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)

On solving a stochastic programming model for perishable inventory control

This paper describes and analyses a Stochastic Programming (SP) model that is used for a specific inventory control problem for a perishable product. The decision maker is confronted with a non-stationary random demand for a fixed shelf life product and wants to make an ordering plan for a finite horizon that satisfies a service level constraint. In literature several approaches have been described to generate approximate solutions. The question dealt with here is whether exact approaches can be developed that generate solutions up to a guaranteed accuracy. Specifically, we look into the implications of a Stochastic Dynamic Programming (SDP) approach

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