What is the cost difference between Ferguson$$s proposal to order $4$ cases each time and Patrachalaski$$s proposal to order $32$ cases each time?

The annual ordering cost for Ferguson$$s proposal is $$8,601\mathrm{.}60$ in comparison to Patrachalski$$s it is $$1,075\mathrm{.}20.$ The annual inventory carrying cost for Ferguson$$s proposal is $$1,075\mathrm{.}20$ and Patrachalski$$s is $$8,601\mathrm{.}60.$ Despite having different ordering and inventory carrying costs, both proposals result in the same annual total of $$9,676\mathrm{.}80.$

Lewin suggested looking at economic order quantity. Based on the lowest total annual cost, what order quantity should Martin recommend?

Based on the lowest total annual cost which is $$6,082\mathrm{.}48,$ Martin should recommend $170$ units per order.

Let's explore the concept of $$robustness$.$ Lewins proposal to use economic order quantity may be unrealistic since SMC would like to place orders in the whole cases. If the order quantity is decreased to the nearest whole case $($ which is a $2\mathrm{.}78\%$ reduction$)$ what percent would your total annual cost change? What percent would your annual total cost change if the order quantity is increased to the nearest whole case? Hint: Use Formula $(\{$New Total Cost$/$ Old Total Cost$\}-1)$

If the order quantity is decreased to the nearest whole case, which is $11$ cases, the new

order quantity would be $165$ units. The total annual cost would change by $\mathrm{.}04\%.$ The total

cost would increase by $\mathrm{.}04\%.$ If the order quantity is increased to the nearest whole case,

which would be $12$ cases, the annual total cost would increase by $0\mathrm{.}17\%.$