Using set covering with item sampling to analyze the infeasibility of linear programming test assembly models

This article shows how set covering with item sampling (SCIS) methods can be used in the analysis and preanalysis of linear programming models for test assembly (LPTA). LPTA models can construct tests, fulfilling a set of constraints set by the test assembler. Sometimes, no solution to the LPTA model exists. The model is then said to be infeasible. Causes of infeasibility can be difficult to find. A method is proposed that constitutes a helpful tool for test assemblers to detect infeasibility beforehand and, in the case of infeasibility, give insight into its causes. This method is based on SCIS. Although SCIS can help to detect feasibility or infeasibility, its power lies in pinpointing causes of infeasibility such as irreducible infeasible sets of constraints. Methods to resolve infeasibility are also given, minimizing the model deviations. A simulation study is presented, offering a guide to test assemblers to analyze and solve infeasibility. Index terms: mathematical programming, linear programming, infeasibility, optimal test assembly, test assembly, test design, set covering, item sampling

An interactive method to solve infeasibility in linear programming test assembling models

In optimal assembly of tests from item banks, linear programming (LP) models have proved to be very useful. Assembly by hand has become nearly impossible, but these LP techniques are able to find the best solutions, given the demands and needs of the test to be assembled and the specifics of the item bank from which it is assembled. However, sometimes even LP techniques do not offer an acceptable solution to the test assembler. Infeasibility occurs when the demands are contradictory. These contradictions may be rather complex, especially when stated in terms of LP models. Techniques are described that can solve these infeasibility problems in different manners. The objectives are twofold. First, the assembler is given a helping hand to identify the bottlenecks in the specifications of the LP model. Second, a solution is forced, such that the test assembler is always presented a test as close as possible to the original specifications. These objectives should be realizable both automatically and interactively with the test assembler

An interactive method to solve infeasibility in linear programming test assembling models

In optimal assembly of tests from item banks, linear programming (LP) models have proved to be very useful. Assembly by hand has become nearly impossible, but these LP techniques are able to find the best solutions, given the demands and needs of the test to be assembled and the specifics of the item bank from which it is assembled. However, sometimes even LP techniques do not offer an acceptable solution to the test assembler. Infeasibility occurs when the demands are contradictory. These contradictions may be rather complex, especially when stated in terms of LP models. Techniques are described that can solve these infeasibility problems in different manners. The objectives are twofold. First, the assembler is given a helping hand to identify the bottlenecks in the specifications of the LP model. Second, a solution is forced, such that the test assembler is always presented a test as close as possible to the original specifications. These objectives should be realizable both automatically and interactively with the test assembler