step change in agri-food logistics ecosystems (project scale)
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STEP CHANGE IN AGRI-FOOD LOGISTICS ECOSYSTEMS (PROJECT SCALE)
http://www.projectscale.eu/
Modeling a stochastic inventory routing problem for perishable products with
environmental considerationsM. 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
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
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.
Authors Topics
Federgruen et al. 1986 Perishability, Demand uncertainty
Treitl et al. 2012 Traveled distance, vehicle load and speed
Al-ehashem and Rekik 2013 Traveled distance
Le et al. 2013 Perishability
Coelho and Laporte 2014 Perishability
Jia et al. 2014 Perishability
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(μit,σit)
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
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).
Stochastic chance-constrained programming model (MPF)
Minimise Expected inventory cost + Expected waste cost + Fuel cost from transportation operations + Driver cost
Stochastic chance-constrained programming model (MPF)
Inventory decisions:
Inventory balance
Waste calculation
Service level
Routing decisions:
Flow conservation
Each vehicle at most 1 route
per period
Vehicle capacities
Eliminate subtours
Deterministic approximation MPF and
variations
Benefits of including perishability and explicit fuel consumption considerations in the model
* Simulation model
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.
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.
Base case solution
Base case solution of MPF
Base case solution-III
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
Environmental impact minimization M`PF
Minimise Exp. inv. cost + Exp. waste cost + Fuel cost + Driver cost
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.
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