A reactive simheuristic using online data for a real‐life inventory routing problem with stochastic demands

• Published date: 01 November 2020
• Author: Javier Panadero,Angel A. Juan,David Raba,Alejandro Estrada‐Moreno
• Date: 01 November 2020
• DOI: http://doi.org/10.1111/itor.12776

Intl. Trans. in Op. Res. 27 (2020) 2785–2816

DOI: 10.1111/itor.12776

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A reactive simheuristic using online data for a real-life

inventory routing problem with stochastic demands

David Rabaa,c,∗, Alejandro Estrada-Morenob, Javier Panaderocand

Angel A. Juanc

aInsylo Technologies Inc., Girona, Spain

bDepartment of Computer Engineering and Mathematics, Universitat Rovira i Virgili, Tarragona, Spain

cIN3–Computer Science Department, Universitat Oberta de Catalunya, Castelldefels, Spain

E-mail: david.raba@insylo.com [Raba]; alejandro.estrada@urv.cat [Estrada-Moreno];

jpanaderom@uoc.edu [Panadero]; ajuanp@uoc.edu [Juan]

Received 5 May2019; received in revised form 28 October 2019; accepted 7 January 2020

Abstract

In the context of a supply chain for the animal-feed industry, this paper focuses on optimizing replenishment

strategies for silos in multiple farms. Assuming that a supply chain is essentially a valuechain, our work aims

at narrowing this chasm and putting analytics into practice by identifying and quantifying improvements

on specific stages of an animal-feed supply chain. Motivated by a real-life case, the paper analyses a rich

multi-period inventory routing problem with homogeneous fleet, stochastic demands, and maximum route

length. After describing the problem and reviewing the related literature, we introduce a reactive heuristic,

which is then extended into a biased-randomized simheuristic. Our reactive approach is validated and tested

using a series of adapted instances to explore the gap betweenthe solutions it provides and the ones generated

by existing nonreactive approaches.

Keywords:multi-period inventory routing problem; stochastic demands; online data;biased randomization; simheuristics

1. Introduction

Livestock consume approximately 477 M tonnes of feed each year in the EU (Kleter et al., 2018).

From this, 154 M tonnes of compound feed—typically preserved and stored in silos to supplement

their own feed—were produced bythe EU in 2015 (mainly for cattle, pigs, and poultry, respectively)

to supplement their own feed. In the EU28, there are more than 800,000 silos on industrial livestock

farms used to store compound feed according to animal production and consumption (FEFAC,

2016). For farmers, the feeding process at the farm has evolved from one of trial-and-error to

∗Corresponding author.

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2786 D. Raba et al. / Intl. Trans.in Op. Res. 27 (2020) 2785–2816

precision planning. As feed accounts for a large portion of the final cost of animal production,

growers have to deal with specific feeding programs to maximize the feed profitability. Thus, in the

case of pork, feed accounts for between 50% and 70% of the total cost of production (Rocadem-

bosch et al., 2016). These specific feeding programs lead farmers to schedule precise feed deliveries

with appropriate formulas. Setting service level targets are pure guesswork without inventory op-

timization, as we agree on the service level as the probability that no shortages occur between a

refilling order is placed and its delivery time.In feed manufacturing, distribution, and replenishment

planning, the benefits of good demand forecasting include the capability of reducing feed stocks,

minimize wrong or excessive orders, diminish urgent orders, reduce the safety stock and, in general,

the uncertainty in the supply chain. Furthermore, it allows feed manufacturers to secure availability

of raw materials and operate with lower capacities, service times, and production buffers. For these

reasons, as increased feed prices have had biggest impact on animal growers and feed manufacturers

margins, there is a clear ongoing need for the investment in how animal feed distribution to farms

is managed. In this context, the current study adds to a literature that is scarce with respect to

the impact of combining inventory management and routing decisions in real-life environments

(Coelho et al., 2013).

In the present work,we first propose a constructive heuristic for the multi-period inventoryrouting

problem (IRP). This heuristic allows for establishing good refill policies for each customer-period

combination, that is, those individual refill policies that minimize the total expected cost over the

periods. This cost is the aggregation of both expected inventory and routing costs. Our heuristic,

which also uses biased-randomized techniques (Grasas et al., 2017; Estrada-Moreno et al., 2019a,

2019b, 2019c), is then extended into a simheuristic algorithm (Juan et al., 2018), which allows us

to consider the inventory changes between periods generated by the random demands. Note that

the specific values of these random demands in one period might have a significant effect on the

quantities to be delivered in the next period. Therefore, they might also impact on the associated

routing plans. In addition, we also modify the former strategy by using online data on the real

demands as it becomes available. This allows us to update the refill strategy at each period, thus

generating a reactive algorithm. A range of computational experiments are carried out in order to

evaluate the potential benefits of our simulation–optimization approachfor the discovery of insights

that can then influence decisions and drive changes to the process of animal feed distribution to

farms (Fig. 1).

The remainder of this paper is structured as follows: Section 2 describes a typical agri-food

supply chain; Section 3 provides a literature review, while Sections 4 and 5 describe the problem

addressed and our solution approach; Section 6 presents the computational experiments carried

out and the obtained results; we also include a discussion in Section 7 with insights that would help

to influence current business strategies; finally, the conclusions drawn from this study and lines for

further research are summarized in Section 8.

2. Overview of the agri-food supply chain

The agricultural industry is a typical application area of innovative supply chain management

concepts such as vendor managed inventories (VMI), which are based on the collaboration among

different actors in the value chain. VMI represents a trade-off solution for suppliers and producers,

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D. Raba et al. / Intl. Trans.in Op. Res. 27 (2020) 2785–2816 2787

Fig. 1. Animal-feed delivery supply chain from mill to farm.

where cost reduction benefits both, with savings obtained from distribution and production costs

due to an accurate demand forecast, along with effortless inventory management for the customer.

Supplier has to decide then when,how much,andhow to serve a client, typically based on agreed

policies. The most used policies in practice are the order-up-to-full-capacity policy—where the

quantity delivered to the customer is that to fill its inventory capacity—or the order-to-a-maximum-

level policy—where supplier decides to deliver a specific amount to reach a given percentage of the

holding capacity. Success of VMI implementation requires sharing demand and inventory status

information with their feed suppliers, so that suppliers can take over the inventory control and

purchasing function from the farmers. There are two drawbacks of VMI: (i) traditional fattening

farms are reluctant and/or skeptical about sharing production plans with feed producers; and (ii) it

requires the solving of the associated IRP, which is an NP-hard combinatorial optimization problem

(Coelho et al., 2013).

The number of works dealing with the animal-feed business is scarce. In Hunt et al. (2003), a

business analysis was performed, with the purpose of understanding and identifying the distinct

actors involved in a supply chain. The work also discusses new strategies from the business point

of view. The whole supply chain was modeled and simulated to illustrate VMI as a new business

model. Although manufacturing and retail companies are used to VMI practices, most companies

from the agri-food sector have not even began to experiment with this concept. The main barriers

that have stopped its adoption come from the business model itself. Although in countries like Spain

the supply chain is owned and controlled by large companies, other countries use a free-market

schema—where a variety of actors are involved. The former are clearly aware of VMI benefits, and

try to optimize the full value chain. In free-market environments, where feed manufacturers could

be involved in a more competitive market with other players, more aggressive strategies are needed

to enroll key players with innovative VMI strategies.

An example of an agri-foodsupply chain can be seen in Fig. 2. A central depot delivers animal feed

to a set of farms, which are responsible for the feeding of their livestock. Traditionally, the supply

process is based on two separated decisions. Each farm places replenishment orders according to

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