Suppose that Westside Auto of Problem 4, with D = 12,000 units per year, C,, = (2.50)(0.20) = $0.50, and Co = $25, decided to operate with a backorder inventory policy. Backorder costs are estimated to be $5 per unit per year.

 

Identify the following:

 

a. Minimum cost order quantity

b. Maximum number of backorders

c. Maximum inventory

d. Cycle time

e. Total annual cost

let us analyze the question first

annual demand(D) = 12000 units

holding cost (Ch) = 0.50

ordering cost (Co) =25

annual back order cost (Cb)= 5

 

answer

 

a. Minimum cost order quantity

 

to calculate, we use the planned back order formula given as :

 

Minimum cost order quantity (Q_opt) = ?C2CoD??? x ?CsCs+Cc???

 

Minimum cost order quantity (Q_opt) =??0.52x12000x25??? x ?50.5+5???

 

Minimum cost order quantity (Q_opt) =1095.445115 x 1.048808848

 

Minimum cost order quantity (Q_opt) = 1148.91

 

Minimum cost order quantity(Q_opt) =1149

 

 

b. Maximum number of back orders

we will use the following formula

 

S_opt = Q_opt x ?Ch+CbCh??

 

S_opt = 1149 x ?0.5+50.5??

 

S_opt = 1149 x 0.09090909

 

S_opt =104.46

 

 

 

 

c. Maximum inventory

 

this is given by the following formula

 

= Q_opt - S_opt

 

=1149 - 104.46

 

=1044.54

 

=1045

 

 

 

 

 

d. Cycle time

 

cycle time = ?DailyDemandQuantity??

 

so the first step will be calculating the daily demand given by:

daily demand = (annual demand)/ days in a year

daily demand = 12000/365

daily demand =32.8

daily demand =33 units

 

 

cycle time = ?DailyDemandQuantity??

 

cycle time = 1149/33

 

cycle time =34.82 days

 

cycle time =35 days

 

 

 

e. Total annual cost

 

this is given by the following formula

 

total cost = ?Ch2Q(Q−S)2?+CoQD?+Cb2QS2??

 

total cost = ?0.5X2X114910452?+25X114912000?+5X2X1149104.462??

 

total cost =237.60 + 261.10 +23.74

 

total cost =522.44