LSA_9-10-11_location_discrete_models.pdf

Once we find the convergent solution to lr we need to

Info icon This preview shows page 9. Sign up to view the full content.

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
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern