* Corresponding author.
E-mail: bhuniaak@rediffmail.com, aakbarshaikh@gmail.com (A. K. Bhunia)
© 2013 Growing Science Ltd. All rights reserved.
doi: 10.5267/j.ijiec.2013.01.004
International Journal of Industrial Engineering Computations 4 (2013)241–258
Contents lists available at GrowingScience
International Journal of Industrial Engineering Computations
homepage: www.GrowingScience.com/ijiec
A two warehouse deterministic inventory model for deteriorating items with a linear trend in
time dependent demand over finite time horizon by Elitist Real-Coded Genetic Algorithm
A.K. Bhunia
a*
, Ali Akbar Shaikh
a
, A.K. Maiti
b
and M.Maiti
b
a
Department of Mathematics, University of Burdwan, Burdwan-713104, W.B., India
b
Department of Applied Mathematics, Vidyasagar University, Midnapore-721102, W.B., India
C H R O N I C L E A B S T R A C T
Article history:
Received September252012
Received in revised format
December 28 2012
Accepted January2 2013
Available online
5January 2013
This paper deals with a deterministic inventory model developed for deteriorating items having
two separate storage facilities (owned and rented warehouses) due to limited capacity of the
existing storage (owned warehouse) with linear time dependent demand (increasing) over a fixed
finite time horizon. The model is formulated with infinite replenishment and the successive
replenishment cycle lengths are in arithmetic progression. Partially backlogged shortages are
allowed. The stocks of rented warehouse (RW) are transported to the owned warehouse (OW) in
continuous release pattern. For this purpose, the model is formulated as a constrained non-linear
mixed integer programming problem. For solving the problem, an advanced genetic algorithm
(GA) has been developed. This advanced GA is based on ranking selection, elitism, whole
arithmetic crossover and non-uniform mutation dependent on the age of the population. Our
objective is to determine the optimal replenishment number, lot-size of two-warehouses (OW and
RW) by maximizing the profit function. The model is illustrated with four numerical examples
and sensitivity analyses of the optimal solution are performed with respect to different
parameters.
© 2013 Growing Science Ltd. All rights reserved
Keywords:
Inventory management
Two-storage
Deterioration
Genetic algorithm
Partial backlogging
Finite time horizon
1. Introduction
In the existing literature, it is found that the classical inventory models generally deal with a single
storage facility. The basic assumption in these models is that the management owned a storage with
unlimited capacity. In the field of inventory management, this is not always true. When an attractive
price discount for bulk-purchase is available or the cost of procuring goods is higher than the other
inventory related costs or there are some problems in frequent procurement or the demand of items is
very high, management then decides to purchase a huge quantity of items at a time. These items cannot
be stored in the existing storage viz., the owned warehouse (OW) with limited capacity. Then for
storing the excess items, one (sometimes more than one) additional warehouse is hired on a rental
basis. This rented warehouse (RW) may be located near the OW or a little away from it. It is generally
assumed that the holding cost in RW is greater than the same as in OW. Hence, the items are stored