Orders overstock from

We add (56.4 X 10) + (1.51 X 110) to the expected profit from the first seven-week half because there is effectively no overstock that must be sold to the discount store at the end of the first seven weeks or understock where margin is lost. Our analysis indicates that allowing for a second order in the season increases profits by 30,070 — 29,767 = 303 even if there is no improvement in forecast accuracy for the second seven-week period. The profit increase will be smaller, however, if we assume that customers who do not find the product at the end of the first seven weeks are unwilhng to wait for the second order to arrive. Observe that as a result of allow-ingasecondorder,thetotalorderquantityhasdecreasedfrom358shawlstol95 + 140.1 = 335.1 shawls. The expected overstock at the end of the season has decreased from 79.8 to 56.4 shawls and the expected understock has decreased to 1.51. 

As in the previous analysis, we assume that the buyer is accurately able to predict sales for the first seven-week period after observing sales for the first week. She thus accounts for the overstock and understock at the end of the first seven week period when placing her second order. Given an expected overstock of 56.4 shawls and an expected understock of 1.51 from the first order, the net second order is thus 151 - 56.4 -l- 1.51 = 96.11 shawls. With 151 shawls at the start of the second seven weeks, we obtain... 

Expected profit from second order (using Equation 13.3) = 15,254 Expected overstock (using Equation 13.4) = 11.3 Expected understock(using Equation 13.5) = 0.30... 

Again observe that there is no overstock cost at the end of the first seven weeks and we have assumed that customer orders that are understocked in the first order are served from the second order. Thus, the net profits for the season are 14,670 (first seven weeks) + 56.4 X 10 (no overstock at the end of first seven weeks) +1.51 X 110 (understock is served from second order) -I- 15,254 (second seven weeks) = 30,654. If forecast accuracy improves as a result of observing early seasonal demand, the season s profit increases by 30,654 — 29,767 = 887. The expected overstock at the end of the season has now declined to 11.3 units and the expected understock to 0.3 units. A second order and improved forecast accuracy as a result of seeing early season sales thus increase profits and decrease overstocks and understock. 

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. 

For the 120 style/colors in this department, we determined that the initial order quantity by solving problem (PHr) using the heuristic modified to include returns. We then observed x, the sales until the second week and set the reorder quantity Q2 using the procedure developed in Sect. 3. Since at the end of the season we knew total sales and actual sales per week for each dress, we were able to calculate the stockouts, overstock, backorders, dollar sales and profits that would have resulted from our ordering policy. To compare our method with the current ordering rules, we also calculated these... 

Observe that although the total orders placed by our method and existing practice are similar, the composition of these orders across the two periods is different Our heuristic reduces overstocks, stockouts and backorders enough to increase profits compared with the current rule by from 2.23 to 4.92% of current sales, depending on the value of Cb. Profit before tax for this retailer is around 3% of sales. Consequently, our heuristic offers the potential to approximately double profit. 

Our results also show the impact of Cb on the solution. Order quantities for the current rule do not change, as the current rule does not eonsider Cb in determining order quantities. When Cb = 5, we order a smaller initial quantity as backorders are now relatively less expensive. This in turn increases backorders and stockouts, but reduces overstocks, which increases profit improvement from 3.52 to 4.92%. On the other hand when Cb = 15, we order a larger initial quantity as backorders are relatively more expensive. This reduces backorders and stockouts, but increases overstocks, which reduces the profit improvement from 3.52 to 2.23%. 

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