Optimal Ordering Policies for Inventory Problems With Dynamic Information Delays

We develop a model of oligopoly competition involving innovation effort, market entry and production flexibility under demand uncertainty. Several heterogeneous firms make efforts to develop new prototypes; if they succeed, they hold a shared option to enter a new market under stochastic demand. We derive analytic results for the Markov perfect equilibrium accounting for development effort, market entry and production decisions and complement these by numerical analyses. Firm value—which embeds real options—is not convex increasing in demand but exhibits “competitive waves” due to market entries by rivals. A firm with a development advantage (“innovator”) exerts greater innovation effort if the market is a niche, whereas another benefiting from economies of scale (“incumbent”) invests more if the market is larger. Positive externalities benefit the incumbent in the development stage, whereas the innovator is better off in counteracting negative externalities. Demand volatility raises firm incentives to innovate as it enhances the value of firm market‐entry and production flexibility.

“…Control‐theoretic methods relying on filtering theory can help deal with “partially observed systems” (see, e.g, Bensoussan , Bensoussan et al. ).…”

Section: Resultsmentioning

confidence: 99%

Disruptive Innovation, Market Entry and Production Flexibility in Heterogeneous Oligopoly

Chevalier‐Roignant

Flath

Trigeorgis

2019

“…However, special care is taken to formulate the problem so that the dimension of the state vector does not increase with time. This provides an easy passage to the infinite horizon setting (Bensoussan et al 2007a). It is not hard to see that the base‐stock policy would remain optimal in the infinite horizon problems.…”

Section: Discussionmentioning

confidence: 99%

Optimal Ordering Policies for Stochastic Inventory Problems with Observed Information Delays

Bensoussan

Çakanyıldırım

Feng

et al. 2009

Self Cite

Information delays exist in an inventory system when it takes time to collect, process, validate, and transmit inventory/demand data. A general framework is developed in this paper to describe information flows in an inventory system with information delays. We characterize the sufficient statistics for making optimal decisions. When the ordering cost is linear, the optimality of a state‐dependent base‐stock policy is established even when information flows are allowed to cross over time. Additional insights into the problem are obtained via a comparison between our models and the models with stochastic order lead times. We also show that inventory can substitute for information and vice versa.

“…In such cases, Bensoussan et al. (, ) show a state‐dependent basestock policy to be optimal. Kök and Shang () and Huh et al.…”

Section: Introductionmentioning

confidence: 99%

Managing Inventory with Cash Register Information: Sales Recorded but Not Demands

Bensoussan

Çakanyıldırım

et al. 2016

Self Cite

Inventory inaccuracy is common in many businesses. While retailers employ cash registers to enter incoming orders and outgoing sales, inaccuracy arises because they do not record invisible demand such as spoilage, damage, pilferage, or returns. This setting results in incomplete inventory and demand information. An important inventory control problem therefore is to maximize the total expected discounted profit under this setting. Allowing for dependence between demand and invisible demand, we obtain the associated dynamic programming equation with an infinite‐dimensional state space, and reduce it to a simpler form by employing the concept of unnormalized probability. We develop an analytical upper bound on the optimal profit as well as an iterative algorithm for an approximate solution of the problem. We compare profits of the iterative solution and the myopic solution, and then to the upper bound. We see that the iterative solution performs better than the myopic solution, and significantly so in many cases. Furthermore, it gives a profit not far from the upper bound, and is therefore close to optimal. Using our results, we also discuss meeting inventory service levels.