A Sequential Stochastic Assignment Problem TeX Export

@article{dlr-72, abstract = {Suppose there are n men available to perform n jobs. The n jobs occur in sequential order with the value of each job being a random variable X. Associated with each man is a probability p. If a "p" man is assigned to an "X = x" job, the (expected) reward is assumed to be given by px. After a man is assigned to a job, he is unavailable for future assignments. The paper is concerned with the optimal assignment of the n men to the n jobs, so as to maximize the total expected reward. The optimal policy is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy. In particular, if <tex-math>\$p\_{1}\leq p\_{2}\leq \cdots \leq p\_{n}\$</tex-math> the optimal choice in the initial stage of an n stage assignment problem is to use p_i if x falls into an ith nonoverlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the p's. The optimal policy is also presented for the generalized assignment problem, i.e., the assignment problem where the (expected) reward if a "p" man is assigned to an "x" job is given by a function r(p, x).}, author = {Derman, Cyrus and Lieberman, Gerald J. and Ross, Sheldon M.}, citeulike-article-id = {6032391}, citeulike-linkout-0 = {http://dx.doi.org/10.2307/2629351}, citeulike-linkout-1 = {http://www.jstor.org/stable/2629351}, doi = {10.2307/2629351}, issn = {00251909}, journal = {Management Science}, keywords = {dyncomp, mechanism\_design}, number = {7}, pages = {349--355}, posted-at = {2009-10-29 14:42:42}, priority = {2}, publisher = {INFORMS}, title = {A Sequential Stochastic Assignment Problem}, url = {http://dx.doi.org/10.2307/2629351}, volume = {18}, year = {1972} }

TY - JOUR ID - dlr-72 L3 - citeulike-article-id:6032391 N2 - Suppose there are n men available to perform n jobs. The n jobs occur in sequential order with the value of each job being a random variable X. Associated with each man is a probability p. If a "p" man is assigned to an "X = x" job, the (expected) reward is assumed to be given by px. After a man is assigned to a job, he is unavailable for future assignments. The paper is concerned with the optimal assignment of the n men to the n jobs, so as to maximize the total expected reward. The optimal policy is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy. In particular, if <tex-math>$p_{1}\leq p_{2}\leq \cdots \leq p_{n}$</tex-math> the optimal choice in the initial stage of an n stage assignment problem is to use p_i if x falls into an ith nonoverlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the p's. The optimal policy is also presented for the generalized assignment problem, i.e., the assignment problem where the (expected) reward if a "p" man is assigned to an "x" job is given by a function r(p, x). IS - 7 JF - Management Science SN - 00251909 EP - 355 TI - A Sequential Stochastic Assignment Problem PB - INFORMS VL - 18 SP - 349 KW - dyncomp KW - mechanism_design AU - Derman, Cyrus AU - Lieberman, Gerald AU - Ross, Sheldon PY - 1972/// UR - http://dx.doi.org/10.2307/2629351 ER -