ROP With Variable Demand and Lead Time Data Risk of Stock Out Assume the maximum risk of stock out we wish to take is 1%. What is the ROP? Average demand per week = 200 Stdv of demand per week = 50 Average lead time in weeks = 3 Stdv of lead time in weeks = 2 Service level: 95% Safety stock will become: Lead time and demand are normally distributed New ROP = ROP With Variability Service level 90% 95% 99% 99.9% Note: 1 Service level = stockout risk Key Z-Values Z-value 1.28 1.65 2.33 3.08
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.The materials manager of a tire manfacturer must predict periodically place order for a key chemical one of the raw materials used in manufacturing uses the chemical at a rate of 300lbs each week and the lead time of delivery is 4 days. Assume that the manufacturing operation runs 5 days a week. At what point should the chemical be reorderedd a. when 1200lbs are remaining b. where 0lbs are remaining c. where 375lbs are remaining d. when 240lbs are remHenrique Correa's bakery prepares all its cakesbetween 4 A.M. and 6 A.M. so they will be fresh when customersarrive. Day-old cakes are virtually always sold, but at a 50% discountofT the regular $ 10 price. The cost of baking a cake is $6, anddemand is estimated to be normally distributed, with a mean of25and a standard deviation of 4. What is the optimal stocking level?
- [item no. 9] In marginal analysis with discrete distributions for single-period inventory models, the value of ML/(ML+MP) is 0.8. The probability distribution of sales is given by the following by the table below. Find the optimal number of units to order. Daily demand 80 90 100 110 120 Probability that demand will be at this level 0.10 0.20 0.30 0.30 0.10 a. 90 units b. 110 units c. 100 units d. 80 unitsChange the ordering simulation so that emergencyorders are never made. If demand in any week isgreater than supply, the excess demand is simplylost. Simulate the same (s, S) policies as in theexample.The lead time demand for bathing suits is governed bythe discrete random variable shown in Table 11. Thecompany sells an average of 10,400 suits per year. The costof placing an order for bathing suits is $30, and the cost ofholding one bathing suit in inventory for a year is $3. Thestockout cost is $3 per bathing suit. Use marginal analysisto determine the optimal order quantity and the reorderpoint.Lead TimeDemand Probability180 .30190 .30200 .15210 .10220 .15
- A component used in a manufacturing facility is ordered from an outside supplier.Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks isWeek 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. (Hint:Express h as the holding cost per thousand units.)d. Which method resulted in the lowest-cost policy for this problem?A component used in a manufacturing facility is ordered from an outside supplier.Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks isWeek 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. (Hint:Express h as the holding cost per thousand units.)a. What ordering policy is recommended by the Silver–Meal heuristic?A component used in a manufacturing facility is ordered from an outside supplier.Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks isWeek 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. (Hint:Express h as the holding cost per thousand units.)c. What ordering policy is recommended by the least unit cost heuristic?
- A component used in a manufacturing facility is ordered from an outside supplier.Because the component is used in a variety of end products, the demand is high. Estimated demand (in thousands) over the next 10 weeks isWeek 1 2 3 4 5 6 7 8 9 10Demand 22 34 32 12 8 44 54 16 76 30The components cost 65 cents each and the interest rate used to compute the holding cost is 0.5 percent per week. The fixed order cost is estimated to be $200. (Hint:Express h as the holding cost per thousand units.)b. What ordering policy is recommended by the part period balancing heuristic?A hot dog vendor at Wrigley Field sells hot dogs for$1.50 each. He buys them for $1.20 each. All the hot dogshe fails to sell at Wrigley Field during the afternoon can besold that evening at Comiskey Park for $1 each. The dailydemand for hot dogs at Wrigley Field is normally distributedwith a mean of 40 and a standard deviation of 10.a If the vendor buys hot dogs once a day, how manyshould he buy?b If he buys 52 hot dogs, what is the probability that hewill meet all of the day’s demand for hot dogs at Wrigley?The Swedish company Rossons Sport sells skis endski-equipment. They purchase skis at a price of $260 per pair andsales price is $420. Skis not sold this season can be sold early nextseason at a discounted price, $200. In addition they estimate thestock holding cost between seasons to be $25 per pair of skis.Past sales shows that demand per season is normal distributedwith a mean of 459 pairs and a standard deviation of 56.a) Calculate the shortage and overage cost per pairb) Advice Rossons Sport how many pair of skis they should purchasec) What is the service level?