A novel mathematical model with an LCA-based solution method to minimize earliness-tardiness costs on a single machine by considering batch delivery

This paper addresses a practical but complicated version of Just in Time (JIT) problem in which a set of available jobs with known processing times and due dates are processed on a single machine and delivered in batches of arbitrary size. A new mathematical model is developed to minimize the non-convex sum of earliness-tardiness and delivery costs criteria. Due to the limitations imposed by the large size complexity of the proposed model and its nonlinear nature, we use the recently proposed league championship algorithm (LCA) to solve arbitrary test problem instances of the problem on hand. Since LCA works in continuous space, we use several representational schemes to map the solutions generated by LCA to discrete space and compare the output of the algorithm under each mapping scenario. To measure how effective LCA is in comparison with the mathematical modeling approach and other heuristic methods, we use the Lingo system and a discrete version of the Imperialistic Competitive Algorithm (ICA) as the comparator algorithms, respectively. Experimental results show that LCA is strongly efficient and dominates the comparator algorithms. At the same time, the time saved by LCA to report the final output is significant, which recommends the use of this algorithm for other practical optimization problems.