The Multi-Location Transshipment Problem with Positive Replenishment Lead Times
Most past research on transshipment overlooks the positive replenishment lead times. Although Tagaras and Cohen(1992) had studied two-location inventory systems with non-negligible lead times, their research has not been proven to generalizable to a multi-location setting, and their heuristic method cannot be guaranteed to provide optimal values. This paper uses simulation optimization by combining LP/network flow formulation and infinitesimal perturbation analysis to examine the multi-location transshipment problem with positive replenishment lead times, and demonstrates how to obtain the optimal values of the base stock quantities by the sample-path-based stochastic optimization procedure. The main contributions of this paper are four points, the first two are business application contributions and later two are methodology contributions: 1) This is the first paper that has solved a multi-location transshipment problem with positive replenishment lead times to optimality. 2) This paper establishes the negative relationship between the transshipment performance and demand correlation at different lead time settings. 3) Measured by optimal objective value, the performance of our algorithm is shown to be significantly better than existing algorithms. 4) Using a more elegant duality-based gradient computation method instead of decision tree method or Glasserman's recursion method, the efficiency of our algorithm is significantly higher than existing algorithms.