. (2004). Two-warehouse inventory models for deteriorating items with shortages under inflation. European Journal of Operational Research, 157, 344-356.
Yang, H. L. (2006). Two-warehouse partial backlogging inventory models for deteriorating items under inflation. International Journal of Production Economics, 103, 362-370.
Zhou, Y. W. (2003). A multi-warehouse inventory model for items with time-varying demand and shortages. Computers & Operations Research, 30, 2115-2134.
Zhou,Y. W. & Yang, S. L. (2003). A two-warehouse inventory model for items with stock-level-dependent demand rate. International Journal of Production Economics, 95, 215-228.
Zhou,Y. W., (1998). An optimal EOQ model for deteriorating items with two warehouses and time varying demand. Mathematica Applicata, 10, 19-23.
Anily, S. & Federgruen, A. (1990). One warehouse multiple retailer systems with vehicle routing costs. Management Sciences ,36, 92- 114.
Baker, R. C., & Urban, T. L. (1985). A deterministic inventory system with an inventory-level-dependent demand rate. Journal of Operational Research Society, 39, 823-831.
Baumol, W. J., & Vinod, H.C. (1970). An inventory theoretic model of freight transport demand. Management Science 16, 413-421.
Benkherouf, L. (1997). A deterministic order level inventory model for deteriorating items with two storage facilities, International Journal of Production Economics ,48, 167-175.
Bhunia, A. K. & Maiti, M. (1994). A two warehouse inventory model for a linear trend in demand. Opsearch ,31, 318-329.
Bhunia, A. K. & Maiti, M. (1995). A deterministic two storage inventory model for variable production and inventory level dependent demand rate. Cashiers du Cero,37,17-24.
Bhunia, A.K. & Maiti, M. (1998). A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages. Journal of Operational Research Society ,49, 289-292.
Buffa, F., & Munn, J. (1989). A recursive algorithm for order cycle time that minimizes logistics cost. Journal of Operational Research Society, 40, 367-377.
Constable, G. K., & Whybark, D. C. (1978). Interactions of transportation and inventory decisions, Decision Sciences, 9, 688-699.
Das, B., Maity, K., & Maiti, M. (2007). A two warehouse supply chain model under possibility/ necessity/ credibility measures. Mathematical and Computer Modeling, 46, 398-409.
Datta, T. K., & Pal, A. K. (1990). A note on an inventory model with inventory level-dependent demand rate. Journal of Operational Research Society, 41, 971-975.
Dave, U. (1988). On the EOQ models with two levels of storage, Opsearch, 25, 190-196.
Dey, J. K., Mondal, S. K., & Maiti, M. (2008). Two storage inventory problem with dynamic demand and interval valued lead-time over finite time horizon under inflation and time-value of money, European Journal of Operational Research, 185, 170-194.
Dye, C.Y., Ouyang, L. Y., & Hsieh, T. P. (2007). Deterministic inventory model for deteriorating items with the capability constraint and time-proportional backlogging rate. European Journal of Operational Research, 178, 789-807.
Gen, M. & Cheng, R. (2000). Genetic Algorithms and Engineering Optimization. John Wiley & Sons Inc.
Giri, B. C., & Chaudhuri, K. S. (1998). Deterministic models for perishable inventory with stock –dependent demand rate and non-dependent holding cost. European Journal of Operational Research, 105, 467-474.
Giri, B. C., Pal, S., Goswami, A & Chaudhuri, K. S. (1996). An inventory model for deteriorating items and stock-dependent demand rate. European Journal of Operational Research, 95, 604-610.
Goldberg, D. E. (1989). Genetic Algorithms: Search, Optimization and Machine Learning; Addison Wesley.
Goswami, A. & Chaudhuri, K. S. (1992). An economic order quantity model for items with two level of storage for a linear trend in demand. Journal of Operational Research Society, 43, 157-167.
Goyal, S. K., & Gunasekaran, A. (1995). An integrated production – inventory marketing model for deteriorating items. Computers and Industrial Engineering, 28, 755-762.
Hartely, R.V. (1976). Operations Research- A Managerial Emphasis., Good Year Publishing Company, California, 315-317.
Holland, J. H. (1975). Adaptation of Natural and Artificial system, University of Michigan Press, Ann Arbor.
Jaggi, C. K. & Arneja, N. (2011). Stochastic integrated vendor–buyer model with unstable lead time and setup cost. International Journal of Industrial Engineering Computations, 2(1), 123-140.
Kar, S., Bhunia, A. K., & Maiti, M, (2001). Deterministic inventory model with levels of storage, a linear trend in demand and a fixed time horizon. Computer and Operations Research, 28, 1315-1331.
Kotler, P. (1971). Marketing Decision Making: A Model Building Approach. Holt. Rinehart, Winston, New York .
Ladany, S., & Sternleib, A. (1974). The intersection of economic ordering quantities and marketing policies, AIIE Transactions, 6, 35-40.
Luo, W. (1998). An integrated inventory system for perishable goods with backordering. Computers and Industrial Engineering, 34, 685-693.
Mandal, B.N., & Phaujdar, S. (1989). An inventory model for deteriorating items and stock-dependent consumption rate. Journal of Operational Research Society, 4, 483-488.
Michalawicz, Z. (1996). Genetic Algorithms + Data structure= Evaluation Programs. Springer Verlog, Berlin.
Mondal, B., Bhunia, A. K., & Maiti, M. (2007). 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), 243-267.
Niu, B., & Xie, J. (2008). A note on Two-warehouse inventory model with deterioration under FIFO dispatch policy. European Journal of Operational Research, 190, 571-577.
Padmanabhan, G., & Vrat, P., (1995). EOQ models for perishable items under stock-dependent selling rate. European Journal of Operational Research, 86, 281-292.
Pakkala, T. P. M., & Achary, K. K. (1992-a). A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate. European Journal of Operational Research , 57, 71-76.
Pakkala, T. P. M., & Achary, K. K. (1992-b). Discrete time inventory model for deterministic inventory model for deteriorating items with two warehouses, Opsearch, 29 (1992-b), 90-103.
Pal, A. K., Bhunia, A.K., & Mukherjee, R.N. (2004). A marketing-oriented inventory model with three-component demand rate dependent on displayed stock level (DSL). Journal of the Operational Research Society, 56, 113-118.
Pal, A. K., Bhunia, A. K., & Mukherjee, R. N. (2006). 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, 977-991.
Pal, P., Das, B., Panda, A. & Bhunia, A. K. (2005). An application of real-coded genetic algorithm for mixed integer non-linear programming in an optimal two-warehouse inventory policy for deteriorating items with a linear trend in demand and a fixed planning horizon. International Journal of Computer Mathematics, 82(2), 167-175.
Pal, S., Goswami, A. & Chaudhuri, K. S., (1993). A deterministic inventory model for deteriorating items and stock-dependent demand rate. International Journal of Production Economics, 32, 291-299.
Rong, M., Mahapatra, N. K., & Maiti, M. (2008). A two warehouse inventory model for a deteriorating item with partially/ full backlogged shortage and fuzzy lead time. European Journal of Operational Research, 189, 69-75.
Sarkar, B. R., Mukherjee, S., & Balan, C. V., (1997). An order-level lot-size inventory model with inventory-level dependent demand and deterioration. International Journal of Production Economics, 48, 227-236.
Sarma, K. V. S. (1983). A deterministic inventory model with two levels storage and an optimum release rule. Opsearch, 20, 175-180.
Sarma, K. V. S. (1983). A deterministic order-level inventory model for deteriorating items with two storage facilities. European Journal of Operational Research ,29, 70-72.
Subramanyam, S., & Kumaraswamy, S. (1981). EOQ formula under varying marketing policies and conditions. AIIE Transtions ,13, 312-314.
Urban, T. C. (1992). Deterministic inventory models incorporating marketing decisions. Computers & Industrial Engineering, 22, 85-93.
Urban, T. L. (1995). Inventory models with the demand rate dependent on stock and shortage levels. International Journal of Production Economics ,40, 21-28.
Yang, H. L. (2004). Two-warehouse inventory models for deteriorating items with shortages under inflation. European Journal of Operational Research, 157, 344-356.
Yang, H. L. (2006). Two-warehouse partial backlogging inventory models for deteriorating items under inflation. International Journal of Production Economics, 103, 362-370.
Zhou, Y. W. (2003). A multi-warehouse inventory model for items with time-varying demand and shortages. Computers & Operations Research, 30, 2115-2134.
Zhou,Y. W. & Yang, S. L. (2003). A two-warehouse inventory model for items with stock-level-dependent demand rate. International Journal of Production Economics, 95, 215-228.
Zhou,Y. W., (1998). An optimal EOQ model for deteriorating items with two warehouses and time varying demand. Mathematica Applicata, 10, 19-23.