Question

Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $10 each from its Asian supplier, TeddySports. Unfortunately, at the time of order placement, demand is still uncertain. Teddy Bower forecasts that its demand is normally distributed with mean of 2,100 and standard deviation of 1,200. Teddy Bower sells these parkas at $22 each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity and receives a tax credit of 20% COGS. Teddy has decided to sell rainboots to supplement its parkas product offerings. Rainboots are also procured from an outside supplier at a cost of $10/rainboot, but this time the supplier is located in South Carolina. As a result, it only takes the supplier 3 weeks to fulfill an order (once placed) and it costs $300 to ship the order. As with parkas, demand for rainboots is uncertain; as opposed to parkas, demand for rainboots exists throughout the year. Teddy Bower has the ability to carry inventory at a minimal annual carrying cost estimated to be 10% of the product cost (any unsold rainboots can be held in inventory to meet future demand). Teddy Bower estimates the annual demand for rainboots to be normally distributed with a mean of 4000 and standard deviation of 1000. Given the high profit margin on rainboots, Teddy Bower does not want to lose more than 2% of potential sales for rainboots. When should Teddy Bower submit an order to its supplier for (more) rainboots? When the current inventory (in-stock) is… a. between 250-350 b. between 350-450 c. between 550-650 d. between 650-750 e. between 750-850 How much should Teddy Bower order? a. 500 to 1000 b. 1000 to 1500 f. 1500 to 2000 g. 2000 to 2500 h. 2500 to 3000 i.

Answer 1

Pregunta 1 Fashionables is a franchisee of The restrained, the famous retailer of trendy apparel. Prior to the winter season, The restrained offers Fashionables the alternative of five distinct colours of a particular sweater design. The sweaters are knit abroad via hand, and on the grounds that of the leadtimes involved, Fashionables will must order its assortment prematurely of the promoting season. As per the contracting terms furnished by The confined, Fashionables will also no longer be able to cancel, modify or reorder sweaters for the duration of the promoting season. Demand for each colour throughout the season is in most cases disbursed with a median of 500 and a usual deviation of 200. Extra, you can also assume that the demands for each and every sweater are unbiased of those for a different colour. The confined offers the sweaters to Fashionables on the wholesale price of $forty per sweater, and Fashionables plans to sell every sweater on the retail rate of $70 per unit. The limited delivers orders positioned with the aid of Fashionables in truckloads at a price of $2,000 per truckload. The transportation fee of $2,000 is borne via Fashionables. Count on except in any other case distinctive that all the sweaters ordered by way of Fashionables will match into one truckload. Additionally count on that every one different related charges, corresponding to unpacking and handling, are negligible. The restrained does not receive any returns of unsold stock. However, Fashionables can sell the entire unsold sweaters on the end of the season at the hearth-sale prices of $20 every. A) what number of items of each and every sweater-variety must Fashionables order to maximise its expected profit? B) If Fashionables desires to make sure a 97.5% in-inventory chance, what must its order variety be for every sort of sweater? C) If Fashionables desires to make certain a ninety seven.5% fill cost, what should its order number be for each variety of sweater? For the subsequent three materials (d ­ e) assume Fashionables' orders 725 of each sweater. D) what is Fashionables' expected profit? E) what is Fashionables' expected fill expense for every sweater? F) what is the stockout probability for each sweater? G) Now consider that The restricted broadcasts that the unit of truckload potential is 2500 whole models of sweaters. If Fashionables orders more than 2500 models in whole (actually, from 2501 to 5,000 items in total), it's going to have got to pay for 2 truckloads. What now is trendy's highest quality order wide variety for each sweater?

Universidad de Chile Facultad de Cs. Físicas y Matemáticas Departamento de Ingeniería Industrial

IN47B Ingeniería de Operaciones IN404 Gestión de Operaciones II Profesores: C. Bravo, M. Olivares, F. Ordóñez

Respuesta:

Q 9.Four a) Use show off 9.6. The underage cost is Cu 70 forty 30 and the overage fee is Co 40 20 20 . The primary ratio is Cu /(Co Cu ) 30 / 50 zero.6 . From the average typical Distribution perform table, (zero.25) 0.5987 and (0.26) 0.6026 , so we decide upon z zero.26 . Convert that z-statistic into z 500 0.26 200 552 . Be aware that the fee an order range Q of a truckload has no affect on the profit maximizing order wide variety. B) Use showcase 9.Eleven. We need to in finding the z in the common common Distribution (z ) zero.9750 considering the fact that (z ) is the in-inventory function desk such that likelihood. We see that (1.Ninety six) zero.9750 , so we decide upon z 1.96 . Convert z 500 1.96 200 892 . To Q c) Use exhibit 9.10. We first to find our target misplaced sales with the equation L( z ) ( / ) (1 Fill fee) 0.0625 . We see within the normal common Loss operate desk that L(1.14) zero.0634 and L(1.15) zero.0621 , so we use the circular up rule to decide on the better z, z = 1.15. Now convert to Q: Q 500 1.15 200 730 . D) If 725 items are ordered, then the corresponding z-statistic is z Q / (725 500) / 200 1.Thirteen . We have got to evaluation lost sales, anticipated earnings and expected left over stock earlier than we will overview the anticipated revenue. Anticipated lost earnings with the normal common is bought from the ordinary natural Loss operate table, L(1.13) zero.0646 . Anticipated L(z ) 200 zero.0646 12.9 . Anticipated sales is 500 ­ 12.9 = misplaced sales is 487.1. Expected left over stock is 725 ­ 487.1 = 237.9. Anticipated profit is
expected revenue 70 forty 9855 487.1 forty 20 237.9

So the expected profit per sweater is 9,855. The whole expected profit is 5 times that quantity, minus 2000 times the number of truckloads required. 1 12.9 / 500 ninety seven.4% . E) The fill rate is 1 anticipated lost revenue / f) The stockout probability is the probability demand exceeds the order (1.13) 12.9% . Number 725, which is 1 g) If we order the anticipated revenue maximizing order wide variety for each and every sweater, then that equals 5 552 2,760 sweaters. With an order variety of 552 sweaters expected lost earnings is 56.5 200 L(zero.26) 200 zero.2824 , expected earnings is 500 ­ 56.5 = 443.5 and expected left over stock is 552 ­ 443.5 = 108.5. Expected profit per sweater is anticipated profit 70 forty 443.5 forty 20 108.5
11,135

Universidad de Chile Facultad de Cs. Físicas y Matemáticas Departamento de Ingeniería Industrial

IN47B Ingeniería de Operaciones IN404 Gestión de Operaciones II Profesores: C. Bravo, M. Olivares, F. Ordóñez

due to the fact two truckloads are required, the whole profit is then 5 11,136 2 2000 51, 675 . If we order best 500 models per sweater style, then we can overview the anticipated revenue per sweater to be 11,010. Total revenue is then 5 11,010 2000 53,050. Thus, we're at an advantage simply ordering one truckload with 500 sweaters of every type.