Programming Cases

The Economic Order Quantity model is one of the oldest mathematical model for solving a simple inventory management problem, involving fixed and uniform demand. It was developed by Ford W. Harris in 1913 [1].

The model has just one decision variable,

There are

*Q*, representing the order quantity, and the following model parameters:*D*– annual demand,*c*– fixed setup cost of one-time order (order handling cost),*h*– annual unit holding cost per inventory item,*y*– the length of the year in days.There are

*D*/*Q*orders, each incurring a cost of*c*dollars. The highest inventory level is*Q*and the lowest—zero. Since demand is uniformly distributed, the average inventory level is*Q*/2 = (0 +*Q*)/2. Thus, the average holding cost is*h*·*Q*/2. Putting the two costs together, the average inventory cost (annually) is given by the following function:The optimal solution (order quntity) is a

*Q*^{*}value that minimizes the average inventory cost,*AIC*(*Q*^{*}):Notation ⌈ ⌉ stands here for rounding up to the nearest integer.

Additional characteristics of this model are:

*t*- the length of the single inventory cycle,*n*- the number of the inventory cyclesThe

*t*and*n*parameters are calculated as follows:Develop a Python application that will print the following report:

- The optimal solution,
*Q*^{*}. In*Python*use variable name**optQ**. - The average inventory cost for the optimal solution,
*AIC*(*Q*^{*}) (variable name**aic**). - The length of the inventory cycle for the optimal solution (variable name
**t**). - The number of the inventory cycles for the optimal solution (variable name
**n**).

Test your application for the following data:

- Variable
**D**= 4320 - Variable
**c**= 10.0 - Variable
**h**= 4.8 - Variable
**y**= 360

Round up the optimal solution and the cycle,

*t*, value to an integer (use the*math.ceil*fucntion). Adjust the optimal solution so it will be a multiple of the daily demand value (*d*). Recalculate the average annual inventory cost for the new*Q*^{*}value.References

[1] | Letkowski, J. (2018). Decision models for the newsvendor problem – learning cases for business analytics, Journal of Instructional Pedagogies, Volume 21 (), AABRI Academic Journals - JIP. Manuscript. |