Multi-period Inventory Routing Problem under Carbon Emission Regulations Chun Cheng, Mingyao Qi, Xingyi Wang, Ying Zhang (2016)

Multi-period Inventory Routing Problem under Carbon Emission Regulations
Chun Cheng, Mingyao Qi, Xingyi Wang, Ying Zhang (2016)

ABSTRACT

-Analyzes the impact of carbon emission regulations on inventory routing problem (IRP)
-In every period, vehicles depart from depot to pickup products from supplier to meet the assembly plant's demand (deterministic & time-varying)
-Carbon emissions are generated by fuel consumption
-A series of mixed integer non-linear programming models are constructed & linearization methods are used
-A hybrid genetic algorithm (HGA) is proposed
-Numerical test are performed to show the effectiveness of the algorithm

Problem Description

-This paper focuses on Multi-period Inventory Routing Problem (MIRP) in an inbound product collection system consisting of an assembly plant, depot, and suppliers
-Each supplier offers distinctive product (all products are ready for collection)
-Demand is specific & deterministic
-Carbon emission regulations are imposed in each period

Objective

Determine when to visit the suppliers, corresponding quantities collected & the vehicle schedules such that the total cost of the supply chain is minimized

Formulation

Computation of fuel consumption (based on travel distance, truckload & speed):

Formulation of traditional MIRP:

Formulation with a carbon cap and offset policy:

Formulation with a carbon cap and trade policy:

Formulation with a carbon taxing policy:

Flowchart of the solution procedure

Numerical Tests & Analyses

Data sets are based on Lee et al. (2013) http://www.mie.utoronto.ca/labs/iir/IRP

Evaluation of HGA

-Proposed HGA is implemented in C++ language
-Mathematical formulation is solved by CPLEX 12.6 to obtain the best integer solution & best bound
-HGA can find optimal solution with less time for 17 out of 18 small-sized problems & the average gap is 0.04%
-For medium and large sized problem, the average gape are 4.25% and 5.32% respectively

Comparison with the traditional MIRP model (Observation)

1) The reaction to carbon cap varies significantly due to different industries
2) A tighter carbon cap can paradoxically lead to higher carbon emission level
3) Increasing fuel cost will lead to increase in cost & decrease in emissions
4) A higher unit carbon price does not always result in a better environmental benefit (Appropriate taxing level should be carefully determined)