Question

With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct? 

 

• A. Curve P1: Total cost, Curve P2: Holding cost, Curve P3: Setup cost, and Curve P4: Production cost.
• B. Curve P1: Holding cost, Curve P2: Setup cost, Curve P3: Production cost, and Curve P4: Total cost.
• C. Curve P1: Production cost, Curve P2: Holding cost, Curve P3: Total cost, and Curve P4: Setup cost.
• D. Curve P1: Total cost, Curve P2: Production cost, Curve P3: Holding cost, and Curve P4: Setup cost.

Hint:

Remember the classic shape of the EOQ cost curves: Holding cost goes up (linear), Setup cost comes down (hyperbolic), and Total cost is U-shaped. The optimal order quantity (EOQ) is at the point where the holding cost curve intersects the setup cost curve, which is also the minimum of the total cost curve.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The Economic Order Quantity (EOQ) model is a classic inventory management model that aims to determine the optimal order quantity that minimizes the total inventory costs. These costs are typically the sum of ordering costs (setup costs), holding costs (carrying costs), and the cost of goods (production cost).
Step 2: Key Formula or Approach:
We need to understand how each cost component behaves as a function of the order quantity.
- Holding Cost: The cost to hold inventory. It increases linearly as the order quantity increases (since the average inventory level increases). This should be a line with a positive slope starting from the origin.
- Setup Cost (or Ordering Cost): The cost incurred each time an order is placed. The total setup cost for a given period decreases as the order quantity increases because fewer orders are needed to meet the same demand. This curve is hyperbolic.
- Production Cost (or Purchase Cost): The actual cost of the items. In the basic EOQ model, the cost per unit is constant regardless of the order quantity. This will be a horizontal line if we are plotting cost per unit.
- Total Cost: The sum of all the above costs. It is the sum of an increasing function (holding cost) and a decreasing function (setup cost), which results in a U-shaped curve. The minimum point of this curve corresponds to the EOQ.
Step 3: Detailed Explanation:
Let's match the curves in the graph with the cost behaviors:
- Curve P4: is a horizontal line, indicating a cost that is constant per unit of order quantity. This represents the Production cost.
- Curve P2: is a straight line increasing from the origin. This represents the Holding cost, which is directly proportional to the quantity.
- Curve P3: is a decreasing curve that approaches zero as the order quantity gets larger. This represents the Setup cost.
- Curve P1: is a U-shaped curve, which is the sum of the increasing holding cost (P2) and the decreasing setup cost (P3). This represents the Total cost.
Step 4: Final Answer:
The correct matching is:
P1: Total cost
P2: Holding cost
P3: Setup cost
P4: Production cost
This corresponds to option (A).
Step 5: Why This is Correct:
The shapes of the curves P1, P2, P3, and P4 perfectly match the theoretical behavior of the total cost, holding cost, setup cost, and production cost, respectively, as functions of order quantity in the EOQ model.