Solving the simple plant location problem using a data correcting approach

The Data Correcting Algorithm is a branch and bound algorithm in which thedata of a given problem instance is ‘corrected’ at each branching in such a waythat the new instance will be as close as possible to a polynomially solvableinstance and the result satisfies an acceptable accuracy (the difference betweenoptimal and current solution). In this paper the data correcting algorithm isapplied to determining exact and approximate optimal solutions to the simpleplant location problem. Implementations of the algorithm are based on apseudo-Boolean representation of the goal function of the SPLP and a newreduction rule. We study the efficiency of the data correcting approach usingtwo different bounds, the combinatorial bound and the Erlenkotter bound. Wepresent computational results on several benchmark instances of the simpleplant location problem, which confirm the efficiency of the data-correcting approach.

A Decomposition Algorithm for Nested Resource Allocation Problems

We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict convexity or differentiability is needed. The method solves a hierarchy of resource allocation subproblems, whose solutions are used to convert constraints on sums of resources into bounds for separate variables at higher levels. The resulting time complexity for the integer problem is $O(n \log m \log (B/n))$, and the complexity of obtaining an $\epsilon$-approximate solution for the continuous case is $O(n \log m \log (B/\epsilon))$, $n$ being the number of variables, $m$ the number of ascending constraints (such that $m < n$), $\epsilon$ a desired precision, and $B$ the total resource. This algorithm attains the best-known complexity when $m = n$, and improves it when $\log m = o(\log n)$. Extensive experimental analyses are conducted with four recent algorithms on various continuous problems issued from theory and practice. The proposed method achieves a higher performance than previous algorithms, addressing all problems with up to one million variables in less than one minute on a modern computer.Comment: Working Paper -- MIT, 23 page

Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer

The extensive intratumor heterogeneity revealed by sequencing cancer genomes is an essential determinant of tumor progression, diagnosis, and treatment. What maintains heterogeneity remains an open question because competition within a tumor leads to a strong selection for the fittest subclone. Cancer cells also cooperate by sharing molecules with paracrine effects, such as growth factors, and heterogeneity can be maintained if subclones depend on each other for survival. Without strict interdependence between subclones, however, nonproducer cells can free-ride on the growth factors produced by neighboring producer cells, a collective action problem known in game theory as the “tragedy of the commons,” which has been observed in microbial cell populations. Here, we report that similar dynamics occur in cancer cell populations. Neuroendocrine pancreatic cancer (insulinoma) cells that do not produce insulin-like growth factor II (IGF-II) grow slowly in pure cultures but have a proliferation advantage in mixed cultures, where they can use the IGF-II provided by producer cells. We show that, as predicted by evolutionary game theory, producer cells do not go extinct because IGF-II acts as a nonlinear public good, creating negative frequency-dependent selection that leads to a stable coexistence of the two cell types. Intratumor cell heterogeneity can therefore be maintained even without strict interdependence between cell subclones. Reducing the amount of growth factors available within a tumor may lead to a reduction in growth followed by a new equilibrium, which may explain relapse in therapies that target growth factors

Equivalent instances of the simple plant location problem

In this paper we deal with a pseudo-Boolean representation of the simple plant location problem. We define instances of this problem that are equivalent, in the sense that each feasible solution has the same goal function value in all such instances. We further define a collection of polytopes whose union describes the set of instances equivalent to a given instance. We use the concept of equivalence to develop a method by which we can extend the set of instances that we can solve using our knowledge of polynomially solvable special cases. We also present a new preprocessing rule that allows us to determine sites in which facilities will not be located in an optimal solution and thereby reduce the size of a problem instance.

A general solution framework for component commonality problems

Component commonality, the use of the same version of a component across multiple products, is increasingly considered as a promising way to offer high external variety while retaining low internal variety in operations. However, increasing commonality has both positive and negative cost effects, so that optimization approaches are required to identify an optimal commonality level. As a more or less of components influences nearly every process step along the supply chain, it is not astounding that a multitude of diverging commonality problems is investigated in literature, each of which developing a specific algorithm designed for the respective commonality problem considered. The paper on hand aims at a general framework, flexible and effcient enough to be applied to a wide range of commonality problems. Such a procedure basing on a two-stage graph approach is presented and tested. Finally, flexibility of the procedure is shown by customizing the framework to account for different types of commonality problems.Product variety, Component commonality, Optimization, Graph approach

Primal-dual variable neighborhood search for the simple plant-location problem

Copyright @ 2007 INFORMSThe variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n = 15,000 users, and m = n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m = n = 7,000; and (iii) exact solutions of instances with variable fixed costs and up to m = n = 15, 000.This work is supported by NSERC Grant 105574-02; NSERC Grant OGP205041; and partly by the Serbian Ministry of Science, Project 1583

Branch and peg algorithms for the simple plant location problem

The simple plant location problem is a well-studied problem in combinatorial optimization. It is one of deciding where to locate a set of plants so that a set of clients can be supplied by them at the minimum cost. This problem of ten appears as a subproblem in other combinatorial problems. Several branch and bound techniques have been developed to solve these problems. In this paper we present a few techniques that enhance the performance of branch and bound algorithms. The new algorithms thus obtained are called branch and peg algorithms, where pegging refers to assigning values to variables outside the branching process. We present exhaustive computational experiments which show that the new algorithms generate less than 60% of the number of subproblems generated by branch and bound algorithms, and in certain cases require less than 10% of the execution times required by branch and bound algorithms.