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Engineering Computer Science Operations Research : Applications and Algorithms

From the information, observe that during the next four quarters, Dorian Auto must meet the demand for cars. Consider the following events: x t = Number of cars produced at the beginning of each quarter(t=1,2,3,4) d t = Demand during each quarter t i t = Number of cars on hand at end of time t Total cost (TC) = {cost of increasing quarterly production capacity+cost of maintaining a car of production capacity+variable cost of producing a car+holding cost} Total cost (TC) = 100(x t +1)+50(i t +x t -d t )+2000x t +150(i t +x t -d t ) Inventory at end of quarter t={inventory at end of quarter(t-1)+(quartertproduction-demand oftquarter)} i t = i t-1 +(x t -d t ) For 1 st quarter, i 1 =300+x 1 -4000 For 2 nd quarter, i 2 =i 1 +x 2 -2000

From the information, observe that during the next four quarters, Dorian Auto must meet the demand for cars. Consider the following events: x t = Number of cars produced at the beginning of each quarter(t=1,2,3,4) d t = Demand during each quarter t i t = Number of cars on hand at end of time t Total cost (TC) = {cost of increasing quarterly production capacity+cost of maintaining a car of production capacity+variable cost of producing a car+holding cost} Total cost (TC) = 100(x t +1)+50(i t +x t -d t )+2000x t +150(i t +x t -d t ) Inventory at end of quarter t={inventory at end of quarter(t-1)+(quartertproduction-demand oftquarter)} i t = i t-1 +(x t -d t ) For 1 st quarter, i 1 =300+x 1 -4000 For 2 nd quarter, i 2 =i 1 +x 2 -2000

Solution Summary: The author explains that Dorian Auto must meet the demand for cars during the next four quarters.

Operations Research : Applications and Algorithms

Operations Research : Applications and Algorithms

4th Edition

ISBN: 9780534380588

Author: Wayne L. Winston

Publisher: Brooks Cole

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Expert Solution & Answer

Chapter 4, Problem 24RP

Explanation of Solution

From the information, observe that during the next four quarters, Dorian Auto must meet the demand for cars.

Consider the following events:

x_t = Number of cars produced at the beginning of each quarter(t=1,2,3,4)

d_t = Demand during each quarter t

i_t = Number of cars on hand at end of time t

Total cost (TC) = {cost of increasing quarterly production capacity+cost of maintaining a car of production capacity+variable cost of producing a car+holding cost}

Total cost (TC) = 100(x_t+1)+50(i_t+x_t-d_t)+2000x_t+150(i_t+x_t-d_t)

Inventory at end of quarter t={inventory at end of quarter(t-1)+(quartertproduction-demand oftquarter)}

i_t = i_t-1+(x_t-d_t)

For 1^st quarter,

i₁=300+x₁-4000

For 2^nd quarter,

i₂=i₁+x₂-2000

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Chapter 4, Problem 23RP

Chapter 4, Problem 26RP

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Chapter 4 Solutions

Operations Research : Applications and Algorithms

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.4 - Prob. 1P Ch. 4.4 - Prob. 2P Ch. 4.4 - Prob. 3P Ch. 4.4 - Prob. 4P Ch. 4.4 - Prob. 5P Ch. 4.4 - Prob. 6P Ch. 4.4 - Prob. 7P

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