Cost of overstocking

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... 

Having identified the factors that influence the optimal level of product availability, we now focus on actions a manager can take to improve supply chain profitability. We have shown in Section 13.2 that the costs of overstocking and understocking have a direct impact on both the... 

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

If there were no demand uncertainty, demand over the season would be 280 shawls with a profit of 280 X 110 = 30,800. Observe that expected profit is reduced by 30,800 - 29,767 = 1,033 = 798 + 235 because of uncertainty. Thus, uncertainty reduces the expected profit by the expected cost of overstocking and understocking. 

When ordering multiple products under a limited supply capacity, the allocation of capacity to products should be based on their expected marginal contrihntion to profits. This approach allocates a relatively higher fraction of capacity to products that have a high margin relative to their cost of overstocking. 

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. 

The structure of a buyback clause leads to the entire supply chain reacting to the order placed by the retailer and not to actual customer demand. If a supplier is selling to multiple retailers, it produces based on the orders placed by each retailer. Each retailer bases its order on its cost of overstocking and understocking (see Chapter 13). After actual sales materialize, unsold inventory is returned to the supplier separately from each retailer. As a result, the structure of the buyback clause increases information distortion when a supplier is selling to multiple retailers. At the end of the sales season, however, the snpplier does obtain information on actual sales. Information distortion is driven primarily by the fact that inventory is disaggregated at the retailers based on an ordering decision made when demand is uncertain. If inventory is produced by the supplier and sent out only as needed to the retailers, information distortion can be reduced. 

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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