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G-Motor manufactures airplane engines and has an annual capacity of K units. For the current production facilities, the company has an annual cost of $C, million. G-motor plans to expand its current aircraft engine capacity in light of anticipated growth in aircraft engine demand in the coming years. The company intends to expand its manufacturing capacity by establishing new facilities. Production facilities can be set up in two ways (called as type A and type B). While the cost of establishing a type A manufacturing facility in any given year is $C4, the production capacity of such a facility is Pa units. The cost of establishing a Type B manufacturing facility is $Cg, and the anticipated production capacity is Pg units. Annual expenditures for any facility of type A or B are projected to be $E million dollars. G-Motor aims to make a decision about the establishment of a new facility during the planned period t=2022, 2023,.,T. The demand for aircraft engines in the coming years is forecasted as d, for each year. G-Motor is unable to maintain inventory because to a lack of available storage space, and all aircraft engines produced in any given year are deemed to be used to meet that year's demand. Inability to satisfy demand incurs a unit cost of $b, in year t. G-Motor can build just one new manufacturing facility each year, and a facility constructed in year t can be used to meet demand beginning in year t+1. Formulate a dynamic programming recursion that minimize the costs related to the opening new facilities decisions at the end of planning year T (Define State, Stage, Decision, Recursion formula, and Solution procedure).

G-Motor manufactures airplane engines and has an annual capacity of K units. For the current production facilities, the company has an annual cost of $C, million. G-motor plans to expand its current aircraft engine capacity in light of anticipated growth in aircraft engine demand in the coming years. The company intends to expand its manufacturing capacity by establishing new facilities. Production facilities can be set up in two ways (called as type A and type B). While the cost of establishing a type A manufacturing facility in any given year is $C4, the production capacity of such a facility is Pa units. The cost of establishing a Type B manufacturing facility is $Cg, and the anticipated production capacity is Pg units. Annual expenditures for any facility of type A or B are projected to be $E million dollars. G-Motor aims to make a decision about the establishment of a new facility during the planned period t=2022, 2023,.,T. The demand for aircraft engines in the coming years is forecasted as d, for each year. G-Motor is unable to maintain inventory because to a lack of available storage space, and all aircraft engines produced in any given year are deemed to be used to meet that year's demand. Inability to satisfy demand incurs a unit cost of $b, in year t. G-Motor can build just one new manufacturing facility each year, and a facility constructed in year t can be used to meet demand beginning in year t+1. Formulate a dynamic programming recursion that minimize the costs related to the opening new facilities decisions at the end of planning year T (Define State, Stage, Decision, Recursion formula, and Solution procedure).

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter3: Introduction To Linear Programming
Section3.1: What Is A Linear Programming Problem?
Problem 4P
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Q2 G-Motor manufactures airplane engines and has an annual capacity of K units. For the current production facilities, the company has an annual cost of $C, million. G-motor plans to expand its current aircraft engine capacity in light of anticipated growth in aircraft engine demand in the coming years. The company intends to expand its manufacturing capacity by establishing new facilities. Production facilities can be set up in two ways (called as type A and type B). While the cost of establishing a type A manufacturing facility in any given year is $Ca, the production capacity of such a facility is Pa units. The cost of establishing a Type B manufacturing facility is $C3, and the anticipated production capacity is Pg units. Annual expenditures for any facility of type A or B are projected to be $E million dollars. G-Motor aims to make a decision about the establishment of a new facility during the planned period t=2022, 2023,.,T. The demand for aircraft engines in the coming years is forecasted as d; for each year. G-Motor is unable to maintain inventory because to a lack of available storage space, and all aircraft engines produced in any given year are deemed to be used to meet that year's demand. Inability to satisfy demand incurs a unit cost of $b, in year t. G-Motor can build just one new manufacturing facility each year, and a facility constructed in year t can be used to meet demand beginning in year t+1. Formulate a dynamic programming recursion that minimize the costs related to the opening new facilities decisions at the end of planning year T (Define State, Stage, Decision, Recursion formula, and Solution procedure).
Transcribed Image Text:Q2 G-Motor manufactures airplane engines and has an annual capacity of K units. For the current production facilities, the company has an annual cost of $C, million. G-motor plans to expand its current aircraft engine capacity in light of anticipated growth in aircraft engine demand in the coming years. The company intends to expand its manufacturing capacity by establishing new facilities. Production facilities can be set up in two ways (called as type A and type B). While the cost of establishing a type A manufacturing facility in any given year is $Ca, the production capacity of such a facility is Pa units. The cost of establishing a Type B manufacturing facility is $C3, and the anticipated production capacity is Pg units. Annual expenditures for any facility of type A or B are projected to be $E million dollars. G-Motor aims to make a decision about the establishment of a new facility during the planned period t=2022, 2023,.,T. The demand for aircraft engines in the coming years is forecasted as d; for each year. G-Motor is unable to maintain inventory because to a lack of available storage space, and all aircraft engines produced in any given year are deemed to be used to meet that year's demand. Inability to satisfy demand incurs a unit cost of $b, in year t. G-Motor can build just one new manufacturing facility each year, and a facility constructed in year t can be used to meet demand beginning in year t+1. Formulate a dynamic programming recursion that minimize the costs related to the opening new facilities decisions at the end of planning year T (Define State, Stage, Decision, Recursion formula, and Solution procedure).
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