Two heuristics for coordinating production planning and transportation planning

In this study, a coordinated production and transportation planning problem is addressed. A fleet of heterogeneous vehicles is considered. The transportation costs consist of two terms: a term represents the fixed cost for each vehicle used and another term for the variable cost which is the marginal transportation cost times the transportation quantity. The problem is formulated as a mixed-integer linear programming model (MILP) and a Non-Linear Programming model (NLP). The problem is unsolvable when the size increases beyond a certain magnitude. Therefore, two heuristics are developed. One of them is a decomposition-based heuristic (termed DBH). It combines solutions by decomposing the original problem into production and transportation subproblems and iteratively improves the combined solutions. The other heuristic is based on Lagrangian relaxation (called LRBH). The performance of these heuristics is evaluated by comparing their results with optimal solutions for small-sized instances and with Lagrangian-relaxation-based lower bounds for medium- or large-sized instances. The results indicate that although these heuristics use distinct mechanisms, they are both efficient and have comparable performances. The average cost gap for DBH as well as LRBH is around 0.79%$ 0.79\% $ compared with optimal solutions. They are 4.43 and 4.53%$ 4.53\% $, respectively, when compared with Lagrangian-relaxation-based lower bounds.