Inventory Power of Two Policy For A Serial System

Serial System: Manufacturer → Warehouse → Retail Store

A warehouse supplies a retail store with Graphene. The store faces a steady annual demand of 2,400 units.
Each order placed by the store costs $30, and the holding cost rate is 25% of the item’s value ($20 per unit).

The warehouse replenishes the item from an external supplier.
Each order the warehouse places costs $200, and its holding cost rate is 15% of the item’s value ($15 per unit).

Assume a year has 52 weeks, and both locations operate under a Power-of-Two (PO2) policy with a 1-week base period.

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Required

1. (a) Determine the optimal EOQ and order interval for the retail store and warehouse (ignore PO2 restriction).

2. (b) Round each order interval to the nearest Power-of-Two number of weeks.

3. (c) Suggest a synchronized PO2 plan for the two levels.

(a) EOQ and Optimal Order Interval (no PO2 restriction)

Formula:

Formula:

$$Q^{\ast }=\sqrt{\frac{2Kd}{hc}},T^{\ast }=\frac{Q^{\ast }}{d}\text{ (in years)}\text{<br>}$$

✅ Final PO2 Serial System Summary

Location	EOQ (units)	EOQ Interval (weeks)	PO2 Interval (weeks)	PO2 Q (units)
Retail Store	170	3.7	4	185
Warehouse	654	14.2	16	739

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💬 Interpretation

• The retail store orders 185 units every 4 weeks.

• The warehouse orders 739 units every 16 weeks from the supplier.

• The Power-of-Two synchronization ensures that every fourth store order triggers one warehouse order — simple and coordinated.

Code from ChatGPT

import numpy as np

import matplotlib.pyplot as plt

# ----------------------------

# Basic data for Graphene system

# ----------------------------

# Retail store parameters

d_store = 2400       # annual demand (units)

K_store = 30         # ordering cost ($)

h_store = 0.25       # holding cost rate

c_store = 20         # unit cost ($)

Q_star_store = 170   # EOQ

Q_po2_store = 185    # PO2

# Warehouse parameters

d_wh = 2400

K_wh = 200

h_wh = 0.15

c_wh = 15

Q_star_wh = 654

Q_po2_wh = 739

# ----------------------------

# Cost function

# ----------------------------

def total_cost(Q, K, d, h, c):

    return K * d / Q + h * c * Q / 2

# Range of Q values

Q_store = np.linspace(50, 400, 300)

Q_wh = np.linspace(200, 1200, 300)

# Compute total costs

cost_store = total_cost(Q_store, K_store, d_store, h_store, c_store)

cost_wh = total_cost(Q_wh, K_wh, d_wh, h_wh, c_wh)

# EOQ and PO2 total costs

cost_store_star = total_cost(Q_star_store, K_store, d_store, h_store, c_store)

cost_store_po2 = total_cost(Q_po2_store, K_store, d_store, h_store, c_store)

cost_wh_star = total_cost(Q_star_wh, K_wh, d_wh, h_wh, c_wh)

cost_wh_po2 = total_cost(Q_po2_wh, K_wh, d_wh, h_wh, c_wh)

# ----------------------------

# Plot

# ----------------------------

plt.figure(figsize=(9,6))

# Retail store curve

plt.plot(Q_store, cost_store, label='Retail Store', color='blue')

plt.scatter(Q_star_store, cost_store_star, color='blue', marker='o', s=80, label='EOQ (Store)')

plt.scatter(Q_po2_store, cost_store_po2, color='cyan', marker='s', s=80, label='PO2 (Store)')

# Warehouse curve

plt.plot(Q_wh, cost_wh, label='Warehouse', color='green')

plt.scatter(Q_star_wh, cost_wh_star, color='green', marker='o', s=80, label='EOQ (Warehouse)')

plt.scatter(Q_po2_wh, cost_wh_po2, color='lime', marker='s', s=80, label='PO2 (Warehouse)')

# ----------------------------

# Formatting

# ----------------------------

plt.title('Graphene Inventory Cost Curves')

plt.xlabel('Order Quantity (units)')

plt.ylabel('Total Annual Cost ($)')

plt.grid(True, linestyle='--', alpha=0.6)

plt.legend()

plt.tight_layout()

# Show graph

plt.show()