Our group member Aneela, works for the particular store mentioned above. She collected the data from the sales personnel according to the sales and quantities the store reported during her interview with the managers and back stock employees at the store. During our research the manager informed us that the store does not order the units of pants in fact the corporate office has a set amount of inventory which is allocated to different stores and that they are delivered accordingly. The inventory is allocated to the store on the basis of the sales from the previous year. Thus one can notice that the corporate office utilizes the Naïve method to allocate inventory for the upcoming year.
The team identified the following data that needed to be gathered.
1. Number of units of product available in the store.
2. Number of units sold per month.
3. Profit per unit for each of the items sold per month.
Obtaining reasonable estimates of these quantities required enlisting the help of key personnel of the store, e.g. the general manager and the manager. Staff in the replenishing department provided information about the units available in the back stock room. The manager provided the information about the units that arrive in the store and the sales that took place on that particular month. As this is the classic product mix type our team undertook the formulation of corresponding mathematical model.
Formulation of Linear Programming Problem.
To formulate the mathematical (linear programming) model for this problem.
Table 1:.
DATE RANGE:03/01/15-03/15/15.
934457 202084 215801.
AIDEN SLIM FIT EMERSON SLOAN FIT.
KHAKI PANTS CHINO PANTS ANKLE PANTS.
UNITS SOLD 406 231 154.
NET SALES $12,847.66 $7,300.04 $7,294.46.
SELLING PRICE 31.64 each 31.6 each 47.36 each.
PROFIT/UNIT $6.32 $6.32 $9.47.
.
CONSTRAINTS: .
UNITS DELIVERED 500 250 250.
Table 2:.
Constraints Number of Units Delivered.
Khaki Pants 500.
Chino Pants 250.
Ankle Pants 250.
Decision Variables:.