Interval goal programming (IGP) with a marginal penalty function (PF) was first proposed by Charnes and Collomb in 1972, and further improved by Kvanli and other researchers. Recently, Lu and Chen proposed an efficient logarithmic method to formulate IGP with an S‐shaped PF. However, their method requires adding many binary variables when the problem size becomes large, which increases the computational burden in the solution process. This study proposes an efficient approach for the S‐shaped PF. The arbitrary PF frequently appears in the fields of business and industry. However, none of the previous approaches have addressed arbitrary PFs without adding binary variables. The proposed approach can be easily extended to formulate an arbitrary PF in which binary variables are no longer required, regardless of the number of break points. The proposed method can improve the efficiency of IGP for solving large size management and decision problems in considering PFs. In order to demonstrate the correctness, usefulness of the proposed model, illustrative examples are provided.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.