A manager of an inventory system believes that inventory models are important de
ID: 2757940 • Letter: A
Question
A manager of an inventory system believes that inventory models are important decision-making aids. The manager has experience with the EOQ policy, but has never considered a backorder model because of the assumption that backorders were "bad" and should be avoided. However, with upper management's continued pressure for cost reduction, you have been asked to analyze the economics of a backorder policy for some products that can possibly be backordered. For a specific product with D = 730 units per year, Co = $160, Ch = $3, and Cb = $15, what is the difference in total annual cost between the EOQ model and the planned shortage or backorder model? If required, round your answer to the nearest cent. There is a difference of $ in total annual cost between the EOQ model and the planned shortage or backorder model. If the manager adds constraints that no more than 25% of the units can be backordered and that no customer will have to wait more than 15 days for an order, find there values. Assume 250 working days per year. If required, round your answers to two decimal places. Backordered units = % Backorder period = days Should the backorder inventory policy be adopted?
Explanation / Answer
D = 730 units/year
C0 = $160
Ch = $3/unit/year
Cb = $15/unit/year
Planned shortage model:
Q = 2DC0/Ch(Ch+ Cb/ Cb)
= 2(730)(160)/3(3+15/15)
= 233600/ 3.6
= 64888.888 = 254.732 units
B= Q × (Ch/ (Ch +Cb)
= 254.732 × (3/18)
= 254.732 × 0.166
= 42.455 units
EOQ Model:
Q =2DC0/Ch
= 2(730)(160)/3
= 233600/3
= 77866.666
= 279.045 units
Total cost planned shortage model:
TC = Total annual inventory cost
HC = Annual inventory holding cost
SC = Annual Setup cost
BC = Annual Back Ordering cost
HC= [ (Q-B)2/2Q] × H
= [(254.732 – 42.455)2/2×254.732]× 3
= [45061.524729/ 509.464] × 3
=[88.448] × 3
=$265.346
SC = [D/Q] × C0
= [730/254.732] × 160
= 2.865 × 160
= $458.4
BC = [B2/2Q] × Cb
= [(42.455)2/2×254.732] × 160
= [1802.427025/ 509.464] × 160
= 3.5378 × 160
= $566.0622
Total Cost = HC + SC + BC
= $265.346 + $458.4 + $566.0622
= $1289.8082
Total cost regular EOQ Model:
HC = [Q/2] × Ch
= [279.045/2] × 3
= 139.5225 × 3
= $418.5675
SC = [D/Q] × C0
= [730/279.045] × 160
= 2.616 × 160
= $418.570
TC = HC + SC = $418.5675 + $418.570
= $837.1375
Total cost Difference = $837.1375 - $1289.8082= -$452.6707
Using the Planned Shortage model will result in loss of -$452.6707
Number of orders = D/Q
= 730/254.732
= 2.865 orders
Expected Annual Number of units short = B × (D/Q)
= 42.455 × 2.865 = 121.633
d= D/250 = 730/250 = 2.92 units/day
t2 = 42.455/2.92 = 14.53 days
Since 14.53< 15 and 121.633/730 = 0.166 < 0.25 the back order inventory policy should be adopted but we have to take into consideration the loss in Planned Shortage model.
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