402 research outputs found
Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations
In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements
Dynamic Inventory Control with Satisfaction-Dependent Demand
In this paper, we consider the discrete multiperiod newsvendor dynamic inventory control problem where customers follow a simple satisfaction-based demand process, where their probability of demand depends on whether their demand was satised the last time they demanded a product, and observe the differences between optimal policies and myopic policies which do not directly consider how inventory policies can affect future demand. We conrm the intuitive result that inventory managers should tend to order more than the myopic policy when satised customers are more likely to demand product, and less than the myopic policy when satised customers are less likely to demand. Moreover, we and that, when choosing a fixed order policy, even an empirically myopic solution with perfect demand distribution information will move away from the optimum towards a suboptimal solution.
Deep Neural Newsvendor
We consider a data-driven newsvendor problem, where one has access to past
demand data and the associated feature information. We solve the problem by
estimating the target quantile function using a deep neural network (DNN). The
remarkable representational power of DNN allows our framework to incorporate or
approximate various extant data-driven models. We provide theoretical
guarantees in terms of excess risk bounds for the DNN solution characterized by
the network structure and sample size in a non-asymptotic manner, which justify
the applicability of DNNs in the relevant contexts. Specifically, the
convergence rate of the excess risk bound with respect to the sample size
increases in the smoothness of the target quantile function but decreases in
the dimension of feature variables. This rate can be further accelerated when
the target function possesses a composite structure. Compared to other typical
models, the nonparametric DNN method can effectively avoid or significantly
reduce the model misspecification error. In particular, our theoretical
framework can be extended to accommodate the data-dependent scenarios, where
the data-generating process is time-dependent but not necessarily identical
over time. Finally, we apply the DNN method to a real-world dataset obtained
from a food supermarket. Our numerical experiments demonstrate that (1) the DNN
method consistently outperforms other alternatives across a wide range of cost
parameters, and (2) it also exhibits good performance when the sample size is
either very large or relatively limited
Data-driven Piecewise Affine Decision Rules for Stochastic Programming with Covariate Information
Focusing on stochastic programming (SP) with covariate information, this
paper proposes an empirical risk minimization (ERM) method embedded within a
nonconvex piecewise affine decision rule (PADR), which aims to learn the direct
mapping from features to optimal decisions. We establish the nonasymptotic
consistency result of our PADR-based ERM model for unconstrained problems and
asymptotic consistency result for constrained ones. To solve the nonconvex and
nondifferentiable ERM problem, we develop an enhanced stochastic
majorization-minimization algorithm and establish the asymptotic convergence to
(composite strong) directional stationarity along with complexity analysis. We
show that the proposed PADR-based ERM method applies to a broad class of
nonconvex SP problems with theoretical consistency guarantees and computational
tractability. Our numerical study demonstrates the superior performance of
PADR-based ERM methods compared to state-of-the-art approaches under various
settings, with significantly lower costs, less computation time, and robustness
to feature dimensions and nonlinearity of the underlying dependency
Optimal Dynamic Procurement Policies for a Storable Commodity with L\'evy Prices and Convex Holding Costs
In this paper we study a continuous time stochastic inventory model for a
commodity traded in the spot market and whose supply purchase is affected by
price and demand uncertainty. A firm aims at meeting a random demand of the
commodity at a random time by maximizing total expected profits. We model the
firm's optimal procurement problem as a singular stochastic control problem in
which controls are nondecreasing processes and represent the cumulative
investment made by the firm in the spot market (a so-called stochastic
"monotone follower problem"). We assume a general exponential L\'evy process
for the commodity's spot price, rather than the commonly used geometric
Brownian motion, and general convex holding costs.
We obtain necessary and sufficient first order conditions for optimality and
we provide the optimal procurement policy in terms of a "base inventory"
process; that is, a minimal time-dependent desirable inventory level that the
firm's manager must reach at any time. In particular, in the case of linear
holding costs and exponentially distributed demand, we are also able to obtain
the explicit analytic form of the optimal policy and a probabilistic
representation of the optimal revenue. The paper is completed by some computer
drawings of the optimal inventory when spot prices are given by a geometric
Brownian motion and by an exponential jump-diffusion process. In the first case
we also make a numerical comparison between the value function and the revenue
associated to the classical static "newsvendor" strategy.Comment: 28 pages, 3 figures; improved presentation, added new results and
section
Confidence-based Optimization for the Newsvendor Problem
We introduce a novel strategy to address the issue of demand estimation in
single-item single-period stochastic inventory optimisation problems. Our
strategy analytically combines confidence interval analysis and inventory
optimisation. We assume that the decision maker is given a set of past demand
samples and we employ confidence interval analysis in order to identify a range
of candidate order quantities that, with prescribed confidence probability,
includes the real optimal order quantity for the underlying stochastic demand
process with unknown stationary parameter(s). In addition, for each candidate
order quantity that is identified, our approach can produce an upper and a
lower bound for the associated cost. We apply our novel approach to three
demand distribution in the exponential family: binomial, Poisson, and
exponential. For two of these distributions we also discuss the extension to
the case of unobserved lost sales. Numerical examples are presented in which we
show how our approach complements existing frequentist - e.g. based on maximum
likelihood estimators - or Bayesian strategies.Comment: Working draf
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