In this study, a warehouse layout problem that tries to minimize material handling cost was considered.
Bassan, Roll, and Rosenblatt (1980) were examined the same problem by offering a comparison method
for two alternative shelf arrangement for a rectangular warehouse. They were considered homogeneous items
that have the equal probabilities for picking and putting away in a two-dimensional warehouse. Here, we
extended their study for heterogeneous items stocked multiple-level warehouse.
The yearly throughput of the warehouse is classified into three groups including A, B and C, according to
their turnovers. Considering the turnover rates and stocking periods of the items, probabilities of (picking or
putting) the orders belonging in A, B and C classes are PA, PB and PC, respectively. The main reason of this
classification is to locate the items in the warehouse basing on the closeness to the dock. The total capacity and
yearly throughput of the warehouse, total storage spaces for each item class and the lengths of the aisles and
shelves are entered to the model as the pre-determined parameters. The notation of the parameters and variables
are shown in Table 1. Also, Fig. 1 is given to visualize some of the dimensions given in Table 1.
By using given details, a mathematical model providing the optimal number of storage spaces along a shelf
and the optimum number of shelves is constituted. In other words, the three dimensions of the warehouse
namely, length (u), width (v) and height (h) are obtained by the model solution. The objective function of
the model is constituted from the average travel distances in three dimensions and the unit material handling
cost. Before giving the objective function and constraint formulations, some points should be clarified. The
dock of the warehouse is located at the center of the horizontal wall. In the other word, the distance between
the dock and the left vertical wall is u/2. Also, the probability of carrying an item to right or left side of the
dock is equal. Therefore, the average travel distance in the horizontal axis is given in Eq. (1).