Approximation Algorithms for the Supplier's Supply Chain Scheduling Problem to Minimize Delivery and Inventory Holding Costs

We study the upstream supplier's batch scheduling problem in a supply chain, which was defined by Hall and Potts [Hall, N. G., C. N. Potts. 2003. Supply chain scheduling: Batching and delivery. Oper. Res. 51(4) 566-584]. The supplier has to manufacture multiple products and deliver them to customers in batches. There is an associated delivery cost with each batch. The objective of the supplier is to minimize the total inventory holding and delivery costs. We present simple approximation algorithms for this strongly NP-hard problem, which find a solution that is guaranteed to have a cost at most 3/2 times the minimum. We also prove that the approximation algorithms have worst-case bounds that vary parametrically with the data and that for realistic parameter values are much better than 3/2. The theoretical results are also supported by the findings of a computational study.