Integrated optimization of material supplying, manufacturing, and product distribution: Models and fast algorithms

Motivated by applications in electroplating industry, we study an integrated optimization problem of production and logistics for a manufacturer and a third-party logistics (3PL) provider. The objective is to minimize the total cost which includes costs in transportation and inventory of materials, manufacturing, and inventory and outbound distribution of products. The materials are semi-products supplied by a single supplier, and the transportation of materials are accomplished by a 3PL provider. Semi-products may have different sizes and processing times, and they are processed on a batch-processing facility by the manufacturer. Outbound distribution of final products are accomplished by the same 3PL provider. We consider three different models and propose fast algorithms to solve each model. In the first model, semi-products have identical sizes and an optimal algorithm is proposed. In the second model, semi-products have identical processing times and an approximation algorithm is proposed. The algorithm has absolute and asymptotic worst case ratios of 1.5 and 1.223, respectively. In the third model, semi-products have arbitrary sizes and processing times and an approximation algorithm is proposed. The absolute and asymptotic worst case ratios of the algorithm are 2.181 and 2, respectively. The running time of the optimal algorithm of the first model is O(nlog n), while that of the approximation algorithms are O(n ² ).