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 = 800 units per year, Co = $150, Ch = $5, and Cb = $30, what is the difference 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, should the backorder inventory policy be adopted? Assume 250 working days per year.

Answer 1

Case 1: Cost and EOQ calculations without backorders:

Calculation of EOQ

Demand = 800,the ordering cost = 150,holding cost = 5

Cost Calculation:

Case 2: Cost and EOQ calculations with backorders:

Calculation of EOQ:

Demand = 800,the ordering cost = 150,holding cost = 5,back order cost = 30

Cost Calculation:

S* is the maximum number of backorders

Q* is the minimum cost order

We have found S* ,put in above eqn

Calculate the difference in total annual cost when backorders are and are not used

The company saves 81.26 in total annual cost when backorders are used

The proportion of backorders to units is 0.14 or 14%

The demand per day is 3.2 units

The manager can adopt the new backorder policy.The backorder length is 10.56 days and the backorders make up a maximum of 14% of inventory.Both stipulations for the new policy have been met with 250 working days a year