The data-driven newsvendor problem:Achieving on-target service-levels using distributionally robust chance-constrained optimization

The classical approach to the newsvendor problem is to first estimate the demand distribution (or assume it to be given) and then determine the optimal inventory level. Data-driven optimization offers an alternative, where the inventory level is determined directly from the data. In this paper, we consider the data-driven newsvendor problem under a service-level constraint. We show that existing approaches to this problem suffer from overfitting, resulting in service-levels that are below the target service-level. We propose new data-driven approaches and corresponding mathematical optimization models based on methods of distributionally robust chance-constrained optimization—which have not yet been applied and empirically tested in the context of the data-driven newsvendor problem. We assess the effectiveness of our approaches by means of an extensive numerical study. To that end, we conduct structured experiments based on simulation as well as experiments based on a real-life bikesharing system where we consider the daily usage data along with information on weather and seasonal factors. The results demonstrate that our methods achieve on-target service-levels even in absence of large amounts of data. All in all, our study provides ample empirical evidence that distributionally robust chance-constrained optimization is a viable approach for addressing the data-driven newsvendor problem

Order acceptance in food processing systems with random raw material requirements

This study considers a food production system that processes a single perishable raw material into several products having stochastic demands. In order to process an order, the amount of raw material delivery from storage needs to meet the raw material requirement of the order. However, the amount of raw material required to process an order is not exactly known beforehand as it becomes evident during processing. The problem is to determine the admission decisions for incoming orders so as to maximize the expected total revenue. It is demonstrated that the problem can be modeled as a single resource capacity control problem. The optimal policy is shown to be too complex for practical use. A heuristic approach is proposed which follows rather simple decision rules while providing good results. By means of a numerical study, the cases where it is critical to employ optimal policies are highlighted, the effectiveness of the heuristic approach is investigated, and the effects of the random resource requirements of orders are analyzed

An extended mixed-integer programming formulation and dynamic cut generation approach for the stochastic lot sizing problem

We present an extended mixed-integer programming formulation of the stochastic lot-sizing problem for the static-dynamic uncertainty strategy. The proposed formulation is significantly more time efficient as compared to existing formulations in the literature and it can handle variants of the stochastic lot-sizing problem characterized by penalty costs and service level constraints, as well as backorders and lost sales. Also, besides being capable of working with a predefined piecewise linear approximation of the cost function-as is the case in earlier formulations-it has the functionality of finding an optimal cost solution with an arbitrary level of precision by means of a novel dynamic cut generation approach

Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing

In this paper, we develop mixed integer linear programming models to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under Bookbinder and Tan's static-dynamic uncertainty strategy. Our models build on piecewise linear upper and lower bounds of the first order loss function. We discuss different formulations of the stochastic lot sizing problem, in which the quality of service is captured by means of backorder penalty costs, non-stockout probability, or fill rate constraints. These models can be easily adapted to operate in settings in which unmet demand is backordered or lost. The proposed approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the above problem, which have been previously tackled via ad-hoc solution methods; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds. Our computational study demonstrates the effectiveness and flexibility of our models.Comment: 38 pages, working draf

An inventory control policy for liquefied natural gas as a transportation fuel

In this paper, we study a novel stochastic inventory management problem that arises in storage and refueling facilities for Liquefied Natural Gas (LNG) as a transportation fuel. In this inventory problem, the physio-chemical properties of LNG play a key role in the design of inventory policies. These properties are: (1) LNG suffers from both quantity decay and quality deterioration and (2) the quality of on-hand LNG can be upgraded by mixing it with higher-quality LNG. Given that LNG quality can be upgraded, an inventory control policy for this problem needs to consider the removal of LNG as a decision variable. We model and solve the problem by means of a Markov Decision Process (MDP) and study the structural characteristics of the optimal policy. The insights obtained in the analysis of the optimal policy are translated into a simple, though effective, inventory control policy in which actions (i.e., replenishment and/or removal) are driven by both the quality and the quantity of the inventories. We assess the performance of our policy by means of a numerical study and show that it performs close to optimal in many numerical instances. The main conclusion of our study is that it is important to take quality into consideration when design inventory control policies for LNG, and that the most effective way to cope with quality issues in an LNG inventory system involves both the removal and the replenishment of inventories

Heuristics for the stochastic economic lot sizing problem with remanufacturing under backordering costs

We consider a production system where demand can be met by manufacturing new products and remanufacturing returned products, and address the economic lot sizing problem therein. The system faces stochastic and time-varying demands and returns over a finite planning horizon. The problem is to match supply with demand, while minimizing the total expected cost which is comprised of fixed production costs and inventory (holding and backordering) costs. We introduce heuristic policies for this problem which offer different levels of flexibility with respect to production decisions. We present computational methods for these policies based on convex optimization and certainty equivalent mixed integer programming, and numerically assess their cost performance and computational efficiency by means of simulation