 # A3501 Case Study

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BACKGROUND
In OA3501, Inventory Models, a plethora of tools and models were introduced so Operations Research Supply Managers could clearly optimize on hand material and reduce overall inventory costs. Utilizing these tools efficiently and effectively will balance inventory needs and requirements by minimizing cost to order and hold material. The models and calculations discussed in OA3501 are the foundation for understanding the functionality of all inventory aspects.
PROBLEM STATEMENT
During the class, Professor Maher taught nearly fifteen different models and decision making tools for managers to understand, adopt and utilize to further research at school and work. With that in mind, the tools provided were not interactive and didn’t
The only addition to the model is that the User will be prompted to enter number of levels and demand per level. A nonlinear solver is setup similar to the EOQ except the optimal order quantity is constrained by the levels minimum and maximum quantities entered by the User.
Results
The Quantity Discount model results can be seen in Figure 3 on the next page.
From the User inputs made per level the model will display each levels solutions along with the optimal solution. For example, in Figure 3, level 3 had the best quantity discount solution.
Wagner-Whitin
This dynamic lot-size model is an optimum variable order size problem that takes into the account of demand per period entered by the User. The model will calculate the TVC in a matrix format for all possible ordering alternatives specified by user inputting the number of periods in the planned horizon, furthermore, providing a path leading to optimal total cost and ordering scheme.
The spares model then calculates failure, downtime cost, holding cost, spare not used cost and makes the recommendation to either buy or not to buy the spare units. With my engineering experience it is known that the failure rate is based on a rate per million hours for expensive mechanical and electronical systems.
So, therefore, E[Failures] = (Required parts per system) * (Failure rate per million hours) * (Spares not available (hours)). Also, by the Palm’s Theorem the E[μ]=Lambda=average annual usage(m)*System life time (T) (Sherbrooke, 2004). To calculate the number of spares required to purchase. The CDF of a Poisson Distribution is used in excel as Poisson.dist(x(vector),μ,True) to create a table by the service rate (α) decided by the user with a VLOOKUP formula to identify the number of spares required to purchase (O’Connor, 2016). Lastly, are the calculations for determining if the User should by or not buy the spares. Keeping in mind that spare replacement is based on part failure rate with an exponential distribution we can consider the following:
Results
In Figure 5, it can be seen that when Total Cost is less than Downtime Cost then User should buy the spare parts. Figure 5. Spares Results

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