A quadratic programming approach to a survey sampling cost minimization problem

An analytical algorithmic methodology developed by Kabe [1-3], and Scobey and Kabe [4] for solving matrix quadratic programming problems (QPP), and for solving matrix linear programming problems (LPP) is utilized here to minimize the cost of conducting a certain census sampling survey. For carrying on the survey, the city is divided into pn blocks, the (i, j) − th block contains xij households and the i − th census enumerator visits xij households to be surveyed and the cost of visiting a single household in the (i, j) − th block is, say, cij, monetary units. This census survey cost minimization problem is a LPP, and is solved here by using a certain QPP solving methodology. This LPP is exactly similar to the usual standard transportation problem.