UTILIZATION ROUGH CONCEPT TO SOLVE DE NOVO PROGRAMMING PROBLEM UNDER AMBIGUITY: REAL CASE STUDY - Hussein, Iftikhar Ali; Zahar, Hagazy; Saied, Naglaa Ragaa; Rabie, Rabie Mosaad (Journal of mechanics of continua and mathematical sciences, 2025)
Multi-objective Linear Programming (MOLP) traditionally optimizes multiple conflicting objectives simultaneously. This research extends the De Novo Programming (DNP) concept, which focuses on optimal system design, to situations with uncertainty in resource allocation and budget constraints. A novel mathematical model, Rough Interval Multi-Objective De Novo Programming (RIMODNP), has been introduced. This model incorporates the Rough Interval (RI) concept, where all problem coefficients are represented by lower and upper interval bounds, each having two terms (upper and lower). The study outlines the mathematical formulation of the RIMODNP model, detailing the methodology used to transform its uncertain nature into deterministic sub-problems. It presents two primary approaches, Zeleny's and the Optimum-Path Ratio Method, for finding optimal designs. Applied to the Baghdad Water Department, the model optimizes resource allocation for increased water production, improved water quality, and reduced water loss while considering unknown constraints. The results, obtained by solving the deterministic sub-problems, provide the decision-maker with a range of optimal system designs. The application to the Baghdad Water Department shows significant increases in profit and cost savings across different scenarios, highlighting the model's ability to offer robust and effective solutions under conditions of uncertainty.