statistics
Project Description:
hej,
i have got these questions from a course simulation of production system. it would be great if, i can get the solutions of these question. i also have a deadline to show it on friday (28.3.2014) this week.
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home work for simulation of production system
instruction: make your excel le (each model can be on a separate worksheet in one excel le).
exercise 1. fred is in charge of inventory at the bedrock company. he would like to be able to guarantee a high service level, say at least 98%, for product p. this means that fred must find a policy which will ensure that there is always sufficient stock on hand to meet a variable demand pattern, as well as the uncertainty associated with delivery times.
freds current policy is to place an order for 30 units of product p whenever onhand inventory falls to the reorder level of 15 units or less. having studied sales records for product p over the past six months, fred has now produced the following data tables for demand and lead times:
daily demand for product p 0 1 2 3 4 5 6
probability 0.03 0.05 0.13 0.25 0.22 0.20 0.12
lead time (days) 1 2 3
probability 0.20 0.50 0.30
lost sales occur when there is insufficient stock on hand to meet demand. service level, expressed as a percentage, is defined as
service level = 1  (lost sales)/(total demand) = (demand satisfied)/(total demand)
for example, if total demand is 60 and lost sales are 2, then service level = 12=60 = 96:7%.
assume that the beginning inventory is 30. simulate for 30 days in your simulation table.
answer the questions below:
(a)under the current policy and using 100 replicates, estimate the service level and the average inventory on hand. report 95% confidence intervals for both kpis.
(b)propose an inventory policy (reorder point and order quantity) that can reduce average inventory while satisfying the requirement of 98% service level. for this policy, report 95% confidence intervals for the service level and the average inventory on hand.
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exercise 2. acme equipment company is considering the development of a new machine that would be marketed to tire manufacturers. research and development costs for the project are expected to be about $4 million but could vary between $3 and $6 million. the market life for the product is estimated to be 3 to 8 years with all intervening possibilities being equally likely. the company thinks it will sell 250 units per year, but acknowledges that this figure could be as low as 50 or as high as 350. the company will sell the machine for about $23,000. finally, the cost of manufacturing the machine is expected to be $14,000 but could be as low as $12,000 or as high as $18,000. the companys cost of capital is 15%.
hint:
you only need to calculate present value for pro ts because the r&d cost is already a present value.
excel has a pv(: : :) function to compute the present value. see excel help for details.
(a)create an excel model to calculate the possible net present values (npvs) that could result from taking on this project.
(b)replicate the model 500 times. what is the expected npv for this project? report a 95% confidence interval.
(c)what is the probability of this project generating a positive npv for the company? that is, the other simulation output is an indicator variable (1 if making pro t and 0 if making a loss).
i have got these questions from a course simulation of production system. it would be great if, i can get the solutions of these question. i also have a deadline to show it on friday (28.3.2014) this week.
=======================================
home work for simulation of production system
instruction: make your excel le (each model can be on a separate worksheet in one excel le).
exercise 1. fred is in charge of inventory at the bedrock company. he would like to be able to guarantee a high service level, say at least 98%, for product p. this means that fred must find a policy which will ensure that there is always sufficient stock on hand to meet a variable demand pattern, as well as the uncertainty associated with delivery times.
freds current policy is to place an order for 30 units of product p whenever onhand inventory falls to the reorder level of 15 units or less. having studied sales records for product p over the past six months, fred has now produced the following data tables for demand and lead times:
daily demand for product p 0 1 2 3 4 5 6
probability 0.03 0.05 0.13 0.25 0.22 0.20 0.12
lead time (days) 1 2 3
probability 0.20 0.50 0.30
lost sales occur when there is insufficient stock on hand to meet demand. service level, expressed as a percentage, is defined as
service level = 1  (lost sales)/(total demand) = (demand satisfied)/(total demand)
for example, if total demand is 60 and lost sales are 2, then service level = 12=60 = 96:7%.
assume that the beginning inventory is 30. simulate for 30 days in your simulation table.
answer the questions below:
(a)under the current policy and using 100 replicates, estimate the service level and the average inventory on hand. report 95% confidence intervals for both kpis.
(b)propose an inventory policy (reorder point and order quantity) that can reduce average inventory while satisfying the requirement of 98% service level. for this policy, report 95% confidence intervals for the service level and the average inventory on hand.
==========================================================
exercise 2. acme equipment company is considering the development of a new machine that would be marketed to tire manufacturers. research and development costs for the project are expected to be about $4 million but could vary between $3 and $6 million. the market life for the product is estimated to be 3 to 8 years with all intervening possibilities being equally likely. the company thinks it will sell 250 units per year, but acknowledges that this figure could be as low as 50 or as high as 350. the company will sell the machine for about $23,000. finally, the cost of manufacturing the machine is expected to be $14,000 but could be as low as $12,000 or as high as $18,000. the companys cost of capital is 15%.
hint:
you only need to calculate present value for pro ts because the r&d cost is already a present value.
excel has a pv(: : :) function to compute the present value. see excel help for details.
(a)create an excel model to calculate the possible net present values (npvs) that could result from taking on this project.
(b)replicate the model 500 times. what is the expected npv for this project? report a 95% confidence interval.
(c)what is the probability of this project generating a positive npv for the company? that is, the other simulation output is an indicator variable (1 if making pro t and 0 if making a loss).
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