Cost of understocking

The cost of overstocking, denoted by Cg, is the loss incurred by a firm for each unsold unit at the end of the selling season. The cost of understocking, denoted by C , is the margin lost by a firm for each lost sale because there is no inventory on hand. The cost of understocking should include the margin lost from current sales, as well as future sales if the customer does not return. In summary, the two key factors that influence the optimal level of product availability are... 

In the L. L. Bean example, we have a cost of overstocking of Q = c — s = 5 and a cost of understocking of C = p - i = 55. As these costs change, the optimal level of product availability also changes. In the next section, we develop the relationship between the desired CSL and the cost of overstocking and understocking for seasonal items. 

Co. Cost of overstocking by one unit, Co = c — s C Cost of understocking by one unit, C = p — c CSL Optimal cycle service level 0 Corresponding optimal order size... 

We have assumed that C is the cost of losing one unit of demand during the stockout period. From comparing Equations 13.6 and 13.7, observe that for the same cost of understocking, a supply chain should offer a higher cycle service level if sales are lost rather than back-logged. In Example 13-5, we evaluate the optimal cycle service level if demand is lost during the stockout period (see worksheet Examples 13-4,5). 

The cost of understocking can also be decreased by providing the customer with a substitute product. Decreasing the cost of understocking allows a firm to increase profits by providing a lower level of product availability (because there are alternatives available to serve the customer), thus decreasing the amount of excess inventory at the end of the season. 

Given that the cost of overstocking is 10 per shawl and the cost of understocking is 110 per shawl, we obtain... 

Assume that the demand is a continuous nonnegative random variable with density functiony(x) and cumulative distribution function F(x). C is the margin per unit and, as a result, the cost of understocking per unit. Cg is the cost of overstocking per unit. 

We first consider the case of the independent retailer. The retailer has a margin of 5 per disc and can potentially lose 5 for each unsold disc. The retailer thus has a cost of overstocking = 5 and a cost of understocking C = 5. Using Eqnation 13.1, it is optimal for the retailer to aim for a service level of 5/(5 + 5) = 0.5 and order NORMINV(0.5,1000,300) = 1,000 discs. From Equation 13.3, the retailer s expected profits are 3,803, and the manufacturer makes 4,000 from selling 1,000 discs. The total supply chain profit with an independent retailer is thus 3,803 + 4,000 = 7,803. 

Assume that the manufacturer has a production cost v the retailer charges a retail price p and can salvage any leftover units for sr. The optimal order quantity 0 ordered by the retailer is evaluated using Equations 13.1 and 13.2, where the cost of understocking is C = (1 - f)p - c and the cost of overstocking is C = c - Sr. We thus obtain... 

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