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Capacity Investment Planning Model for Chemical Processes

This document presents a capacity investment planning model designed for processes within the chemical engineering and materials science domains, emphasizing decision-making under uncertainty. The model focuses on maximizing net present value through strategic expansions, production levels, and network optimization. Key variables include the timing and sizing of capital investments, processing capacities, demands, and market availability, with constraints on expansions and budget allocations over multiple time periods. It outlines foundational formulas used to integrate costs, revenues, and operational parameters effectively.

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Capacity Investment Planning Model for Chemical Processes

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

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

  3. Design Variables: to be decided before the uncertainty reveals 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 { } x = Y E Q , , it it it W S P it jlt jlt Capacity Investment Planning Control Variables:selected after uncertain parameters become known. Assume them known for the time being!!!! { } ys = , , 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 W: Operating level of of process i in period t and scenario s

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

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

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

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

  8. MODEL I : Processes i,=1,…,NP J : Raw materials and Products, j=1,…,NC T: Time periods. T=1,…,NT L: Markets, l=1,..NM SETS Yit: An expansion of process I in period t takes place (Yit=1), does not take place (Yit=0) Eit: Expansion of capacity of process i in period t. Qit: Capacity of process i in period t. Wit: Utilized capacity of process i in period t. Pjlt : Amount of raw material/intermediate product j consumed from market l in period t Sjlt : Amount of intermediate product/product j sold in market l in period t VARIABLES ηij : Amount of raw material/intermediate product j used by process i μij : Amount of product/intermediate product j consumed by process i γjlt : Sale price of product/intermediate product j in market l in period t Γjlt : Cost of product/intermediate product j in market l in period t δit : Operating cost of process i in period t αit : Variable cost of expansion for process i in period t βit : Fixed cost of expansion for process i in period t Lt : Discount factor for period t PARAMETERS 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 NEXPt: maximum number of expansions in period t

  9. MODEL OBJECTIVE FUNCTION INVESTMENT DISCOUNTED REVENUES Yit: An expansion of process I in period t takes place (Yit=1), does not take place (Yit=0) Eit: Expansion of capacity of process i in period t. Wit: Utilized capacity of process i in period t. Pjlt : Amount of raw material/interm. product j consumed from market l in period t Sjlt : Amount of intermediate product/product j sold in market l in period t γjlt : Sale price of product/intermediate product j in market l in period t Γjlt : Cost of product/intermediate product j in market l in period t δit : Operating cost of process i in period t αit : Variable cost of expansion for process i in period t βit : Fixed cost of expansion for process i in period t Lt : Discount factor for period t I : Processes i,=1,…,NP J : Raw mat./Products, j=1,…,NC T: Time periods. T=1,…,NT L: Markets, l=1,..NM

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

  11. MODEL UTILIZED CAPACITY IS LOWER THAN TOTAL CAPACITY MATERIAL BALANCE BOUNDS INTEGER VARIABLES NONNEGATIVITY Yit: An expansion of process I in period t takes place (Yit=1), does not take place (Yit=0) Eit: Expansion of capacity of process i in period t. Qit: Capacity of process i in period t. Wit: Utilized capacity of process i in period t. Pjlt : Amount of raw material/intermediate product j consumed from market l in period t Sjlt : Amount of intermediate product/product j sold in market l in period t I : Processes i,=1,…,NP J : Raw mat./Products, j=1,…,NC T: Time periods. T=1,…,NT L: Markets, l=1,..NM 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

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