96 research outputs found
Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes
We consider the canonical periodic review lost sales inventory system with
positive lead-times and stochastic i.i.d. demand under the average cost
criterion. We introduce a new policy that places orders such that the expected
inventory level at the time of arrival of an order is at a fixed level and call
it the Projected Inventory Level (PIL) policy. We prove that this policy has a
cost-rate superior to the equivalent system where excess demand is back-ordered
instead of lost and is therefore asymptotically optimal as the cost of losing a
sale approaches infinity under mild distributional assumptions. We further show
that this policy dominates the constant order policy for any finite lead-time
and is therefore asymptotically optimal as the lead-time approaches infinity
for the case of exponentially distributed demand per period. Numerical results
show this policy also performs superior relative to other policies
Learning to Order for Inventory Systems with Lost Sales and Uncertain Supplies
We consider a stochastic lost-sales inventory control system with a lead time
over a planning horizon . Supply is uncertain, and is a function of the
order quantity (due to random yield/capacity, etc). We aim to minimize the
-period cost, a problem that is known to be computationally intractable even
under known distributions of demand and supply. In this paper, we assume that
both the demand and supply distributions are unknown and develop a
computationally efficient online learning algorithm. We show that our algorithm
achieves a regret (i.e. the performance gap between the cost of our algorithm
and that of an optimal policy over periods) of when
. We do so by 1) showing our algorithm cost is higher by at most
for any compared to an optimal constant-order policy
under complete information (a well-known and widely-used algorithm) and 2)
leveraging its known performance guarantee from the existing literature. To the
best of our knowledge, a finite-sample (and polynomial in )
regret bound when benchmarked against an optimal policy is not known before in
the online inventory control literature. A key challenge in this learning
problem is that both demand and supply data can be censored; hence only
truncated values are observable. We circumvent this challenge by showing that
the data generated under an order quantity allows us to simulate the
performance of not only but also for all , a key
observation to obtain sufficient information even under data censoring. By
establishing a high probability coupling argument, we are able to evaluate and
compare the performance of different order policies at their steady state
within a finite time horizon. Since the problem lacks convexity, we develop an
active elimination method that adaptively rules out suboptimal solutions
Base-stock policies for lost-sales models: Aggregation and asymptotics
This paper considers the optimization of the base-stock level for the classical periodic review lost-sales inventory
system. The optimal policy for this system is not fully understood and computationally expensive to obtain.
Base-stock policies for this system are asymptotically optimal as lost-sales costs approach infinity, easy to
implement and prevalent in practice. Unfortunately, the state space needed to evaluate a base-stock policy
exactly grows exponentially in both the lead time and the base-stock level. We show that the dynamics
of this system can be aggregated into a one-dimensional state space description that grows linearly in the
base-stock level only by taking a non-traditional view of the dynamics. We provide asymptotics for the
transition probabilities within this single dimensional state space and show that these asymptotics have good
convergence properties that are independent of the lead time under mild conditions on the demand distribution.
Furthermore, we show that these asymptotics satisfy a certain
ow conservation property. These results lead
to a new and computationally efficient heuristic to set base-stock levels in lost-sales systems. In a numerical
study we demonstrate that this approach performs better than existing heuristics with an average gap with
the best base-stock policy of 0.01% across a large test-bed
Data Driven Optimization: Theory and Applications in Supply Chain Systems
Supply chain optimization plays a critical role in many business enterprises. In a data driven environment, rather than pre-specifying the underlying demand distribution and then optimizing the system’s objective, it is much more robust to have a nonparametric approach directly leveraging the past observed data. In the supply chain context, we propose and design online learning algorithms that make adaptive decisions based on historical sales (a.k.a. censored demand). We measure the performance of an online learning algorithm by cumulative regret or simply regret, which is defined as the cost difference between the proposed algorithm and the clairvoyant optimal one.
In the supply chain context, to design efficient learning algorithms, we typically face two major
challenges. First, we need to identify a suitable recurrent state that decouples system dynamics into cycles with good properties: (1) smoothness and rich feedback information necessary to apply the zeroth order optimization method effectively; (2) convexity and gradient information essential for the first order methods. Second, we require the learning algorithms to be adaptive to the physical constraints, e.g., positive inventory carry-over, warehouse capacity constraint, ordering/production capacity constraint, and these constraints limit the policy search space in a dynamic fashion. To design efficient and provably-good data driven supply chain algorithms, we zoom into the detailed structure of each system, and carefully trade off between exploration and exploitation.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/150030/1/haoyuan_1.pd
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