Solving Example 1

Given Data:

• Annual usage (D) = 5400 units
• Cost per unit (C) = 365 Sh/unit
• Ordering cost (S) = 55 Sh/order
• Carrying cost (H) = $28\% \times 365$ = $0.28 \times 365$ = 102.2 Sh/unit/year

Part (a) Determine the optimal number of units per order (EOQ)

The Economic Order Quantity (EOQ) formula is:

$EOQ = \sqrt{\frac{2DS}{H}}$

Substitute the values:

$EOQ = \sqrt{\frac{2 \times 5400 \times 55}{102.2}} = \sqrt{\frac{594000}{102.2}} = \sqrt{5812.13} \approx 76.26 \, \text{units/order}$

Part (b) Find the optimal number of orders per year

$\text{Number of orders/year} = \frac{D}{EOQ}$

$\text{Number of orders/year} = \frac{5400}{76.26} \approx 70.83 \, \text{orders/year}$

Part (c) Find the annual total inventory cost

The total inventory cost consists of:

1. Ordering cost = $\text{Number of orders/year} \times S$
2. Carrying cost = $\frac{EOQ}{2} \times H$

$\text{Ordering cost} = 70.83 \times 55 = 3895.65 \, \text{Sh/year}$

$\text{Carrying cost} = \frac{76.26}{2} \times 102.2 = 38.13 \times 102.2 = 3895.59 \, \text{Sh/year}$

$\text{Total inventory cost} = \text{Ordering cost} + \text{Carrying cost} = 3895.65 + 3895.59 = 7791.24 \, \text{Sh/year}$

Final Answers:

(a) EOQ = 76.26 units/order
(b) Number of orders/year = 70.83 orders/year
(c) Total inventory cost = 7791.24 Sh/year

Let me know if you'd like to proceed with the next example or clarify any part of this solution! Here are five related questions and one tip for you:

Related Questions:

1. How does the carrying cost affect the EOQ calculation?
2. Can the EOQ model be applied to perishable goods? Why or why not?
3. What changes in the total cost if the carrying cost percentage increases?
4. How would the EOQ change if the ordering cost doubles?
5. What alternative methods exist for determining order quantities apart from EOQ?

Tip:

Always double-check units (e.g., annual vs monthly demand) when applying formulas to ensure accurate calculations.