# A column generation-based algorithm for solving combined inventory and routing problems

Carlos Alberto Franco Franco, Juan Carlos Figueroa-Garcia

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

This paper presents a column generation algorithm for solving combined vehicle and inventory problems. This problem is based on the idea of coordinating customer inventory levels through a minimum routing cost. This is a combinatory decision problem since vehicle routing and inventory problems, are combined. Using the column generation method, we can iteratively generate interesting routes to the system, based on their dual costs, this is routes that will improve the quality of the objective function because its reduced costs are negatives. The initial mixed integer problem has to be relaxed for getting its reduced costs. The sub problem is defined as the shortest path problem that returns a set of desirable routes. Finally, when the set of desirable routes is obtained, the mixed integer model should select a set of routes that fulfill both minimum shipping costs and the constraints of the system.
Original language English (US) 305-313 9 Ingeniare 24 2 Published - 2016

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Costs
Vehicle routing
Freight transportation

### Cite this

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title = "A column generation-based algorithm for solving combined inventory and routing problems",
abstract = "This paper presents a column generation algorithm for solving combined vehicle and inventory problems. This problem is based on the idea of coordinating customer inventory levels through a minimum routing cost. This is a combinatory decision problem since vehicle routing and inventory problems, are combined. Using the column generation method, we can iteratively generate interesting routes to the system, based on their dual costs, this is routes that will improve the quality of the objective function because its reduced costs are negatives. The initial mixed integer problem has to be relaxed for getting its reduced costs. The sub problem is defined as the shortest path problem that returns a set of desirable routes. Finally, when the set of desirable routes is obtained, the mixed integer model should select a set of routes that fulfill both minimum shipping costs and the constraints of the system.",
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A column generation-based algorithm for solving combined inventory and routing problems. / Franco Franco, Carlos Alberto; Figueroa-Garcia, Juan Carlos .

In: Ingeniare, Vol. 24, No. 2, 2016, p. 305-313.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A column generation-based algorithm for solving combined inventory and routing problems

AU - Franco Franco, Carlos Alberto

AU - Figueroa-Garcia, Juan Carlos

PY - 2016

Y1 - 2016

N2 - This paper presents a column generation algorithm for solving combined vehicle and inventory problems. This problem is based on the idea of coordinating customer inventory levels through a minimum routing cost. This is a combinatory decision problem since vehicle routing and inventory problems, are combined. Using the column generation method, we can iteratively generate interesting routes to the system, based on their dual costs, this is routes that will improve the quality of the objective function because its reduced costs are negatives. The initial mixed integer problem has to be relaxed for getting its reduced costs. The sub problem is defined as the shortest path problem that returns a set of desirable routes. Finally, when the set of desirable routes is obtained, the mixed integer model should select a set of routes that fulfill both minimum shipping costs and the constraints of the system.

AB - This paper presents a column generation algorithm for solving combined vehicle and inventory problems. This problem is based on the idea of coordinating customer inventory levels through a minimum routing cost. This is a combinatory decision problem since vehicle routing and inventory problems, are combined. Using the column generation method, we can iteratively generate interesting routes to the system, based on their dual costs, this is routes that will improve the quality of the objective function because its reduced costs are negatives. The initial mixed integer problem has to be relaxed for getting its reduced costs. The sub problem is defined as the shortest path problem that returns a set of desirable routes. Finally, when the set of desirable routes is obtained, the mixed integer model should select a set of routes that fulfill both minimum shipping costs and the constraints of the system.

M3 - Article

VL - 24

SP - 305

EP - 313

JO - Ingeniare

JF - Ingeniare

SN - 0718-3291

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