Heuristics for joint decisions in production, transportation, and order quantity

An attempt is made to tackle joint decisions in assigning production, lot size, transportation, and order quantity for single and multiple products in a production–distribution network system with multiple suppliers and multiple destinations. The approach hinges on providing an optimized solution to the joint decision model (JDM) through a two-layer decomposition (TLD) method that combines several heuristics. By combining the Lagrange multipliers and introducing a number of artificial variables into the two-layer decomposition, a Lagrange relaxation decomposition (LRD) method with heuristics is developed to solve multiproduct joint decision problems (JDM-M). Using the LRD, the JDM-M model is solved by decomposing into two subproblems in two layers. The first layer is the joint decisions in assigning production, transportation flow, and lot size (APLS-TF) using the assignment heuristic AH-M. The second layer is the joint decisions in transportation and order quantity (TOQ-M) using a revised BH heuristic. Combined with Lagrange multipliers, the APLS-TF model takes into consideration the transportation costs together with production costs when it assigns annual production among suppliers. In essence, the algorithm assigns annual production simultaneously with annual transportation flows. Simulations on different sizes of problems and problems with large variances in data have shown that the LRD is effective, and in general more effective than the TLD.