Question 3B (20 Marks) CWD sports center sells Mountain Bikes, which it orders from the USA. Because of shipping and handling costs, each order must be for 20 Bikes. Because of the time it takes to receive an order, the company places an order every time the present stock drops to 10 Bikes. It costs $20 to place an order. It costs the company $100 in lost sales when a customer asks for a Bike and the warehouse is out of stock. It costs $50 to keep each Bike stored in the warehouse. If a customer cannot purchase a Bike when it is requested, the customer will not wait until one comes in but will go to a competitor. The following probability distribution for demand for Bikes has been and the time required to receive an order once it is placed (lead time) has the following probability distribution: Lead time Demand/ (weeks) Probability week Probability 1 0.45 1 0.15 2 0.30 2 0.25 3 0.25 3 0.40 4 4 0.20 The company has 15 Bikes in stock. Orders are always received at the beginning of the week. Note that a lead time of 2 weeks imply that an order placed in week one will arrive in week 4. Required a) Construct the appropriate random number mappings for the random variables starting with .00. (2.5 marks for demand and 1.5 mark for lead time) b) Simulate CWD's ordering and sales policy for 20 weeks. c) Compute the average cost of the policy 56 demand 15 84 .16 .12 .55.16 .84 63 .33 .57 .18 .26 .23 .52 .37 .70 .56 lead time .47 .74 .35 .56 .64 .21 .55 .01 .40 Use the following headings MonthOI URAI RN D DF EI SO order RN lead-time IC SOC OC TC .99 .16 ल .31
Question 3B (20 Marks) CWD sports center sells Mountain Bikes, which it orders from the USA. Because of shipping and handling costs, each order must be for 20 Bikes. Because of the time it takes to receive an order, the company places an order every time the present stock drops to 10 Bikes. It costs $20 to place an order. It costs the company $100 in lost sales when a customer asks for a Bike and the warehouse is out of stock. It costs $50 to keep each Bike stored in the warehouse. If a customer cannot purchase a Bike when it is requested, the customer will not wait until one comes in but will go to a competitor. The following probability distribution for demand for Bikes has been and the time required to receive an order once it is placed (lead time) has the following probability distribution: Lead time Demand/ (weeks) Probability week Probability 1 0.45 1 0.15 2 0.30 2 0.25 3 0.25 3 0.40 4 4 0.20 The company has 15 Bikes in stock. Orders are always received at the beginning of the week. Note that a lead time of 2 weeks imply that an order placed in week one will arrive in week 4. Required a) Construct the appropriate random number mappings for the random variables starting with .00. (2.5 marks for demand and 1.5 mark for lead time) b) Simulate CWD's ordering and sales policy for 20 weeks. c) Compute the average cost of the policy 56 demand 15 84 .16 .12 .55.16 .84 63 .33 .57 .18 .26 .23 .52 .37 .70 .56 lead time .47 .74 .35 .56 .64 .21 .55 .01 .40 Use the following headings MonthOI URAI RN D DF EI SO order RN lead-time IC SOC OC TC .99 .16 ल .31
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 56P
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Transcribed Image Text:Question 3B (20 Marks)
CWD sports center sells Mountain Bikes, which it orders from the USA. Because of shipping
and handling costs, each order must be for 20 Bikes. Because of the time it takes to receive an
order, the company places an order every time the present stock drops to 10 Bikes. It costs $20
to place an order. It costs the company $100 in lost sales when a customer asks for a Bike and
the warehouse is out of stock. It costs $50 to keep each Bike stored in the warehouse. If a
customer cannot purchase a Bike when it is requested, the customer will not wait until one
comes in but will go to a competitor. The following probability distribution for demand for
Bikes has been and the time required to receive an order once it is placed (lead time) has the
following probability distribution:
Lead time
Demand/
(weeks)
Probability week
Probability
1
0.45
1
0.15
2
0.30
2
0.25
3
0.25
3
0.40
4
4
0.20
The company has 15 Bikes in stock. Orders are always received at the beginning of the week.
Note that a lead time of 2 weeks imply that an order placed in week one will arrive in week 4.
Required
a) Construct the appropriate random number mappings for the random variables starting
with .00. (2.5 marks for demand and 1.5 mark for lead time)
b) Simulate CWD's ordering and sales policy for 20 weeks.
c) Compute the average cost of the policy
56
demand 15 84 .16 .12 .55.16 .84 63 .33 .57 .18 .26 .23 .52 .37 .70 .56
lead time .47 .74 .35 .56
.64 .21 .55 .01 .40
Use the following headings
MonthOI URAI RN D DF EI SO order RN
lead-time IC
SOC OC TC
.99 .16
ल
.31
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