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1 CAPACITY INVESTMENT PLANNING MODEL CAPACITY INVESTMENT PLANNING MODEL CHE 5480- Spring 2003 University of Oklahoma School of Chemical Engineering and.

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Presentation on theme: "1 CAPACITY INVESTMENT PLANNING MODEL CAPACITY INVESTMENT PLANNING MODEL CHE 5480- Spring 2003 University of Oklahoma School of Chemical Engineering and."— Presentation transcript:

1 1 CAPACITY INVESTMENT PLANNING MODEL CAPACITY INVESTMENT PLANNING MODEL CHE 5480- Spring 2003 University of Oklahoma School of Chemical Engineering and Materials Science Prof. M. Bagajewicz CHE 5480- Spring 2003 University of Oklahoma School of Chemical Engineering and Materials Science Prof. M. Bagajewicz

2 2 Process Planning Under Uncertainty OBJECTIVES: Maximize Net Present Value Maximize Net Present Value Production Levels Production Levels DETERMINE: Network Expansions Network Expansions TimingSizingLocation GIVEN: Process Network Process Network Set of Processes Set of Chemicals A A 1 1 C C 2 2 D D 3 3 B B Forecasted Data Forecasted Data Demands & Availabilities Costs & Prices Capital Budget

3 3 Capacity Investment Planning Design Variables: to be decided before the uncertainty reveals  x  E it Y,, Q Y: Decision of building process i in period t E: Capacity expansion of process i in period t Q: Total capacity of process i in period t Control Variables: selected after uncertain parameters become known. Assume them known for the time being!!!! Control Variables: selected after uncertain parameters become known. Assume them known for the time being!!!! S: Sales of product j in market l at time t and scenario s S: Sales of product j in market l at time t and scenario s P: Purchase of raw mat. j in market l at time t and scenario s P: Purchase of raw mat. j in market l at time t and scenario s W: Operating level of of process i in period t and scenario s  ysys  P jlt S,, W it

4 4 ExampleExample Project Staged in 3 Time Periods of 2, 2.5, 3.5 years Process 1 Chemical 1 Process 2 Chemical 5 Chemical 2 Chemical 6 Process 3 Chemical 3 Process 5 Chemical 7 Chemical 8 Process 4 Chemical 4

5 5 Period 1 2 years Process 1 Chemical 1 Chemical 5 Process 3 Chemical 3 Chemical 7 10.23 kton/yr 22.73 kton/yr 5.27 kton/yr 19.60 kton/yr SolutionSolution

6 6 Period 2 2.5 years Process 1 Chemical 1 Chemical 5 Process 3 Chemical 3 Process 5 Chemical 7 Chemical 8 Process 4 Chemical 4 10.23 kton/yr 22.73 kton/yr 4.71 kton/yr 41.75 kton/yr 20.87 kton/yr SolutionSolution

7 7 Period 3 3.5 years Chemical 1 Process 2 Chemical 5 Chemical 2 Chemical 6 Process 3 Chemical 3 Process 5 Chemical 7 Chemical 8 Process 4 Chemical 4 22.73 kton/yr 22.73 ton/yr 80.77 kton/yr 44.44 kton/yr 14.95 kton/yr 29.49 kton/yr 43.77 kton/yr 29.49 kton/yr 21.88 kton/yr Process 1 SolutionSolution

8 8 MODELMODEL SETS I : Processes i,=1,…,NP J : Raw materials and Products, j=1,…,NC T: Time periods. T=1,…,NT L: Markets, l=1,..NM Y it : An expansion of process I in period t takes place (Yit=1), does not take place (Yit=0) E it : Expansion of capacity of process i in period t. Q it : Capacity of process i in period t. W it : Utilized capacity of process i in period t. P jlt : Amount of raw material/intermediate product j consumed from market l in period t S jlt : Amount of intermediate product/product j sold in market l in period t VARIABLES η ij : Amount of raw material/intermediate product j used by process i μ ij : Amount of product/intermediate product j consumed by process i γ jlt : Sale price of product/intermediate product j in market l in period t Γ jlt : Cost of product/intermediate product j in market l in period t δ it : Operating cost of process i in period t α it : Variable cost of expansion for process i in period t β it : Fixed cost of expansion for process i in period t L t : Discount factor for period t Lower and upper bounds on a process expansion in period t Lower and upper bounds on availability of raw material j in market l in period t Lower and upper bounds on demand of product j in market l in period t Maximum capital available in period t PARAMETERS NEXP t : maximum number of expansions in period t

9 9 MODELMODEL OBJECTIVE FUNCTION I : Processes i,=1,…,NP J : Raw mat./Products, j=1,…,NC T: Time periods. T=1,…,NT L: Markets, l=1,..NM Y it : An expansion of process I in period t takes place (Yit=1), does not take place (Yit=0) E it : Expansion of capacity of process i in period t. W it : Utilized capacity of process i in period t. P jlt : Amount of raw material/interm. product j consumed from market l in period t S jlt : Amount of intermediate product/product j sold in market l in period t γ jlt : Sale price of product/intermediate product j in market l in period t Γ jlt : Cost of product/intermediate product j in market l in period t δ it : Operating cost of process i in period t α it : Variable cost of expansion for process i in period t β it : Fixed cost of expansion for process i in period t L t : Discount factor for period t DISCOUNTED REVENUES INVESTMENT

10 10 MODELMODEL LIMITS ON EXPANSION I : Processes i,=1,…,NP J : Raw mat./Products, j=1,…,NC T: Time periods. T=1,…,NT L: Markets, l=1,..NM NEXP t : maximum number of expansions in period t α it : Variable cost of expansion for process i in period t β it : Fixed cost of expansion for process i in period t Lower and upper bounds on a process expansion in period t TOTAL CAPACITY IN EACH PERIOD LIMIT ON THE NUMBER OF EXPANSIONS Y it : An expansion of process I in period t takes place (Yit=1), does not take place (Yit=0) E it : Expansion of capacity of process i in period t. Q it : Capacity of process i in period t. LIMIT ON THE CAPITAL INVESTMENT

11 11 MODELMODEL UTILIZED CAPACITY IS LOWER THAN TOTAL CAPACITY I : Processes i,=1,…,NP J : Raw mat./Products, j=1,…,NC T: Time periods. T=1,…,NT L: Markets, l=1,..NM MATERIAL BALANCE BOUNDS Y it : An expansion of process I in period t takes place (Yit=1), does not take place (Yit=0) E it : Expansion of capacity of process i in period t. Q it : Capacity of process i in period t. W it : Utilized capacity of process i in period t. P jlt : Amount of raw material/intermediate product j consumed from market l in period t S jlt : Amount of intermediate product/product j sold in market l in period t NONNEGATIVITY INTEGER VARIABLES Lower and upper bounds on availability of raw material j in market l in period t Lower and upper bounds on demand of product j in market l in period t

12 12 MODELMODEL MATERIAL BALANCE i p k B A C D Reference Component is C “Stoichiometric” Coefficients

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