The inequality you've presented, "DEMAND $!=$ SALES $!=$ ORDERS," lies at the heart of the bullwhip effect, a phenomenon where small fluctuations in demand at the consumer level can lead to amplified variations in orders placed upstream in the supply chain. Let's break down each component of the inequality and then delve into an example to illustrate the concept.

Demand: This refers to the actual consumption or usage of a product or service by end consumers. Demand can be influenced by various factors such as consumer preferences, economic conditions, marketing efforts, etc.

Sales: Sales represent the transactions where products or services are exchanged for money. While sales are directly influenced by demand, they can also be affected by factors like pricing strategies, promotions, distribution channels, etc.

Orders: Orders are the requests placed by retailers or wholesalers to suppliers for replenishing their inventory. These orders are based on sales forecasts, inventory levels, and anticipated demand.

Now, let's consider an example from the automotive industry:

Imagine a car manufacturer $($let$\text{'}$s call it "AutoCo"$),$ a regional distributor, and several car dealerships.

Demand: Consumer demand for cars fluctuates based on various factors like economic conditions, fuel prices, and consumer preferences. During a period of economic growth, demand for cars increases as people have more disposable income. Conversely, during a recession, demand may decrease as people cut back on non$-$essential purchases.

Sales: AutoCo sells cars to regional distributors based on sales forecasts and historical data. The regional distributor, in turn, sells cars to individual dealerships.

Orders: Car dealerships place orders with the regional distributor based on their inventory levels and sales forecasts. However, due to uncertainties in consumer demand and the time lag between placing an order and receiving the inventory, these orders may not always align perfectly with actual consumer demand.

Now, let's examine how the bullwhip effect manifests in this scenario:

Consumer Demand Fluctuation: Suppose there's an unexpected increase in consumer demand for a particular model of car due to a favorable review or a sudden trend. This increase in demand may not be immediately apparent to the dealerships.

Sales Forecasting and Ordering: The dealership, anticipating steady demand based on historical data, may place orders for more units of other models but not enough of the suddenly popular model.

Amplification Up the Supply Chain: The regional distributor receives these orders and interprets them as a sign of increased overall demand. They, in turn, place larger orders with AutoCo to meet the perceived demand.

Excess Inventory or Stockouts: AutoCo, seeing increased orders from the distributor, ramps up production. However, by the time the cars are produced and delivered, the spike in consumer demand may have already passed, resulting in excess inventory. Conversely, if the distributor's orders were insufficient to meet actual consumer demand, there could be stockouts at the dealership level.

This example illustrates how the bullwhip effect can lead to inefficiencies, such as excess inventory, stockouts, and increased costs throughout the supply chain, due to the mismatch between actual consumer demand, sales, and orders.