Production control with backlog-dependent demand

Gershwin, Stanley B.; Tan, Barış; Veatch, Michael H.

doi:10.1080/07408170801975040

Cited by 22 publications

(15 citation statements)

References 26 publications

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“…(See, e.g., [32] for an inventory context and [16] for a production setting.) The specification of our market size uncertainty is closer to the one adopted in Bassamboo et al [7] and Steckley et al [33].…”

Section: Introductionmentioning

confidence: 99%

Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment

Besbes

Maglaras

2009

Operations Research

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We consider a revenue-maximizing make-to-order manufacturer that serves a market of price-and delaysensitive customers and operates in an environment in which the market size varies stochastically over time. A key feature of our analysis is that no model is assumed for the evolution of the market size. We analyze two main settings: (i) the size of the market is observable at any point in time; and (ii) the size of the market is not observable and hence cannot be used for decision making. We focus on high-volume systems that are characterized by large processing capacities and market sizes, and where the latter fluctuate on a slower timescale than that of the underlying production system dynamics. We develop an approach to tackle such problems that is based on an asymptotic analysis and that yields near-optimal policy recommendations for the original system via the solution of a stochastic fluid model. We consider a revenue maximizing make-to-order manufacturer that serves a market of price and delay sensitive customers and operates in an environment in which the market size varies stochastically over time. A key feature of our analysis is that no model is assumed for the evolution of the market size. We analyze two main settings: i) the size of the market is observable at any point in time; and ii) the size of the market is not observable and hence cannot be used for decision-making. We focus on high-volume systems that are characterized by large processing capacities and market sizes, and where the latter fluctuate on a slower time scale than that of the underlying production system dynamics. We develop an approach to tackle such problems that is based on an asymptotic analysis and that yields near-optimal policy recommendations for the original system via the solution of a stochastic fluid model.

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Section: Introductionmentioning

confidence: 99%

Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment

Besbes

Maglaras

2009

Operations Research

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“…Finding the stationary distribution of (x, D) under a hedging point policy for general B(x) appears to require numerical methods. Gershwin et al (2008) finds this distribution when B(x) is piece-wise constant and the recurrent states are bounded below. For a lower bound to exist, we must strengthen Equation (2) to…”

Section: The Defection Modelmentioning

confidence: 97%

“…It is shown in Gershwin et al (2008) that the optimal policy for Equations (3) to (5) has hedging point form: For some z ≥ 0,…”

Section: The Defection Modelmentioning

confidence: 99%

“…This paper provides a further analysis of the model in Gershwin et al (2008). First, it is shown that customer behavior can be understood by decomposing the system into the backlog dynamics, which depend on the defection function, and the surplus dynamics, which depend on the hedging point.…”

Section: Veatchmentioning

confidence: 99%

“…One generalization of the lost sales model is to allow a limited backlog (Martinelli and Valigi, 2004). A more realistic model of customer behavior is considered in the companion paper to this one (Gershwin et al, 2008). If there is finished goods inventory on hand (surplus), customer orders are filled immediately.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The impact of customer impatience on production control

Veatch

2009

IIE Transactions

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Most analyses of make-to-stock production control assume that either all orders are eventually met (complete backordering) or that no customers are willing to wait (lost sales). We consider a more nuanced model of customer behavior, where the fraction of potential customers who place orders depends on the current backlog, and hence the lead time. A continuous one-part-type, single machine model with Markov modulated demand and deterministic production is considered. We show that the impact of customer impatience is captured by one quantity, the mean sojourn time in the backlog states. A simple procedure finds this quantity and the optimal policy, which has hedging point form. In applications, observing the durations of stockouts gives a practical method of incorporating the effect of customer impatience.

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Production Control with Price, Cost, and Demand Uncertainty

Tan

2018

OR Spectrum

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An optimal production flow control problem of a make-to-stock manufacturing firm with price, cost, and demand uncertainty is studied. The objective of the flow rate control problem is maximizing the average profit that is the difference between the expected revenue and the expected production, inventory holding, and backlog costs. The uncertainties in the system are captured jointly in discrete environment states. In each environment state, the price, cost, and demand take different levels. The transitions between different environment states evolve according to a time-homogenous Markov chain. By using a continuous flow model, the optimal production policy is stated as a state-dependent hedging policy. The performance of the system where the production cost alternates between a high and a low cost level and the demand is either constant or also alternates between a high and a low level is analyzed under the double-hedging policy. According to this policy, the producer produces only when the cost is low and the surplus is between the two hedging levels. However when the backlog is below the lower hedging level, the producer produces with the maximum capacity regardless of the cost. The effects of production cost, production capacity, demand variability, and the dependence of the demand and the cost on the performance of the system are analyzed analytically and numerically. It is shown that controlling the production rate optimally allows producers respond to the fluctuations in price, cost, and demand in an effective way and maximize their profits.

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Production control with backlog-dependent demand

Cited by 22 publications

References 26 publications

Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment

Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment

The impact of customer impatience on production control

Production Control with Price, Cost, and Demand Uncertainty

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