$($Inventory Management $$ Part $1)$ FCC Cafeteria, which is a fast lunch spot in $$ankaya University campus,

purchases several basic cooking ingredients from a supplier. The annual usage $($demand$),$ purchasing cost,

and setup $($order$)$ cost of these ingredients are given in the table below. The inventory carrying rate is $0\mathrm{.}10$

per unit per year.

Ingredient A B C

Annual Demand $($in units$)1,0002,0001,000$

Setup Cost $($$ $/$ order$)243$

Purchasing Cost $($$ $/$ unit$)416$

$($a$)$ Assume that all ingredients are ordered independently. What is the total inventory carrying cost of all

ingredients when all ingredients are optimally ordered?

$($b$)$ The cafeteria management wants to order all ingredients in each cycle, which has a fixed common

length for all ingredients. What is the optimal length of this cycle time?

P a g e $2|2$

$($c$)$ Assume that all ingredients are jointly ordered from a supplier. The cafeteria management wants to

order all ingredients in each cycle, which has a fixed common length for all ingredients. The major

setup $($order$)$ cost associated with a group of ingredients is $$141$ per order, and the minor ordering cost

of each ingredient is as given in the table above. Calculate this common cycle time and the total annual

setup $($order$)$ cost when all ingredients are optimally ordered?

$($d$)$ Assume that all ingredients are jointly ordered from a supplier, and all ingredients have varying order

cycles. The major setup $($order$)$ cost associated with a group of ingredients is $$141$ per order, and the

minor ordering cost of each ingredient is as given in the table above. What is the ordering frequency

for the ingredient C $($i$.$e$.,$ mC$)$ if you use the heuristic algorithm discussed in the lecture?