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

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 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 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 Period 1 2 years Process 1 Chemical 1 Chemical 5 Process 3 Chemical 3 Chemical kton/yr kton/yr 5.27 kton/yr kton/yr SolutionSolution

6 Period years Process 1 Chemical 1 Chemical 5 Process 3 Chemical 3 Process 5 Chemical 7 Chemical 8 Process 4 Chemical kton/yr kton/yr 4.71 kton/yr kton/yr kton/yr SolutionSolution

7 Period years Chemical 1 Process 2 Chemical 5 Chemical 2 Chemical 6 Process 3 Chemical 3 Process 5 Chemical 7 Chemical 8 Process 4 Chemical kton/yr ton/yr kton/yr kton/yr kton/yr kton/yr kton/yr kton/yr kton/yr Process 1 SolutionSolution

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