Inventory and Queueing Models

Origin. Soviet operations research drawing on Western foundations (Erlang, Khinchin) with distinctive Soviet contributions; applied to planning materials supply and service systems.

Mechanism. Inventory models trade off ordering costs, holding costs, and stockout costs to determine optimal order quantities and reorder points. Queueing models analyze waiting lines — arrival rates, service rates, queue lengths, waiting times — to size capacity. Both address the fundamental problem of buffering variability: how much slack is needed to achieve a service level.

Procedure. For inventory: identify demand rate, order lead time, ordering cost, holding cost, and stockout cost. Compute the economic order quantity (EOQ) that minimizes total cost. Set the reorder point to cover expected demand during lead time plus safety stock for variability. For queues: identify arrival rate λ and service rate μ. If λ ≥ μ, the queue grows without bound. If λ < μ, compute steady-state queue length and waiting time using queueing formulas. Size capacity so that waiting times meet service targets.

Applies to. Supply chain management, capacity planning, service operations, any system with variability and buffering.

Limitations. The models assume stationary stochastic processes; changing demand patterns invalidate the parameters. EOQ assumes known, constant demand; safety stock calculations assume known demand variability. In Soviet practice, supply disruptions were common and demand was dictated rather than forecasted, making the models of limited use. The models optimize steady state; they say nothing about transient behavior during disruptions.