Download Discrete and Fractional Programming Techniques for Location by Ana Isabel Barros (auth.) PDF

By Ana Isabel Barros (auth.)

At first sight discrete and fractional programming ideas seem to be com­ pletely unrelated fields in operations learn. we'll express how thoughts in either fields could be utilized individually and in a mixed shape to specific types in place research. situation research bargains with the matter of figuring out the place to find amenities, con­ sidering the consumers to be served, in the sort of method convinced criterion is optimized. The time period "facilities" instantly indicates factories, warehouses, colleges, and so on. , whereas the time period "clients" refers to depots, retail devices, scholars, and so forth. 3 easy periods will be pointed out in position research: non-stop place, community position and dis­ crete situation. the diversities among those fields come up from the constitution of the set of attainable destinations for the amenities. consequently, finding amenities within the aircraft or in one other non-stop area corresponds to a continual position version whereas discovering optimum facility destinations at the edges or vertices of a community corresponds to a internet­ paintings position version. eventually, if the prospective set of destinations is a finite set of issues we now have a discrete position version. each one of those fields has been actively studied, arousing excessive dialogue at the benefits and downsides of every of them. the standard requirement that each element within the aircraft or at the community has to be a candidate place element, is likely one of the commonly used arguments "against" non-stop and community situation models.

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1, a free facility r can be fixed open in all descendant nodes of S as soon as ps(r) < 0. Similarly simplification rules to close facilities can also be derived. Observe that the simplification rules proposed by Efroymson and Ray [46) for the uncapacitated facility location problem in the minimization form can be justified using results on supermodular functions. The above remarks suggest to investigate if the general multi-level uncapacitated facility location problem also satisfies the submodularity property.

19). 4. A General Uncapacitated Facility Depot Location Model Considering again Cjk := L;e 1(cijk-A;-O;j-/1ik)+ and defining Jj := fi- Lief Oij and g/. 19). iEJ Notice that if (Cjk- Fjk) kEK < 0 then it is not profitable to have the pair (j, k) operating together, and so ljk = 0 in any optimal solution to (£~SF). This subproblem can be further reduced by dropping some other variables < fj then opening facility j is not profitable, so Yi = 0 (iii) If L:keK(cjk- Fjk)+ in any optimal solution to (£~SF); (iv) If L:jeJ(Cjk- Fjk)+ < g/.

Now let (t, y, z, x) be an optimal solution to (SF). 17)). (SF) :::; rJ(BSF). 0 As will be confirmed by our computational results, (W F) provides a significantly worse upper bound on the optimal value of the problem than (SF) or (BSF). This phenomenon may be explained by the fact that (W F) allows some fractional feasible solutions that are forbidden in (SF) and (BSF). For p Xijk = tjk = Yj = Zk = plq > 1 or q > 1, the solution is a typical example. 22) define facets of the convex hull of the feasible solutions of this problem, see [1].

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