A manager of an inventory system believes that inventory models are important
decision-making aids. Even though often using an EOQ policy, the manager never considered a backorder model because of the assumption that back orderes were “bad” and should be a 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 = #3, and Cb = $20, 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.
great
fastly response
To find the difference in total annual cost between the EOQ model and the planned shortage or backorder model, we need to calculate the total annual cost for each policy and then subtract the total annual cost of the EOQ model from the total annual cost of the backorder model.
1. EOQ Model:
The Economic Order Quantity (EOQ) can be calculated using the formula:
EOQ = √(2DS/Ch)
where D is the demand (800 units per year) and Ch is the cost of holding inventory per unit ($3).
So, EOQ = √(2 * 800 * $150 / $3) = 800 units
The total annual cost for the EOQ model can be calculated using the formula:
Total Annual Cost (EOQ) = Co * (D/EOQ) + Ch * (EOQ/2)
where Co is the cost of placing an order ($150) and Ch is the cost of holding inventory per unit ($3).
Total Annual Cost (EOQ) = $150 * (800/800) + $3 * (800/2) = $150 + $1,200 = $1,350
2. Backorder Model:
Since no more than 25% of the units can be backordered, the maximum backorder level is 25% of the demand:
Maximum Backorder level = 0.25 * D = 0.25 * 800 = 200 units
To calculate the total annual cost for the backorder model, we need to consider the cost of backordering and the cost of holding inventory.
The average backorder level can be calculated as half of the maximum backorder level:
Average Backorder level = 0.5 * Maximum Backorder level = 0.5 * 200 = 100 units
The total annual cost for the backorder model can be calculated using the formula:
Total Annual Cost (Backorder) = Co * (D/EOQ) + Cb * (Average Backorder level)
where Co is the cost of placing an order ($150), Cb is the cost of backordering per unit ($20), and Average Backorder level is the average number of backordered units.
Total Annual Cost (Backorder) = $150 * (800/800) + $20 * 100 = $150 + $2,000 = $2,150
Difference in Total Annual Cost = Total Annual Cost (Backorder) - Total Annual Cost (EOQ) = $2,150 - $1,350 = $800
Now, let's address the manager's constraints:
1. No more than 25% of the units can be backordered:
In our analysis, the backorder model meets this constraint as the average backorder level is 100 units, which is less than 25% of the demand (800 units).
2. No customer will have to wait more than 15 days for an order:
To check if this constraint is met, we need to calculate the backorder fill rate, which represents the percentage of backorders that can be filled within the required time frame.
Backorder Fill Rate = (Average Backorder level / D) * 100
Backorder Fill Rate = (100 / 800) * 100 = 12.5%
Since the backorder fill rate is below 100%, it means that not all backorders can be filled within 15 days. Therefore, the backorder inventory policy may not be suitable to meet the constraint of no customer waiting more than 15 days for an order.
In conclusion, the difference in total annual cost between the EOQ model and the planned shortage or backorder model is $800. However, considering the manager's constraints, it may not be appropriate to adopt the backorder inventory policy.