en Discrete Optimization Discrete Optimization پژوهشی Original <p>We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced first-level mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is developed. The proposed method of cuts generation, separation and strengthening is compared to the Gomory, linear branching and coordinated cutting plane methods. The computational results show that the proposed method is promising but becomes complicated as number of variables increases.</p> Reduced first level, MIP, cutting planes 0 0 http://iors.ir/journal/browse.php?a_code=A-10-603-1&slc_lang=en&sid=1 Godfrey Chagwiza chagwizag@gmail.com 00031947532846001402 00031947532846001402 Yes National University of Science & Technology Brian Jones 00031947532846001403 00031947532846001403 No National University of Science & Technology Senelani Hove- Musekwa 00031947532846001404 00031947532846001404 No National University of Science & Technology Sobona Mtisi 00031947532846001405 00031947532846001405 No Overseas Development Institute, London, SE1 7JD, UK