An effective approach for test-sheet composition with large-scale item banks Gwo-Jen Hwang a , Bertrand M.T. Lin b, * , Tsung-Liang Lin a a Department of Information Management, National Chi Nan University, Pu-Li, Nan-Tou County, Taiwan 545, ROC b Department of Information and Finance Management, National Chiao Tung University, Hsinchu, Taiwan 300, ROC Received 11 October 2003; accepted 29 November 2003 Abstract A well-constructed test sheet not only helps the instructor evaluate the learning status of the students, but also facilitates the diagnosis of the problems embedded in the studentsÕ learning process. This paper addresses the problem of selecting proper test items to compose a test sheet that conforms to such assess- ment requirements as average difficulty degree, average discrimination degree, length of test time, number of test items, and specified distribution of concept weights. A mixed integer programming model is pro- posed to formulate the problem of selecting a set of test items that best fit the multiple assessment require- ments. As the problem is a generalization of the knapsack problem, which is known to be NP-hard in the literature, computational challenge hinders the development of efficient solution methods. Seeking approx- imate solutions in an acceptable time is a viable alternative. In this paper, we propose two heuristic algo- rithms, based upon iterative adjustment, for finding quality approximate solutions. Extensive experiments are also conducted to assess the performances of different solution methods. Statistics from a series of com- putational experiments indicate that our proposed algorithms can produce near-optimum combinations of the test items subject to the specified requirements in a reasonable time. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Computer-aided instruction; Test sheet; Mixed integer programming; Heuristic algorithm; Approximate solution 0360-1315/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compedu.2003.11.004 * Corresponding author. Tel.: +886 3 5131472; fax: +886 3 5729915. E-mail address: bmtlin@mail.nctu.edu.tw (B.M.T. Lin). www.elsevier.com/locate/compedu Computers & Education 46 (2006) 122–139