Approximation Algorithms for Stochastic Inventory Control Models

Approximation Algorithms for Stochastic Inventory Control Model

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277

Optimal Policies for Two Product Inventory Systems With and Without Setup Costs

Optimal Policies for Two Product Inventory Systems With and Without Setup Cost

Approximation algorithms for stochastic inventory control models

In this paper we address the long-standing problem of finding computationally efficient and provably good inventory control policies in supply chains with correlated and nonstationary (time-dependent) stochastic demands. This problem arises in many domains and has many practical applications such as dynamic forecast updates (for some applications see Erkip et al. 1990 and Lee et al. 1999). We consider two classical models, the periodic-review stochastic inventory control problem and the stochastic lot-sizing problem with correlated and non-stationary demands. Here the correlation is inter-temporal, i.e., what we observe in the current period changes our forecast for the demand in future periods. We provide what we believe to be the first computationally efficient policies with constant worst-case performance guarantees; that is, there exists a constant C such that, for any given joint distribution of the demands, the expected cost of the policy is guaranteed to be within C times the expected cost of an optimal policy. More specifically, we provide a worst-case performance guarantee of 2 for the periodic-review stochastic inventory control problem, and a performance guarantee of 3 for the stochastic lot-sizing problem. The models. The details of the periodic-review stochastic inventory control problem ar