The influence of demand variability on the performance of a make-to-stock queue

Variability, in general, has a deteriorating effect on the performance of stochastic inventory systems. In particular, previous results indicate that demand variability causes a performance degradation in terms of inventory related costs when production capacity is unlimited. In order to investigate the effects of demand variability in capacitated production settings, we analyze a make-to-stock queue with general demand arrival times operated according to a basestock policy. We show that when demand inter-arrival distributions are ordered in a stochastic sense, increased arrival time variability indeed leads to an augmentation of optimal base-stock levels and to a corresponding increase in optimal inventory related costs. We quantify these effects through several numerical examplesproduction/inventory; make-to-stock; base-stock; stochastic comparisons; GI/M/1, POLICIES; COSTS; SYSTEMS; LEAD

Developing a closed-form cost expression for an (R,s,nQ) policy where the demand process is compound generalized Erlang.

We derive a closed-form cost expression for an (R,s,nQ) inventory control policy where all replenishment orders have a constant lead-time, unfilled demand is backlogged and inter-arrival times of order requests are generalized Erlang distributedInventory control; Compound renewal process; Generalized Erlang distribution;

Base-stock policies with reservations

All intensively studied and widely applied inventory control policies satisfy demand in accordance with the First-Come-First-Served (FCFS) rule, whether this demand is in backorder or not. Interestingly, this rule is sub-optimal when the fill-rate is constrained or when the backorder cost structure includes fixed costs per backorder and costs per backorder per unit time. In this paper we study the degree of sub-optimality of the FCFS rule for inventory systems controlled by the well-known base-stock policy. As an alternative to the FCFS rule, we propose and analyze a class of generalized base-stock policies that reserve some maximum number of items in stock for future demands, even if backorders exist. Our analytic results and numerical investigations show that such alternative stock reservation policies are indeed very simple and considerably improve either the fillrate or reduce the total cost, without having much effect on the backorder level

Loss systems in a random environment

We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove an if-and-only-if-condition for a product form steady state distribution of the joint queueing-environment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, e.g. from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, e.g. of queueing-inventory processes. We investigate further classical loss systems, where due to finite waiting room loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise. We further investigate the embedded Markov chains at departure epochs and show that the behaviour of the embedded Markov chain is often considerably different from that of the continuous time Markov process. This is different from the behaviour of the standard M/G/1, where the steady state of the embedded Markov chain and the continuous time process coincide. For exponential queueing systems we show that there is a product form equilibrium of the embedded Markov chain under rather general conditions. For systems with non-exponential service times more restrictive constraints are needed, which we prove by a counter example where the environment represents an inventory attached to an M/D/1 queue. Such integrated queueing-inventory systems are dealt with in the literature previously, and are revisited here in detail

How markets slowly digest changes in supply and demand

In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is extremely low, large orders to buy or sell can only be traded incrementally, over periods of time as long as months. As a result order flow is a highly persistent long-memory process. Maintaining compatibility with market efficiency has profound consequences on price formation, on the dynamics of liquidity, and on the nature of impact. We review a body of theory that makes detailed quantitative predictions about the volume and time dependence of market impact, the bid-ask spread, order book dynamics, and volatility. Comparisons to data yield some encouraging successes. This framework suggests a novel interpretation of financial information, in which agents are at best only weakly informed and all have a similar and extremely noisy impact on prices. Most of the processed information appears to come from supply and demand itself, rather than from external news. The ideas reviewed here are relevant to market microstructure regulation, agent-based models, cost-optimal execution strategies, and understanding market ecologies.Comment: 111 pages, 24 figure