Newsvendor Bounds and A Heuristic for Optimal Policies in Serial Supply Chains

We consider the classic N -stage serial supply systems with linear costs and stationary random demands. There are deterministic transportation leadtimes between stages, and unsatisfied demands are backlogged. The optimal inventory policy for this system is known to be an echelon base-stock policy, which can be computed through minimizing N nested convex functions recursively. To identify the key determinants of the optimal policy, we develop a simple and surprisingly good heuristic. This method minimizes 2N separate newsvendor-type cost functions, each of which uses the original problem data only. These functions are lower and upper bounds for the echelon cost functions; their minimizers form bounds for the optimal echelon base-stock levels. The heuristic is the simple average of the solution bounds. In extensive numerical experiments, the average relative error of the heuristic is 0.24%, with the maximum error less than 1.5%. The bounds and the heuristic, which can be easily obtained by simple spreadsheet calculations, enhance the accessibility and implementability of the multiechelon inventory theory. More importantly, the closedform expressions provide an analytical tool for us to gain insights into issues such as system bottlenecks, effects of system parameters, and coordination mechanisms in decentralized systems. (Inventory Policies; Stochastic Demand; Serial System; Closed-Form Solutions; Sensitivity Analysis)