A Global Chance-Constraint for Stochastic Inventory Systems Under Service Level Constraints

We consider a class of production/inventory control problems that has a single product and a single stocking location, for which a stochastic demand with a known non-stationary probability distribution is given. Under the widely-known replenishment cycle policy the problem of computing policy parameters under service level constraints has been modeled using various techniques. Tarim and Kingsman introduced a modeling strategy that constitutes the state-of-the-art approach for solving this problem. In this paper we identify two sources of approximation in Tarim and Kingsman's model and we propose an exact stochastic constraint programming approach. We build our approach on a novel concept, global chance-constraints, which we introduce in this paper. Solutions provided by our exact approach are employed to analyze the accuracy of the model developed by Tarim and Kingsman

Inventory control for a non-stationary demand perishable product: comparing policies and solution methods

This paper summarizes our findings with respect to order policies for an inventory control problem for a perishable product with a maximum fixed shelf life in a periodic review system, where chance constraints play a role. A Stochastic Programming (SP) problem is presented which models a practical production planning problem over a finite horizon. Perishability, non-stationary demand, fixed ordering cost and a service level (chance) constraint make this problem complex. Inventory control handles this type of models with so-called order policies. We compare three different policies: a) production timing is fixed in advance combined with an order up-to level, b) production timing is fixed in advance and the production quantity takes the age distribution into account and c) the decision of the order quantity depends on the age-distribution of the items in stock. Several theoretical properties for the optimal solutions of the policies are presented. In this paper, four different solution approaches from earlier studies are used to derive parameter values for the order policies. For policy a), we use MILP approximations and alternatively the so-called Smoothed Monte Carlo method with sampled demand to optimize values. For policy b), we outline a sample based approach to determine the order quantities. The flexible policy c) is derived by SDP. All policies are compared on feasibility regarding the α-service level, computation time and ease of implementation to support management in the choice for an order policy.National project TIN2015-66680-C2-2-R, in part financed by the European Regional Development Fund (ERDF)

Computing (R, S) policies with correlated demand

This paper considers the single-item single-stocking non-stationary stochastic lot-sizing problem under correlated demand. By operating under a nonstationary (R, S) policy, in which R denote the reorder period and S the associated order-up-to-level, we introduce a mixed integer linear programming (MILP) model which can be easily implemented by using off-theshelf optimisation software. Our modelling strategy can tackle a wide range of time-seriesbased demand processes, such as autoregressive (AR), moving average(MA), autoregressive moving average(ARMA), and autoregressive with autoregressive conditional heteroskedasticity process(AR-ARCH). In an extensive computational study, we compare the performance of our model against the optimal policy obtained via stochastic dynamic programming. Our results demonstrate that the optimality gap of our approach averages 2.28% and that computational performance is good

Ordonnancement de tâches sous contraintes sur des métiers à tisser

Dans une usine de production de textile, il y a des métiers à tisser. Ces métiers à tisser peuvent être configurés de différentes façons. Des tâches doivent être exécutées sur ces métiers à tisser et le temps d’exécution d’une tâche est fonction du métier sur lequel elle est effectuée. De plus, chaque tâche est seulement compatible avec les métiers à tisser étant configurés de certaines façons. Un temps de mise en course peut permettre de configurer ou préparer un métier à tisser pour l’exécution d’une tâche. Le temps de mise en course est dépendant de la tâche qui précède et de celle qui suit. Nous souhaitons alors créer un horaire pour minimiser les temps de fabrication et les retards. Toutefois, certaines contraintes doivent être respectées. Lorsque des préparations surviennent sur des métiers différents en même temps, le nombre d’employés doit être suffisant. Un métier ne peut faire qu’une seule action à la fois. L’ordonnancement d’une seule machine est un problème NP-Difficile. Dans ce projet, il faut ordonnancer environ 800 tâches sur 90 machines dans un horizon de deux semaines, tout en respectant les contraintes de personnel. Des évènements stochastiques doivent être pris en compte pour obtenir un meilleur horaire. Le bris d’un fil n’étant pas un évènement rare, l’occurrence des bris est donnée sous la forme d’une loi de Poisson. Nous proposons alors une approche de résolution utilisant une heuristique de branchement basée sur le problème du commis voyageur. Cette approche permet d’obtenir de bonnes solutions pour le problème d’ordonnancement exploré. Les solutions trouvées sont 5 à 30% meilleures en termes de fonction objectif qu’une heuristique semblable à celle utilisée par l’équipe de planification de notre partenaire industriel. Nous présentons aussi un algorithme pour garantir la robustesse d’un horaire. Notre algorithme permet de générer des horaires plus réalistes et qui résistent bien aux évènements imprévus. La combinaison de ces deux pratiques mène à l’intégration et l’utilisation du produit final par notre partenaire industriel.In a textile factory, there are looms. Workers can configure the looms to weave different pieces of textiles. A loom can only weave a piece of textiles if the piece of textiles is compatible with its loom configuration. To change its configuration, a loom requires a setup. The setups are performed manually by workers. There are also sequence-dependent setups to prepare a loom for the upcoming piece of textiles. We wish to minimize the setups duration and the lateness. A solution must satisfy some constraints. The problem is subject to cumulative resources. The quantity of workers simultaneously configuring machines can’t exceed the total number of employees. A loom can only weave a piece of textiles at a time. Scheduling tasks on a single loom is an NP-Hard problem. In this project, we must schedule tasks an average of 800 tasks on 90 looms with a two-week horizon. Stochastic events might occur and must be accounted for. We must design an algorithm to create robust schedules under uncertainty. As a thread breaking during the weaving process isn’t a rare occurrence, a better schedule could greatly impact the performances of a company when applying the schedule to a real situation. We formulate that the number of breaks per task follows a Poisson distribution. First, we propose a branching heuristic based on the traveling salesperson problem in order to leverage computation times. The solutions found are 5 to 30% better according to their objective function than the ones of a greedy heuristic similar to what our industrial partner uses. We also present a filtering algorithm to guarantee robustness of solutions in respect to a confidence level. This algorithm improves robustness and creates more realist schedules. The algorithm is also efficient in computation time by achieving bound consistency in linear time. Combining both these techniques leads to the integration of our research in the decision system of our industrial partner

Una metodología para la estimación eficiente del stock de referencia en políticas de revisión periódica con demanda discreta

El objetivo de la presente tesis es proponer una metodología para la estimación eficiente del stock de referencia en el diseño de políticas (R, S) cuando se utiliza en nivel de servicio de ciclo como restricción de diseño, asumiéndose que el proceso de demanda es estacionario con una función de probabilidad discreta, independiente, e idénticamente distribuida. Para ello se analiza el comportamiento de cuatro métodos de cálculo, tres aproximados y uno exacto. La aplicación del método exacto supone un elevado esfuerzo computacional cuyo coste no se justifica para cualquier ítem y cualquier circunstancia. Por ello es importante conocer el comportamiento de los métodos aproximados y los riesgos asociados a su utilización. En la práctica, el método más extendido para calcular el nivel de servicio de ciclo, denominado clásico, es una aproximación al cálculo exacto. Sin embargo, en la presente tesis se demuestra que su utilización para la determinación del stock de referencia no siempre asegura cumplir con el criterio de diseño de la política establecido como objetivo. Los métodos analizados son: (1) el método exacto propuesto por Cardós et al. (2006); (2) La aproximación PI derivada por Cardos y Babiloni (2008) a partir de hipótesis para simplificar el método exacto; (3) La aproximación PII derivada por Cardos y Babiloni (2008) a partir de hipótesis para simplificar el método exacto y la aproximación PI; y (4) el método clásico para el cálculo del stock de referencia [ver p. ej. Silver et al. (1998)], denominado aproximación clásica en la presente tesis, que resulta además al asumir hipótesis para simplificar el método exacto, la aproximación PI y la aproximación PII [Cardos y Babiloni (2008)]. La metodología propuesta se fundamenta en un experimento lo suficientemente amplio (115.941 casos) que justifica su validez.Babiloni Griñón, ME. (2009). Una metodología para la estimación eficiente del stock de referencia en políticas de revisión periódica con demanda discreta [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8322Palanci

Mathematical programming heuristics for nonstationary stochastic inventory control

This work focuses on the computation of near-optimal inventory policies for a wide range of problems in the field of nonstationary stochastic inventory control. These problems are modelled and solved by leveraging novel mathematical programming models built upon the application of stochastic programming bounding techniques: Jensen's lower bound and Edmundson-Madanski upper bound. The single-item single-stock location inventory problem under the classical assumption of independent demand is a long-standing problem in the literature of stochastic inventory control. The first contribution hereby presented is the development of the first mathematical programming based model for computing near-optimal inventory policy parameters for this problem; the model is then paired with a binary search procedure to tackle large-scale problems. The second contribution is to relax the independence assumption and investigate the case in which demand in different periods is correlated. More specifically, this work introduces the first stochastic programming model that captures Bookbinder and Tan's static-dynamic uncertainty control policy under nonstationary correlated demand; in addition, it discusses a mathematical programming heuristic that computes near-optimal policy parameters under normally distributed demand featuring correlation, as well as under a collection of time-series-based demand process. Finally, the third contribution is to consider a multi-item stochastic inventory system subject to joint replenishment costs. This work presents the first mathematical programming heuristic for determining near-optimal inventory policy parameters for this system. This model comes with the advantage of tackling nonstationary demand, a variant which has not been previously explored in the literature. Unlike other existing approaches in the literature, these mathematical programming models can be easily implemented and solved by using off-the-shelf mathematical programming packages, such as IBM ILOG optimisation studio and XPRESS Optimizer; and do not require tedious computer coding. Extensive computational studies demonstrate that these new models are competitive in terms of cost performance: in the case of independent demand, they provide the best optimality gap in the literature; in the case of correlated demand, they yield tight optimality gap; in the case of nonstationary joint replenishment problem, they are competitive with state-of-the-art approaches in the literature and come with the advantage of being able to tackle nonstationary problems

Decision support modeling for sustainable food logistics management

Summary For the last two decades, food logistics systems have seen the transition from traditional Logistics Management (LM) to Food Logistics Management (FLM), and successively, to Sustainable Food Logistics Management (SFLM). Accordingly, food industry has been subject to the recent challenges of reducing the amount of food waste and raising energy efficiency to reduce greenhouse gas emissions. These additional challenges add to the complexity of logistics operations and require advanced decision support models which can be used by decision makers to develop more sustainable food logistics systems in practice. Hence, the overall objective of this thesis was to obtain insight in how to improve the sustainability performance of food logistics systems by developing decision support models that can address the concerns for transportation energy use and consequently carbon emissions, and/or product waste, while also adhering to competitiveness. In line with this overall objective, we have defined five research objectives. The first research objective (RO), which is to identify key logistical aims, analyse available quantitative models and point out modelling challenges in SFLM, is investigated in Chapter 2. In this chapter, key logistical aims in LM, FLM and SFLM phases are identified, and available quantitative models are analysed to point out modelling challenges in SFLM. A literature review on quantitative studies is conducted and also qualitative studies are consulted to better understand the key logistical aims and to identify the relevant system scope issues. The main findings of the literature review indicate that (i) most studies rely on a completely deterministic environment, (ii) the food waste challenge in logistics has not received sufficient attention, (iii) traveled distance is often used as a single indicator to estimate related transportation cost and emissions, and (iv) most studies propose single objective models for the food logistics problems. This chapter concludes that new and advanced quantitative models are needed that take specific SFLM requirements from practice into consideration to support business decisions and capture food supply chain dynamics. These findings motivated us to work on the following research objectives RO2, RO3, RO4 and RO5. RO2, which is to analyse the relationship between economic (cost) and environmental (transportation carbon emissions) performance in a network problem of a perishable product, is investigated in Chapter 3. This chapter presents a multi-objective linear programming (MOLP) model for a generic beef logistics network problem. The objectives of the model are (i) minimizing total logistics cost and (ii) minimizing total amount of greenhouse gas emissions from transportation operations. The model is solved using the e-constraint method. This study breaks away from the literature on logistics network models by simultaneously considering transportation emissions (affected by road structure, vehicle and fuel types, weight loads of vehicles, traveled distances), return hauls and product perishability in a MOLP model. We present computational results and analyses based on the application of the model to a real-life international beef logistics chain operating in Nova Andradina, Mato Grosso do Sul, Brazil, and exporting beef to the European Union. Trade-off relationships between multiple objectives are observed by the derived Pareto frontier that presents the cost of being sustainable from the point of reducing transportation emissions. The results indicate the importance of distances between actors in terms of environmental impact. Moreover, sensitivity analysis on important practical parameters show that export ports' capacities put pressure on the logistics system; decreasing fuel efficiency due to the bad infrastructure has negative effects on cost and emissions; and green tax incentives result in economic and environmental improvement. RO3, which is to investigate the performance implications of accommodating explicit transportation energy use and traffic congestion concerns in a two-echelon capacitated vehicle routing problem (2E-CVRP), is investigated in Chapter 4. The multi-echelon distribution strategy in which freight is delivered to customers via intermediate depots rather than using direct shipments is an increasingly popular strategy in urban logistics. Its popularity is primarily due to the fact that it alleviates the environmental (e.g., energy usage and congestion) and social (e.g., traffic-related air pollution, accidents and noise) consequences of logistics operations. This chapter presents a comprehensive mixed integer linear programming formulation for a time-dependent 2E-CVRP that accounts for vehicle type, traveled distance, vehicle speed, load, multiple time zones and emissions. A case study in a supermarket chain operating in the Netherlands shows the applicability of the model to a real-life problem. Several versions of the model, each differing with respect to the objective function, are tested to produce a number of selected Key Performance Indicators (KPIs) relevant to distance, time, fuel consumption and cost. This chapter offers insight in the economies of environmentally-friendly vehicle routing in two-echelon distribution systems. The results suggest that an environmentally-friendly solution is obtained from the use of a two-echelon distribution system, whereas a single-echelon distribution system provides the least-cost solution. RO4, which is to investigate the performance implications of accommodating explicit transportation energy use, product waste and demand uncertainty concerns in an inventory routing problem (IRP), is investigated in Chapter 5. Traditional assumptions of constant distribution costs between nodes, unlimited product shelf life and deterministic demand used in the IRP literature restrict the usefulness of the proposed models in current food logistics systems. From this point of view, our interest in this chapter is to enhance the traditional models for the IRP to make them more useful for decision makers in food logistics management. Therefore, we present a multi-period IRP model that includes truck load dependent (and thus route dependent) distribution costs for a comprehensive evaluation of CO2 emission and fuel consumption, perishability, and a service level constraint for meeting uncertain demand. A case study on the fresh tomato distribution operations of a supermarket chain shows the applicability of the model to a real-life problem. Several variations of the model, each differing with respect to the considered aspects, are employed to present the benefits of including perishability and explicit fuel consumption concerns in the model. The results suggest that the proposed integrated model can achieve significant savings in total cost while satisfying the service level requirements, and thus offers better support to decision makers. RO5, which is to analyse the benefits of horizontal collaboration in a green IRP for perishable products with demand uncertainty, is investigated in Chapter 6. This chapter presents a decision support model, which includes a comprehensive evaluation of CO2 emission and fuel consumption, perishability, and a service level constraint for meeting uncertain demand, for the IRP with multiple suppliers and customers. The model allows to analyse the benefits of horizontal collaboration in the IRP with respect to several KPIs, i.e., total emissions, total driving time, total routing cost comprised of fuel and wage cost, total inventory cost, total waste cost, and total cost. A case study on the distribution operations of two suppliers, where the first supplier produces figs and the second supplier produces cherries, shows the applicability of the model to a real-life problem. The results show that horizontal collaboration among the suppliers contributes to the decrease of aggregated total cost and emissions in the logistics system, whereas the obtained gains are sensitive to the changes in parameters such as supplier size or maximum product shelf life. According to the experiments, the aggregated total cost benefit from cooperation varies in a range of about 4-24% and the aggregated total emission benefit varies in a range of about 8-33%. Integrated findings from Chapters 2, 3, 4, 5 and 6 contribute to the SFLM literature by (i) reflecting the state of the art on the topic of quantitative logistic models which have sustainability considerations, (ii) providing decision support models which can be used by decision makers to improve the performance of the sustainable food logistics systems in terms of logistics cost, transportation energy use and carbon emissions, and/or product waste, and (iii) presenting the applicability of the proposed models in different case studies based on mainly real data, multiple scenarios, and analysis. The developed decision support models exploit several logistics improvement opportunities regarding transportation energy use and emissions, and/or product waste to better aid SFLM, as distinct from their counterparts in literature. To conclude, the case study implementations in this thesis demonstrate that (i) perishability and explicit consideration of fuel consumption are important aspects in logistics problems, and (ii) the provided decision support models can be used in practice by decision makers to further improve sustainability performance of the food logistics systems. </p