Logistic cost gaps between routing with/without considering inventory cost.

Logistic cost gaps between routing with/without considering inventory cost.</p

Performance of operators (%IBest/%Usage).

This paper considers the problem that a depot replenishes several shelters by aerial and land transportation modes for disaster relief. There are two distinguishing features of our problem: one is routing decisions determine replenishment lead times; the other is that we introduce dual sourcing policy into the inventory routing problem. A robust optimization model is proposed to determine the optimal replenishment quantity, replenishment mode, and transportation routes. Then, we decompose the problem into a routing master-problem and a set of inventory sub-problems. A tractable closed-form solution for sub-problem is derived. We further develop an adaptive large neighborhood search algorithm to solve the problem. To demonstrate the feasibility of the algorithm, we conduct a series of numerical experiments on the benchmark test suite with different scales and compare the performance of the proposed algorithm with a genetic algorithm.</div

Logistic cost on instance B-n78 with different removal rate and reaction factor.

Logistic cost on instance B-n78 with different removal rate and reaction factor.</p

Weight of removal/insertion operators in 3000 iterations on instance A-n32.

Weight of removal/insertion operators in 3000 iterations on instance A-n32.</p

Illustration of the dual sourcing inventory routing problem.

Illustration of the dual sourcing inventory routing problem.</p

Interactions between the master-problem and sub-problems.

Interactions between the master-problem and sub-problems.</p

Comparing ALNS with GA.

This paper considers the problem that a depot replenishes several shelters by aerial and land transportation modes for disaster relief. There are two distinguishing features of our problem: one is routing decisions determine replenishment lead times; the other is that we introduce dual sourcing policy into the inventory routing problem. A robust optimization model is proposed to determine the optimal replenishment quantity, replenishment mode, and transportation routes. Then, we decompose the problem into a routing master-problem and a set of inventory sub-problems. A tractable closed-form solution for sub-problem is derived. We further develop an adaptive large neighborhood search algorithm to solve the problem. To demonstrate the feasibility of the algorithm, we conduct a series of numerical experiments on the benchmark test suite with different scales and compare the performance of the proposed algorithm with a genetic algorithm.</div

Logistic cost gaps between dual-sourcing and single replenishment modes.

Logistic cost gaps between dual-sourcing and single replenishment modes.</p

Logistic cost and replenishment quantity gaps between budget and box uncertainty sets.

Logistic cost and replenishment quantity gaps between budget and box uncertainty sets.</p

Routing decisions.

(a) Routing decisions on A-n32. (b) Routing decisions on B-n78.</p