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

Intermittency and obsolescence:A Croston method with linear decay

Only two forecasting methods have been designed specifically for intermittent demand with possible demand obsolescence: Teunter–Syntetos–Babai (TSB) and Hyperbolic-Exponential Smoothing (HES). When an item becomes obsolete the TSB forecasts decay exponentially while those of HES decay hyperbolically. Both types of decay continue to predict nonzero demand indefinitely, and it would be preferable for forecasts to become zero after a finite time. We describe a third method, called Exponential Smoothing with Linear Decay, that decays linearly to zero in a finite time, is asymptotically the best method for handling obsolescence, and performs well in experiments on real and synthetic data

The impact of sweeping the membranes on cervical length and labor: a randomized clinical trial

Objectives: The aim of the study was to investigate to what extent sweeping of the membranes contributes to cervical shortening and if cervical shortening is related to the time to onset of labor and duration of the active phase of labor. Methods: This prospective randomized clinical trial was performed at Baskent University between February and March 2011. Women were randomly assigned to receive membrane sweeping (Sweeping Group) (n=69) or no membrane sweeping (Control Group) (n=71). Cervical length was measured (cervix1) in both groups by examiner 1 and the Bishop Score was determined in the control group and sweeping was performed in the sweeping group by examiner 2. Two days later the patients had another cervical length measurement (cervix 2) by examiner 1, blinded to the group and results of the examiner 2. t test, Mann-Whitney U test and Chi-square test were used for statistical analyses. Results: Cervix 1 was 27.4}8.4 mm and 29.6}8.9 mm (p= 0.14), cervix 2 was 23.3}8.8 mm and 23.8}8.5mm (p= 0.28) and cervical shortening was 5}4 mm and 5}4mm (p= 0.446), time to onset of labor was 6.3}4.6 and 5.7}4.1 (p= 0.38) and duration of labor was 5.8} 2.89 and 5.7} 2.4 (p= 0.82) for the sweeping and the control groups, respectively. Conclusions: Sweeping of the membranes does not reduce cervical length and does not shorten time to onset of labor and duration of the active phase of labor. NCT01309308: Sweeping the Membranes, Cervical Length and Duration of Labor

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

Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

This paper(1) considers a single product and a single stocking location production/inventory control problem given a non-stationary stochastic demand. Under a widely-used control policy for this type of inventory system, the objective is to find the optimal number of replenishments, their timings and their respective order-up-to-levels that meet customer demands to a required service level. We extend a known CP approach for this problem using three cost-based filtering methods. Our approach can solve to optimality instances of realistic size much more efficiently than previous approaches, often with no search effort at all

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

Dynamic pricing with demand disaggregation for hotel revenue management

In this paper we present a novel approach to the dynamic pricing problem for hotel businesses. It includes disaggregation of the demand into several categories, forecasting, elastic demand simulation, and a mathematical programming model with concave quadratic objective function and linear constraints for dynamic price optimization. The approach is computationally efficient and easy to implement. In computer experiments with a hotel data set, the hotel revenue is increased by about 6% on average in comparison with the actual revenue gained in a past period, where the fixed price policy was employed, subject to an assumption that the demand can deviate from the suggested elastic model. The approach and the developed software can be a useful tool for small hotels recovering from the economic consequences of the COVID-19 pandemic

Experimentation with a dynamic pricing approach for hotel industry

A dynamic pricing approach for hotel revenue management is suggested. It aims at increasing revenue over the baseline