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

Abstract

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.

Simple Policies for Dynamic Pricing with Imperfect Forecasts

“…In other words, what can be done when a perfectly specified forecast model is unavailable to the seller? The present work also complements a recent paper by Besbes and Maglaras [2009] which studies issues similar to the ones here albeit in the context of admission control to a queue via modulating prices. Both of the above papers study the relevant systems in a limiting regime that produces a stochastic fluid model.…”

Blind Queues: The Impact of Consumer Beliefs on Revenues and Congestion

“…Finally, our approach complements the perspective in Besbes and Maglaras (2009) and Haviv and Randhawa (2014), where the service firm does not fully know the demand (volume) information.…”

Optimal Pricing and Sequencing in a Make-to-Order System With Batch Demand

“…For fixed i, H i (x) is decreasing in x and does not intersect with H j (x) for j = i. For any point (x, y) above the curve H i (x) and below the curve H i−1 (x) if i > 1, the optimal price for type-2 product is p i , while for any point (x, y) on or below the curve H K−1 (x), the optimal price for type-2 product is p K , and for any point (x, y) above the curve H 1 (x), the optimal price for type-2 product is p 1 .…”

“…He developed a deterministic fluid model to analyze the problem and construct near-optimal sequencing and pricing policies. Subsequently Besbes and Maglaras [1] developed a stochastic fluid model to analyze and make pricing recommendations for an MTO manufacturer operating in an environment with stochastically varying market size. Most recently, Cil et al [4] showed for the problem setting considered in Maglaras [9] that the optimal sequencing policy is a strict priority policy and established a number of monotonicity results for the optimal prices in terms of queue lengths.…”