Supply chain scheduling at the manufacturer to minimize inventory holding and delivery costs

In a supply chain, a manufacturer receives jobs from suppliers at distinct time points, and produces and delivers final products to customers in batches. The manufacturer can be modeled as a single machine in the supply chain and the problem can thus be modelled as minimizing the sum of weighted flow time and the batch delivery costs. Since the problem with arbitrary processing times, release times and weights is strongly NP-hard, we first analyze some polynomially solvable special problems. Then we develop a heuristic algorithm to solve the general problem. We also develop a lower bound to study the performance of our heuristic algorithm and the computational experiments show that the solutions of the heuristic algorithm are close to optimal solution.