The M/M/1 queue with inventory, lost sale, and general lead times

The M/M/1 queue with inventory, lost sale, and general lead times

We consider an M/M/1 queueing system with inventory under the (r,Q) policy and with lost sales, in which demands occur according to a Poisson process and service times are exponentially distributed. All arriving customers during stockout are lost. We derive the stationary distributions of the joint queue length (number of customers in the system) and on-hand inventory when lead times are random...

Analysis of the (Q, r) Inventory Model for Perishables with Positive Lead Times and Lost Sales

Closing the Gap: A Learning Algorithm for the Lost-Sales Inventory System with Lead Times

Introduction The periodic-review inventory control problem with lost-sales and positive lead times is one of the most fundamental yet notoriously difficult problems in the theory of inventory management (see Zipkin (2000)). The model assumes that unmet demand at the end of each period is lost, rather than being backlogged and carried over to the next period. For example, in many retail applicat...

Periodic Review Inventory Control With Lost Sales and Fractional Lead Times

We introduce a single location periodic review inventory control problem with lost sales and fractional lead times. We model the optimal inventory control problem as a stochastic dynamic program and analyze properties of the objective function as well as the optimal policy. We present upper and lower bounds on the optimal policy. These bounds can readily be used in easily computable heuristics....

Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times

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