Introduction to stochastic programming

Research in closed-loop supply chains (CLSCs) has grown rapidly over the last 10 years. The authors offer a critical review of influential CLSC research that takes a business economics perspective. Much of the research was inspired by practice-driven thoughtpieces, and this helped to keep research focused on relevant issues. However, CLSC research has several assumptions, such as perfect substitution between new and remanufactured products that risk becoming institutionalized. There is a strong need to carefully examine current industrial practice so that research remains focused on relevant problems. Deeper understanding of consumer perceptions of remanufactured products, product diffusion, and valuation of returned products are needed for the field to continue to add insights into developing sustainable economies.

Production and Operations Management

/pdf/high-dimensional-statistics-a-non-asymptotic-viewpoint-3e7rtdgg2r.pdf

High-dimensional Statistics: A Non-asymptotic Viewpoint, Martin J. Wainwright, Cambridge University Press, 2019, xvii 552 pages, £57.99, hardback ISBN: 978-1-1084-9802-9

https://cyberleninka.org/article/n/662470.pdf

Literature review of deteriorating inventory models by key topics from 2012 to 2015

Transportation Research, Part A: Policy and Practice

We develop the first approximation algorithms with worst-case performance guarantees for periodic-review perishable inventory systems with general product lifetime, for both backlogging and lost-sales models. The demand process can be nonstationary and correlated over time, capturing such features as demand seasonality and forecast updates. The optimal control policy for such systems is notoriously complicated, thus finding effective heuristic policies is of practical importance. In this paper, we construct a computationally efficient inventory control policy, called the proportional-balancing policy, for systems with an arbitrarily correlated demand process and show that it has a worst-case performance guarantee less than 3. In addition, when the demands are independent and stochastically nondecreasing over time, we propose another policy, called the dual-balancing policy, which admits a worst-case performance guarantee of 2. We demonstrate through an extensive numerical study that both policies perform consistently close to optimal.

/pdf/approximation-algorithms-for-perishable-inventory-systems-25qyumqrhn.pdf

Approximation Algorithms for Perishable Inventory Systems

We consider a periodic-review, single-product inventory system with lost sales and positive lead times under censored demand In contrast to the classical inventory literature, we assume the firm d

Closing the gap: A learning algorithm for lost-sales inventory systems with lead times

We develop new algorithmic approaches to compute provably near-optimal policies for multiperiod stochastic lot-sizing inventory models with positive lead times, general demand distributions, and dynamic forecast updates. The policies that are developed have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. The newly proposed algorithms employ a novel randomized decision rule. We believe that these new algorithmic and performance analysis techniques could be used in designing provably near-optimal randomized algorithms for other stochastic inventory control models and more generally in other multistage stochastic control problems.

/pdf/approximation-algorithms-for-the-stochastic-lot-sizing-3yhvdhjjm5.pdf

Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times

We develop the first nonparametric learning algorithm for periodic-review perishable inventory systems. In contrast to the classical perishable inventory literature, we assume that the firm does no...

Technical Note—Perishable Inventory Systems: Convexity Results for Base-Stock Policies and Learning Algorithms Under Censored Demand

We consider a revenue management problem wherein the seller is endowed with a single type resource with a finite capacity and the resource can be repeatedly used to serve customers. There are multiple classes of customers arriving according to a multi-class Poisson process. Each customer, upon arrival, submits a service request that specifies his service start time and end time. Our model allows customer advanced reservation times and services times in each class to be arbitrarily distributed and correlated. Upon arrival of each customer, the seller must instantaneously decide whether to accept this customer's service request. A customer whose request is denied leaves the system. A customer whose request is accepted is allocated with a specific item of the resource at his service start time. The resource unit occupied by a customer becomes available to other customers after serving this customer. The seller aims to design an admission control policy that maximizes her expected long-run average revenue.

We propose a policy called the ϵ-perturbation class selection policy (ϵ-CSP), based on the optimal solution in the fluid setting wherein customers are infinitesimal and customer arrival processes are deterministic, under the restriction that the seller can utilize at most (1 - ϵ) of her capacity for any ϵ Є(0; 1). We prove that the ϵ-CSP is near-optimal. More precisely, we develop an upper bound of the performance loss of the ϵ-CSP relative to the seller's optimal revenue, and show that it converges to zero with a square-root convergence rate in the asymptotic regime wherein the arrival rates and the capacity grow up proportionally and the capacity buffer level ϵ decays to zero.

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Papers

Approximation Algorithms for Perishable Inventory Systems

Closing the gap: A learning algorithm for lost-sales inventory systems with lead times

Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times

Technical Note—Perishable Inventory Systems: Convexity Results for Base-Stock Policies and Learning Algorithms Under Censored Demand

Revenue Management of Reusable Resources with Advanced Reservations