Chapter 11.S, Problem 6P

a)

Summary Introduction

To calculate: The bullwhip measure of the retailer.

Introduction: Supply chain management is one of the important elements of a business which impacts business product development. With expanding businesses in global conditions, supply chain activities can impact the cost effectiveness of these businesses.

Answer to Problem 6P

The bullwhip measure of the retailer is 2.5.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Weekly}\text{variance}\text{of}\text{demand}=\text{200}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{retailer}=\text{500}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{wholesaler}=6\text{00}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{distributor}=75\text{0}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{manufacturer}=1,35\text{0}\text{units}\end{array}$

Formula:

$\begin{array}{c}\text{Bullwhip}=\frac{\text{Variance}\text{of}\text{orders}}{\text{Variance}\text{of}\text{demand}}\\ =\frac{{\text{σ}}_{\text{order}}^{\text{2}}}{{\text{σ}}_{\text{demand}}^{\text{2}}}\end{array}$

Calculation of bullwhip measure for retailer:

$\begin{array}{c}\text{Bullwhip}=\frac{\text{Variance}\text{of}\text{orders}}{\text{Variance}\text{of}\text{demand}}\\ =\frac{500}{200}\\ =2.5\end{array}$ (1)

The bullwhip measure of the retailer is calculated by dividing the variance of order with the variance of demand. 500 is divided by 200, which gives 2.5 as the bullwhip measure for the retailer.

Hence, the bullwhip measure for the retailer is 2.5

b)

Summary Introduction

To calculate: The bullwhip measure of the wholesaler.

Answer to Problem 6P

The bullwhip measure of the wholesaler is 1.2.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Weekly}\text{variance}\text{of}\text{demand}=\text{200}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{retailer}=\text{500}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{wholesaler}=6\text{00}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{distributor}=75\text{0}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{manufacturer}=1,35\text{0}\text{units}\end{array}$

Formula:

$\begin{array}{c}\text{Bullwhip}=\frac{\text{Variance}\text{of}\text{orders}}{\text{Variance}\text{of}\text{demand}}\\ =\frac{{\text{σ}}_{\text{order}}^{\text{2}}}{{\text{σ}}_{\text{demand}}^{\text{2}}}\end{array}$

Calculation of the bullwhip measure for the wholesaler:

$\begin{array}{c}\text{Bullwhip}=\frac{\text{Variance}\text{of}\text{orders}}{\text{Variance}\text{of}\text{demand}}\\ =\frac{600}{500}\\ =1.2\end{array}$ (2)

The bullwhip measure for the wholesaler is calculated by dividing the variance of order with the variance of demand. 600 is divided by 500, which gives 1.2 as the bullwhip measure for the wholesaler.

Hence, the bullwhip measure for the wholesaler is 1.2.

c)

Summary Introduction

To calculate: The bullwhip measure of the distributor.

Answer to Problem 6P

The bullwhip measure of the distributor is 1.25.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Weekly}\text{variance}\text{of}\text{demand}=\text{200}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{retailer}=\text{500}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{wholesaler}=6\text{00}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{distributor}=75\text{0}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{manufacturer}=1,35\text{0}\text{units}\end{array}$

Formula:

$\begin{array}{c}\text{Bullwhip}=\frac{\text{Variance}\text{of}\text{orders}}{\text{Variance}\text{of}\text{demand}}\\ =\frac{{\text{σ}}_{\text{order}}^{\text{2}}}{{\text{σ}}_{\text{demand}}^{\text{2}}}\end{array}$

Calculation of the bullwhip measure for the distributor:

$\begin{array}{c}\text{Bullwhip}=\frac{\text{Variance}\text{of}\text{orders}}{\text{Variance}\text{of}\text{demand}}\\ =\frac{750}{600}\\ =1.25\end{array}$ (3)

The bullwhip measure for the distributor is calculated by dividing the variance of order with the variance of demand. 750 is divided by 600, which gives 1.25 as the bullwhip measure for the distributor.

Hence, the bullwhip measure for the distributor is 1.25.

d)

Summary Introduction

To calculate: The bullwhip measure of the manufacturer.

Answer to Problem 6P

The bullwhip measure of the manufacturer is 1.8.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Weekly}\text{variance}\text{of}\text{demand}=\text{200}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{retailer}=\text{500}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{wholesaler}=6\text{00}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{distributor}=75\text{0}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{manufacturer}=1,35\text{0}\text{units}\end{array}$

Formula:

$\begin{array}{c}\text{Bullwhip}=\frac{\text{Variance}\text{of}\text{orders}}{\text{Variance}\text{of}\text{demand}}\\ =\frac{{\text{σ}}_{\text{order}}^{\text{2}}}{{\text{σ}}_{\text{demand}}^{\text{2}}}\end{array}$

Calculation of the bullwhip measure for the manufacturer:

$\begin{array}{c}\text{Bullwhip}=\frac{\text{Variance}\text{of}\text{orders}}{\text{Variance}\text{of}\text{demand}}\\ =\frac{1350}{750}\\ =1.8\end{array}$ (4)

The bullwhip measure for the manufacturer is calculated by dividing the variance of order with the variance of demand. 1350 is divided by 750, which gives 1.8 as the bullwhip measure for the manufacturer.

Hence, the bullwhip measure for the manufacturer is 1.8

e)

Summary Introduction

To determine: Which firm exhibits the highest bullwhip effect in the supply chain.

Answer to Problem 6P

The retailer exhibits the highest bullwhip effect in the supply chain.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Weekly}\text{variance}\text{of}\text{demand}=\text{200}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{retailer}=\text{500}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{wholesaler}=6\text{00}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{distributor}=75\text{0}\text{units}\\ \text{Variance}\text{of}\text{order}\text{for}\text{manufacturer}=1,35\text{0}\text{units}\end{array}$

On comparing equations (1), (2), (3) & (4), it can be inferred that retailers have the highest bullwhip effect.

Hence, the retailer exhibits the highest bullwhip effect in the supply chain.