Two efficient heuristic algorithms for the integrated production planning and warehouse layout problem

In (Zhang et al. An integrated strategy for a production planning and warehouse layout problem: modeling and solution approaches,  Omega 68  (2017) 85--94)    the authors have proposed a mixed-integer linear programming model for the integrated production planning and warehouse layout problem. To solve the model, they proposed a Lagrangian relax-and-fix heuristic that takes significant amount of time to stop with gaps above 5$\%$ for large-scale instances. Here, we present two heuristic algorithms to solve the problem. In the first one, we use a greedy approach by allocating  warehouse locations with less reservation  costs, and also less  transportation costs  from the production area to locations and from locations to the output point  to items with higher demands. Then a smaller model is solved. In the second heuristic, first we sort items in descending order according to the fraction of sum of the demands for that item in the time horizon plus the maximum demand for that item in the time horizon and  sum of all its demands in the time horizon. Then we categorize the sorted items into groups of 3, 4, or 5, and solve a small-scale optimization problem for each group, hoping to improve the solution of the first heuristic. Our preliminary numerical results show  the effectiveness of the proposed heuristics.