STEP CHANGE IN AGRI-FOOD LOGISTICS
ECOSYSTEMS (PROJECT SCALE)
http://www.projectscale.eu/
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
Inventory Routing Problem (IRP)
Coordination of inventory management and vehicle
routing
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
* Traditional assumptions for the IRP
Related literature
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
Contribution: Developing a comprehensive stochastic chanceconstrained 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.
Problem description
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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
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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
The fresh tomato distribution operations of a supermarket
chain operating in Turkey.
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
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.
THANK YOU !!
QUESTIONS?? Jacqueline.bloemhof@wur.nl