LSA_9-10-11_location_discrete_models.pdf

# Once we find the convergent solution to lr we need to

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Once we find the convergent solution to (LR), we need to find a feasible solution: • use the solution of x j ’s ; allocate customer demands to nearest open facility. This gives an (feasible) upper bound. max min ( ) , + + u x y j j j ij ij i i j i ij j i f x d y h u y α 1 s t y x i j x j y i j ij j j ij . . , , { , }, ; { , }, , 0 1 0 1 The LR objective function equals min f x d y h j j j ij ij i i j + α s t y x i j y i x j y i j ij j ij j j ij . . , , , { , }, { , }, , = 1 0 1 0 1 maxmin ( ) , + + u x y j j j ij i i ij i j i i f x d h u y u α Logistics Systems Analysis LR Applications – Capacitated Fixed charge Capacitated Fixed charge Integer Program (IP) relax Lagrangian Relaxation (LR) For any given u , the inner minimization problem is reduced to Where This is equivalent to the Uncapacitated Fixed Charge Facility Location Problem (UFCFLP). We should then use algorithm for UFCFLP as a subroutine. maxmin ( ) , u x y j j j ij ij i i j j i ij j j i j f x d y h u h y k x + + 0 α The LR objective function equals max min ( ) ( ) , u x y j j j j j ij i i i ij i j f u k x d h u h y + + 0 α min f x d y h j j j ij ij i i j + α s t y x i j y i h y k x j x j y i j ij j ij j i ij i j j j ij . . , , , , { , }, ; { , }, , = 1 0 1 0 1 s t y x i j y i x j y i j ij j ij j j ij . . , , , { , }, ; { , }, , = 1 0 1 0 1 max min , u x y j j j ij ij i j f x d y + 0 , f f u k d d h u h j j j j ij ij i i i = = + α
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