Optimization of (R, Q) policies for serial inventory systems using the guaranteed service approach

• Serial inventory systems with fixed order costs are considered.
• The guaranteed-service approach is used to optimize (R, Q) policies of the systems.
• A mathematical programming model is established for the optimization problem.
• Operating flexibility effects are explicitly considered in the model.
• The model is optimally solved by an iterative procedure with numerical results.

The guaranteed-service approach (GSA) was recently used to optimally place strategic safety stocks in multi-echelon inventory systems without fixed order costs. Under the GSA, excessive customer demand superior to a bound is fulfilled by using operating flexibility measures such as expediting and overtime. In this paper, the GSA is used to optimize the (R, Q) policy for a continuous review serial inventory system with Poisson demand and fixed order costs at each stocking location. Except for inventory holding costs, we also consider fixed order costs and operating flexibility costs in the system. Firstly, a deterministic mathematical programming model that considers the effects of using operating flexibility measures on the physical flow and the total cost of the system is established for optimizing the inventory policy under a given cycle service level. The model is solved by using an iterative procedure. In each iteration of the procedure, the fill rate of the system is estimated, and two sub-problems of the model, the order size decision sub-problem and the reorder point decision sub-problem, are solved by using dynamic programming algorithms for a given fill rate. With this procedure, the original optimization problem is solved by finding the optimal cycle service level of the system using a line search. Numerical results on randomly generated instances demonstrate the efficiency of the algorithms and the procedure.