1
)
A regional distributor handles automotive spare parts for several car repair shops and service stations. Currently, the company uses a fixed review period system, but without scientific analysis

Question

1
)
 ﻿A regional distributor handles automotive spare parts for several car repair shops and service stations. Currently, the company uses a fixed review period system, but without scientific analysis, leading to missed sales and excess inventory. Management now wants to establish a periodic review inventory policy that ensures high service levels while optimizing inventory costs.
They have selected a high
-
volume item 
(
brake pads
)
 ﻿for pilot analysis and gathered the following data:
Average weekly demand: 
4
0
0
 ﻿units
Standard deviation of weekly demand: 
4
0
 ﻿units
Review period: 
2
 ﻿weeks
Lead time: 
1
 ﻿week
Ordering cost per order: $
1
5
0
Unit cost: $
2
5
Annual holding cost rate: 
2
5
%
 ﻿of unit cost
Desired service level: 
9
8
%
 
(
Z 
=
 
2
.
0
5
)
Operational weeks per year: 
5
2
The management needs to determine the order
-
up
-
to level 
(
T
)
 ﻿and optimal order quantity for any period, along with associated annual costs.
Tasks:
(
1
)
 ﻿Holding Cost Per Unit Per Year
Calculate the annual holding cost per unit based on the given holding cost rate and unit cost.
Formula:
H 
=
 ﻿Holding rate 
×
 ﻿Unit cost
Round your answer to two decimal places.
(
2
)
 ﻿Protect

VIPSolutions · Accepted Answer

Let's solve each part step by step:

---

### (1) **Holding Cost Per Unit Per Year**

**Given:**
- Unit cost = $25  
- Holding cost rate = 25% per year

**Formula:**  
H = Holding rate × Unit cost

**Calculation:**  
H = 0.25 × $25 = **$6.25**

**Answer:**  
**Annual holding cost per unit = $6.25**

---

### (2) **Protection Period Demand**

**Protection period = Review period + Lead time = 2 + 1 = 3 weeks**

- Average weekly demand = 400 units
- Standard deviation of weekly demand = 40 units

**Formulas:**  
- Average demand over protection period = Weekly demand × Protection period  
- Std. deviation over protection period = Std. deviation × √(Protection period)

**Calculations:**  
- Average demand = 400 × 3 = **1,200 units**
- Std. deviation = 40 × √3 ≈ 40 × 1.732 = **69 units** (rounded to nearest unit)

**Answers:**  
- **Average demand over protection period = 1,200 units**  
- **Standard deviation over protection period = 69 units**

---

### (3) **Order-Up-To Level (T)**

**Formula:**  
T = Average demand during protection period + Z × Std. deviation during protection period

- Average demand = 1,200 units (from above)
- Std. deviation = 69 units (from above)
- Z (for 98% service level) = 2.05

**Calculation:**  
T = 1,200 + 2.05 × 69 ≈ 1,200 + 141.45 = **1,341 units** (rounded to nearest unit)

**Answer:**  
**Order-up-to level (T) = 1,341 units**

---

### (4) **Expected Order Quantity Per Review**

**Formula:**  
Q = Average weekly demand × Review period

**Calculation:**  
Q = 400 × 2 = **800 units**

**Answer:**  
**Expected order quantity per review = 800 units**

---

### (5) **Total Annual Inventory Cost**

**Given:**
- Ordering cost per order = $150
- Annual demand = Average weekly demand × 52 weeks = 400 × 52 = **20,800 units**
- Order quantity = 800 units (from above)
- Holding cost per unit per year = $6.25 (from above)
- T = 1,341 units (from above)

#### **Ordering cost per year:**

= (Annual demand / Order quantity) × Ordering cost  
= (20,800 / 800) × $150  
= 26 × $150  
= **$3,900**

#### **Holding cost per year:**

- Average inventory (for periodic review system) ≈ T/2  
= 1,341 / 2 = **670.5 units**

- Holding cost per year = Average inventory × Holding cost per unit  
= 670.5 × $6.25 = **$4,190.63**

#### **Total annual inventory-related cost:**

= Ordering cost + Holding cost  
= $3,900 + $4,190.63  
= **$8,090.63**

**Answer:**  
**Total annual inventory cost = $8,090.63**

---

### (6) **Inventory Review Process Flowchart**

*(Drawn in text - use standard flowchart symbols)*

---

## **Summary Table**

| Step | Answer |
|------|--------|
| (1)  | $6.25 per unit per year |
| (2)  | Avg demand = 1,200 units, Std dev = 69 units |
| (3)  | T = 1,341 units |
| (4)  | Q = 800 units |
| (5)  | $8,090.63 per year |
| (6)  | See flowchart above |

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