In this paper, we minimize the holding cost of the safety stock in the supply chain subject to linear constraints on the service times between the nodes of the network. In the problem, the objective function is concave as we assume the demand to be bounded by a concave function. The optimal solutions of the problem belong to the set of extreme points of the polyhedron, specified by the constraints of the problem. We first characterize the extreme points for the two-layer networks and then provide bounds to use in a branch and bound algorithm. / Singapore-MIT Alliance (SMA)

In this thesis, two-echelon systems with exogenous and endogenous lead times are studied for the orders placed by the retailer(s) from the supplier. The retailer(s) employ periodic-review base-stock policy, namely (R,S) policy. For the case the demand during review period is i.i.d. and the probability distribution is Normal for each review period, a new method is proposed for exogenous lead time case under stationary policy. The results of the proposed method is then compared with the results of the existing methods in the literature and it is concluded that the proposed method provides service levels sufficiently close to target levels whereas the existing methods do not necessarily provide target levels. We use the simulation to study the endogenous replenishment lead time case. The proposed method is modified when the retailer employs stationary policy and it is seen that the proposed method gives no-stockout probabilities close to target levels. Moreover, the impacts of using adaptive policy on the performance of the retailer are studied for endogenous replenishment lead time case. It is concluded that updating of the order-up-to-level deteriorates the performance of the retailer. Finally, it is questioned whether it is beneficial for a retailer to use adaptive policy in a supply chain with two retailers. Simulation results show that the deterioration in the performance of the retailer handling stationary policy is larger compared to the other retailer handling adaptive policy and the deteriorations get larger in the case of an increase in update frequency or in utilization of the supplier.

The implicit assumption in conventional inventory models is that the stored products maintain the same utility forever, i.e., they can be stored for an infinite period of time without losing their value or characteristics. However, generally speaking, almost all products experience some sort of deterioration over time. Some products have very small deterioration rates, and henceforth the effect of such deterioration can be neglected. Some products may be subject to significant rates of deterioration. Fruits, vegetables, drugs, alcohol and radioactive materials are examples that can experience significant deterioration during storage. Therefore the effect of deterioration must be explicitly taken into account in developing inventory models for such products. In most existing deteriorating inventory models, time is treated as a continuous variable, which is not exactly the case in practice. In real-life problems time factor is always measured on a discrete scale only, i.e. in terms of complete units of days, weeks, etc. In this research, we present several discrete-in-time inventory models and identify optimal ordering policies for a single deteriorating product by minimizing the expected overall costs over the planning horizon. The various conditions have been considered, e.g. periodic review, time-varying deterioration rate, waiting-time-dependent partial backlogging, time-dependent demand, stochastic demand etc. The objective of our research is two-fold: (a) To obtain optimal order quantity and useful insights for the inventory control of a single deteriorating product over a discrete time horizon with deterministic demand, variable deterioration rates and waiting-time-dependent partial backlogging ratios; (b) To identify optimal ordering policy for a single deteriorating product over a finite horizon with stochastic demand and partial backlogging. The explicit ordering policy will be developed for some special cases. Through computational experiments and sensitivity analysis, a thorough and insightful understanding of deteriorating inventory management will be achieved.