---
title: "EOQ, stock levels and ROL for cement"
subject: "Construction Management"
chapter: 3
key: "semester_8/construction_management:eoq-cement-2078-kartik"
source: https://www.bctengineer.com/q/semester_8/construction_management/eoq-cement-2078-kartik
site: BCT Engineering
---

# EOQ, stock levels and ROL for cement

Construction Management · Chapter 3: Planning Construction Material

- Asked in: 2078 Kartik, 6 marks
- Video: [Stock Levels: Numerical Problem Solved-Maximum Level-Minimum Level-Reorder Level-Average Stock Level](https://www.youtube.com/watch?v=sGAVkyOE2eE) — Management Tutorials
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/construction_management/eoq-cement-2078-kartik
- Whole chapter: https://www.bctengineer.com/md/semester_8/construction_management/chapter-3

## Question

Calculate EOQ, Maximum Stock level, minimum, average stock level, and ROP/ROL if annual cement required for a construction project is 20000 bags; ordering cost is Rs. 10,000; Carrying cost is 5%; Cement rate is Rs. 900 per bag; Safety stock is 10 days; lead time is 5 days. Also calculate the total inventory cost.

## Short answer

EOQ = sqrt(2*20000*10000/45) = 2981 bags. Daily use = 20000/365 ≈ 54.79 bags; safety = 548 bags; lead consumption =274 bags. ROP =822 bags, max =3529 bags, min =548 bags, avg =2039 bags. Total ordering + carrying cost = Rs 1,34,164; including purchase = Rs 1,81,34,164.

## Answer

#### Data
$D = 20{,}000$ bags/year, $C_o = $ Rs 10,000/order, $P = $ Rs 900/bag, carrying cost = 5% of price, so $C_h = 0.05 \times 900 = $ Rs 45 per bag per year. A working year of 365 days is assumed, so daily use = 20,000/365 = 54.79 bags/day. Safety stock = 10 days, lead time = 5 days.

#### EOQ
$$
EOQ = \sqrt{\frac{2 \times 20000 \times 10000}{45}} = 2981.4\ \text{bags} \approx 2{,}981\ \text{bags}
$$

#### Stock levels
- Safety (minimum) stock = 10 x 54.79 = 547.9 bags $\approx$ 548 bags
- Lead-time consumption = 5 x 54.79 = 274.0 bags
- **Re-order level (ROP/ROL)** = 274.0 + 547.9 = 821.9 bags $\approx$ 822 bags
- **Maximum stock level** = safety stock + EOQ = 547.9 + 2,981.4 = 3,529.3 bags $\approx$ 3,529 bags
- **Minimum stock level** = safety stock $\approx$ 548 bags
- **Average stock level** = (3,529.3 + 547.9)/2 = 2,038.6 bags $\approx$ 2,039 bags

#### Total inventory cost
- Number of orders = 20,000/2,981.4 = 6.71 per year
- Ordering cost = 6.71 x 10,000 = Rs 67,082
- Carrying cost = (EOQ/2) x 45 = 1,490.7 x 45 = Rs 67,082
- Total ordering + carrying cost = Rs 1,34,164
- Purchase cost = 20,000 x 900 = Rs 1,80,00,000

(If the carrying cost of the safety stock is also included, add 547.9 x 45 = Rs 24,658, giving Rs 1,58,822 before purchase cost.)

**Answer: EOQ = 2,981 bags; ROL = 822 bags; maximum = 3,529 bags; minimum = 548 bags; average = 2,039 bags. Total inventory cost (ordering + carrying) = Rs 1,34,164; including the purchase cost, Rs 1,81,34,164.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Carrying cost is 5% of Rs 900/bag. What is Ch?
   A. Rs 5
   B. Rs 45
   C. Rs 450
   D. Rs 900
   Answer: B. 0.05 x 900 = Rs 45 per bag per year. (Key point: Carrying cost)

2. What is EOQ for D = 20000, Co = 10000, Ch = 45?
   A. About 2,981 bags
   B. About 1,490 bags
   C. About 4,216 bags
   D. About 548 bags
   Answer: A. sqrt(2 x 20000 x 10000 / 45) = 2981.4 bags. (Key point: EOQ result)

3. How is the maximum stock level found here?
   A. EOQ only
   B. Safety stock + EOQ
   C. ROL + safety stock
   D. EOQ / 2
   Answer: B. Stock rises from the safety level by one order quantity: 547.95 + 2981.42 = about 3,529 bags. (Key point: Maximum level)

4. At EOQ, how do ordering cost and carrying cost compare?
   A. Ordering cost is double
   B. Carrying cost is double
   C. They are equal (each Rs 67,082)
   D. Both are zero
   Answer: C. At EOQ the two annual costs are equal, giving a total of Rs 134,164. (Key point: Cost at EOQ)

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