Essays on multi-echelon inventory control
Date of Issue2016
College of Business (Nanyang Business School)
Matching demand with supply effectively is a significant objective for supply chain inventory management. Efficient supply chain management requires the effective coordination of shipments from one stage to the next throughout the entire system. The first essay of this thesis studies fixed-interval ordering policies in a serial system. In particular we consider an echelon-stock fixedinterval order-up-to policy for an N-stage serial supply chain. For reasons of mathematical tractability and historic convention, previous studies on periodic-review inventory control policies have typically accounted system costs at the end of each review period. This accounting method, however, often significantly underestimates system costs when inventory related costs actually accrue in continuous time. The main contribution of the current study is two-fold. First, we provide a simple approach to evaluate the inventory related costs in the system continuously in time. This evaluation approach uses only the demand distribution, is easy to follow and compute and can also be used when end-of-period cost accounting is adopted. Second, we provide an intuitive characterization of an optimal ordering policy by simply equating the marginal echelon inventory related cost to the inventory holding cost at the upstream stage. This leads to a simple bottom-up procedure to identify an optimal ordering policy for a given replenishment schedule. Using this solution, we develop a topdown search procedure to identify an optimal replenishment schedule subject to the optimization of the ordering policy. The second essay of this thesis considers a two-level distribution system, in which one central warehouse orders from an external supplier in an interval of a fixed length to supply a group of non-identical retailers. The retailers face independent Poisson processes and order from the warehouse in fixed intervals that are integer-ratio multiples of the warehouse replenishment interval. Optimal inventory control policies for two-level distribution systems are notoriously complicated because of the stock allocation problem when shortage occurs at the warehouse. However, finding warehouse stock allocation policies that are optimal or near-optimal and easy to implement is of practical importance. We assume that the system adopts a base-stock policy, in which the warehouse orders at each review point from the external supplier to raise the echelon-stock inventory position to a fixed base stock level. We investigate different allocation policies for the warehouse to allocate stock to retailers. First, we consider a class of stationary ship-up-to-S policy, in which each retailer’s inventory position is raised to a fixed base-stock level at a shipping point. When facing a shortage, we consider two myopic allocation policies: (1) virtual allocation, where the remaining stock is allocated to satisfy the demand on a first-come first-served basis, (2) myopic optimal allocation, where the remaining stock is allocated to the retailers optimally to minimize system cost. Numerical experiments show that myopic optimal allocation performs better than virtual allocation, particularly in cases with large number of retailers, high service level requirements, large demand rate, large difference between retailers, and short system replenishment cycle. We note that the myopic allocation policies are stationary and myopic in the sense that base-stock levels for retailers are stationary and the warehouse stock will be completely allocated to retailers when facing a shortage. Therefore we construct a heuristic dynamic allocation rule, which explicitly incorporates the benefits of centralizing stock. We demonstrate through numerical experiments that the heuristic allocation rule on average performs at a comparable level with myopic optimal allocation in terms of cost control. However, this heuristic significantly reduces the complexity of system optimization by considering only echelon order-up-to level at the warehouse and can cope with a relatively large number of retailers, a large demand arrival rate and a long replenishment cycle.