Service performance of two-echelon supply chains under linear rationing

Consideration is given to the operation of simple two-echelon divergent supply chains, where one central stock-point feeds several end stock-points. Periodic review echelon order-up-to policies are used to control the chain. Customer demand is imposed at end stock-points and, if unsatisfied, is backordered. In the event of central stock-point shortages, available material has to be rationed. We study a class of practical rationing rules, known as linear rationing (LR), which distributes shortage to end stock-points according to fixed fractions. After developing an alternative definition for the LR class rationing function, we formally show that popular rules, such as fair share (FS) and consistent appropriate share (CAS), belong to the LR class. We also propose a new LR rule that directly extends FS scope and applicability. For normal demand processes, we then develop closed-form customer service models, applicable to any LR rule. Modeling accuracy critically depends on the satisfaction of the standard balance assumption. Using a distribution-free model for a surrogate measure of the balance probability, we discuss the expected balance behavior of LR rules. Monte Carlo simulations reveal the balance assumption to be robust, at least for normally distributed demands, under fairly general conditions. Finally, numerical comparisons of the new LR rule with an existing one show encouraging results for the new rule.