1. STEP CHANGE IN AGRI-FOOD LOGISTICS ECOSYSTEMS (PROJECT SCALE) http://www.projectscale.eu/

2. Modeling a stochastic inventory routing problem for perishable products with environmental considerations M. Soysal, J.M. Bloemhof-Ruwaard, R. Haijema, J.G.A.J. van der Vorst Operations Research and Logistics, Wageningen University Barcelona 2014, 13-18 July

3. Inventory Routing Problem (IRP) 1. When to deliver to each customer, 2. How much to deliver to each customer each time it is served, 3. How to combine customers into vehicle routes Coordination of inventory management and vehicle routing * Traditional assumptions for the IRP

4. Related literature Contribution: Developing a comprehensive stochastic chance- constrained programming model for a generic IRP that accounts for the KPIs of total energy use (emissions), total driving time, total routing cost, total inventory cost, total waste cost, and total cost. AuthorsTopics Federgruen et al. 1986Perishability, Demand uncertainty Treitl et al. 2012Traveled distance, vehicle load and speed Al-ehashem and Rekik 2013Traveled distance Le et al. 2013Perishability Coelho and Laporte 2014Perishability Jia et al. 2014Perishability

5. Problem description  Single vendor, multiple customers  Homogeneous vehicles at the vendor  Routes start and end at the vendor's location  Demand of a customer two or more vehicles  Demand ~ N(μ it,σ it )  Inventory at the customers (Fixed shelf life of m≥2 periods)  The demand should be met with a probability of at least α  The routes and quantity of shipments in each period such that the total cost comprising routing, inventory and waste costs is minimized

6. Fuel consumption estimation Comprehensive emissions model of Barth et al., 2005. Other emission estimation models (Demir et al., 2011). The total amount of fuel used EC (liters) for traversing a distance a (m) at constant speed f (m/s) with load F (kg) is calculated as follows: Same approach in Bektas and Laporte (2011), Demir et al. (2012) and Franceschetti et al. (2013).

7. Stochastic chance-constrained programming model (M PF ) Minimise Expected inventory cost + Expected waste cost + Fuel cost from transportation operations + Driver cost

8. Stochastic chance-constrained programming model (M PF ) Inventory decisions:  Inventory balance  Waste calculation  Service level Routing decisions:  Flow conservation  Each vehicle at most 1 route per period  Vehicle capacities  Eliminate subtours

9. Deterministic approximation M PF and variations Benefits of including perishability and explicit fuel consumption considerations in the model * Simulation model

10. Application 1 DC, 11 supermarkets Planning horizon is four weeks Capacity of vehicles 10 tonnes Random demand means with cv 0.1 Service target 95% Shelf life 2 weeks  The ILOG-OPL development studio and CPLEX 12.6 optimization package and Visual C++ programming language The fresh tomato distribution operations of a supermarket chain operating in Turkey.

11. Key Performance Indicators  Total emissions,  Total driving time,  Total routing cost comprised of fuel and wage cost,  Total inventory cost,  Total waste cost,  Total cost.

12. Base case solution

13. Base case solution of M PF

14. Base case solution-III

15. Sensitivity analysis 13 additional scenarios: Demand means, two additional demand set Coefficient of variation, C = 0.05, 0.1, 0.15, 0.2 Maximum shelf life, m = 2, 3, 4 Holding cost, h = 0.03, 0.06, 0.09, 0.12 Service level, α = 90, 92.5, 95, 97.5

16. Environmental impact minimization M` PF Minimise Exp. inv. cost + Exp. waste cost + Fuel cost + Driver cost

17. Conclusions  We modeled and analysed the IRP to account for perishability, explicit fuel consumption and demand uncertainty.  The model is unique in using a comprehensive emission function and in modeling waste and service level constraints as a result of uncertain demand.  Integrated model more useful than a basic model. THANK YOU !! QUESTIONS?? Jacqueline.bloemhof@wur.nl