Problems of inventory control and customer admission control are considered for a manufacturing system that produces one product to meet random demand. Four admission policies are investigated: lost sales, complete backordering, randomized admission, and partial backordering. These policies are combined with an integral inventory control policy, which releases raw items only when an incoming order is accepted and keeps the inventory position (total inventory minus outstanding orders) constant. The objective is to determine the inventory level and the maximum number of backorders, as well as the admission probability that maximize the mean profit rate of the system. The system is modeled as a closed queueing network and its performance is computed analytically. The optimal parameters for each policy are found using exhaustive search and convex analysis. Numerical results show that managing inventory levels and sales jointly through partial backordering achieves higher profit than other control policies.Note to Practitioners-In stochastic production networks, decisions concerning when to produce and whether to accept or reject an incoming order are often made separately or sequentially. For example, inventory control is often applied assuming that all demand during a stockout period is either completely backlogged or lost. This paper studies two partial backordering policies jointly with an integral inventory control policy, and explores the benefits of coordinated decision making.
This article addresses the problem of dynamic sequencing on n identical parallel machines with stochastic arrivals, processing times, due dates and sequence-dependent setups. The system operates under a completely reactive scheduling policy and the sequence of jobs is determined with the use of dispatching rules. Seventeen existing dispatching rules are considered including standard and setup-oriented rules. The performance of the system is evaluated by four metrics. An experimental study of the system is conducted where the effect of categorical and continuous system parameters on the objective functions is examined. In light of the results from the simulation experiments, a parameterized priority rule is introduced and tested. The simulation output is analyzed using rigorous statistical methods and the proposed rule is found to produce significantly better results regarding the metrics of mean cycle time and mean tardiness in single machine cases. In respect to three machine cases, the proposed rule matches the performance of the best rule from the set of existing rules which were studied in this research for three metrics.
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