Computing Optimal (<i>s, S</i>) Inventory Policies

Veinott, Arthur F.; Wagner, Harvey M.

doi:10.1287/mnsc.11.5.525

“…It is well known that an optimal order-up-to policy exists for this problem for a given ρ 1 and ρ 2 [21]. Theorem 5 highlights that a tolerance gap exists for lot-sizing problems where the action associated with τ * changes the reorder point when the p i are bounded from above by 1/2γ .…”

Section: Tolerance Gapmentioning

confidence: 90%

Sensitivity Analysis in Markov Decision Processes with Uncertain Reward Parameters

Tan

¹

,

Hartman

²

2011

Journal of Applied Probability

10

0

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Sequential decision problems can often be modeled as Markov decision processes. Classical solution approaches assume that the parameters of the model are known. However, model parameters are usually estimated and uncertain in practice. As a result, managers are often interested in how estimation errors affect the optimal solution. In this paper we illustrate how sensitivity analysis can be performed directly for a Markov decision process with uncertain reward parameters using the Bellman equations. In particular, we consider problems involving (i) a single stationary parameter, (ii) multiple stationary parameters, and (iii) multiple nonstationary parameters. We illustrate the applicability of this work through a capacitated stochastic lot-sizing problem.

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“…It is well known that an optimal order-up-to policy exists for this problem for a given ρ 1 and ρ 2 [21]. Proof.…”

Section: Sensitivity Analysis In Markov Decision Processesmentioning

confidence: 97%

Sensitivity Analysis in Markov Decision Processes with Uncertain Reward Parameters

Tan

¹

,

Hartman

²

2011

View full text Add to dashboard Cite

Sequential decision problems can often be modeled as Markov decision processes. Classical solution approaches assume that the parameters of the model are known. However, model parameters are usually estimated and uncertain in practice. As a result, managers are often interested in how estimation errors affect the optimal solution. In this paper we illustrate how sensitivity analysis can be performed directly for a Markov decision process with uncertain reward parameters using the Bellman equations. In particular, we consider problems involving (i) a single stationary parameter, (ii) multiple stationary parameters, and (iii) multiple nonstationary parameters. We illustrate the applicability of this work through a capacitated stochastic lot-sizing problem.

show abstract

“…Let L(y) denote the one-period expected holding and penalty costs when the stock on hand minus backorders is y, and the demand for the period is not included. The function L(y) often appears in the analysis of classical inventory problems (Veinott & Wagner [17]) and is defined by In case R ~ 2 and production takes place in some period t + 1, then the expected costs in period t + 2 are given by L( 8). In each one of the following periods t i with i 3, ... , R, the costs partly depend on the orders for periods t + 2, ... , t + i -1.…”

Section: The (R S) Policymentioning

confidence: 99%