# Sustainable Scheduling of Material Handling Activities in Labor-Intensive Warehouses: A Decision and Control Model

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## Abstract

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_{2}emissions derive from logistical supply chains. The considerable amount of energy required for heating, cooling, and lighting as well as material handling equipment (MHE) in warehouses represents about 20% of the overall logistical costs. The reduction of warehouses’ energy consumption would thus lead to a significant benefit from an environmental point of view. In this context, sustainable strategies allowing the minimization of the cost of energy consumption due to MHE represent a new challenge in warehouse management. Consistent with this purpose, a two-step optimization model based on integer programming is developed in this paper to automatically identify an optimal schedule of the material handling activities of electric mobile MHEs (MMHEs) (i.e., forklifts) in labor-intensive warehouses from profit and sustainability perspectives. The resulting scheduling aims at minimizing the total cost, which is the sum of the penalty cost related to the makespan of the material handling activities and the total electricity cost of charging batteries. The approach ensures that jobs are executed in accordance with priority queuing and that the completion time of battery recharging is minimized. Realistic numerical experiments are conducted to evaluate the effects of integrating the scheduling of electric loads into the scheduling of material handling operations. The obtained results show the effectiveness of the model in identifying the optimal battery-charging schedule for a fleet of electric MMHEs from economic and environmental perspectives simultaneously.

## 1. Introduction

_{2}emissions derive from logistical supply chains [1]. Around 11% of the total greenhouse gas (GHG) emissions generated by the logistics sector across the world are caused by warehousing activities [2]. In recent years, an increasing number of companies have been paying more attention to the environmental and economic impacts of warehouse management. In a recent study, Bartolini et al. introduced the term “green warehousing” (GW) to denote a managerial concept integrating and implementing environmentally friendly operations with the objective of minimizing the energy consumption, energy cost, and GHG emissions of a warehouse [3]. The development of GW approaches is also favored by the decreasing costs of smart devices [4], the large availability of distributed sensors [5] and data analytics tools [6], and, in general, advances of information and communication technologies (ICTs) [7]. The results of recent market surveys show that a sustainable approach to warehouse management allows brand fidelity and stakeholder satisfaction to be increased, as well as improving the ability of companies to quickly and flexibly respond to market changes [8]. Consistent with this approach, the introduction of innovative methodologies aimed at maximizing logistical performance and minimizing resource consumption represents a new challenge for scientific research. Indeed, a sustainable approach allows economic, environmental, and social benefits to be brought to logistical supply chains and represents the new key driver for increasing companies’ competitiveness. Although many studies have been conducted in the area of green logistics, most of them have focused on transport links, while the increasing use of energy resources due to warehouse management is currently a less explored research theme (Figure 1). However, the reckless use of fossil fuels for transportation has a great impact in terms of logistics’ sustainability [9], and the worldwide increase of electrical energy consumption cannot be neglected. According to the International Energy Outlook 2019 [10], in the last ten years, the average worldwide electric energy consumption increased by 16%, while in the industrial sector, an increase of around 25% was observed. In the next thirty years, forecasts predict an increase of electric consumption in the industrial sector of around 47% (Figure 2) [10]. The observed trend highlights a growing need for electric power. Consistent with this consideration, energy-intensive logistical activities require more attention.

- Electric consumption due to direct movements of products or materials both by fixed material handling equipment (FMHE) (such as conveyor systems and automated cranes) and mobile material handling equipment (MMHE) (such as forklift, trucks, etc.);
- electric consumption due to warehouse facilities like heating, lighting, and air conditioning of the building as well as power supplies of computer systems, office equipment, and miscellaneous equipment such as catering appliances.

- Increasing adoption of automated warehouses equipped with electric shuttles, stacker cranes, robots, etc.;
- increasing number of electric forklifts replacing forklifts powered by internal combustion engines thanks to their lower operational and maintenance costs. According to the World Industrial Truck Statistics, the percentage of electric forklifts in the world is over 60% of overall forklifts, and it is very interesting that this trend has grown more than 5% in only five years, from 2014 to 2018 (Figure 3). In the same period, the yearly sales of electric forklifts in Europe have grown by around 40%, and the same trend was observed in other continents (Figure 4).

- Is it possible to adopt DSM to reduce the economic and environmental impacts of electric MMHE recharging?
- Is there an optimal scheduling strategy allowing the minimization of the cost due to electric MMHE recharging while facing sustainability requirements?

## 2. Literature Review

## 3. System Modeling and Problem Formulation

#### 3.1. Problem Statement

#### 3.2. Assumptions

- Each job is composed by an uninterruptible and ordered sequence of picking operations.
- Jobs are executed in accordance with a priority queuing. This is one of the dispatching rules that is commonly used in in the material handling scheduling [44].
- Each forklift can process only one job at a time. The related processing time is known and independent from forklift and job execution order. This is a classical assumption made in the material handling scheduling [44].
- The processing time of each job is less than the fully charged battery capacity. This assumption can be removed by allowing the replacement of batteries within the execution of activities that require a long time.
- Battery usage on each forklift is zero during idling times. This assumption is motivated by the fact the battery leakage constant time is much larger than idling times between consecutive activities [45].
- All jobs are completed within the considered planning horizon. This assumption is straightforwardly verified by suitably setting the value of the planning horizon.
- There are no overlapping constraints between forklifts performing different jobs. This assumption is obviously derived by the independence of activities.
- Change of battery is done in a neglectable time on any forklift. This assumption can be removed by introducing the battery replacement as an activity with non-zero duration.
- Battery charging is an interruptible load and is performed with a fixed energy rate, i.e., we assume a linear recharge of vehicle batteries as in [13].
- The pricing of energy bought from the power grid is variable during the planning window but known ahead of time. This is a classical assumption in the field of DSM [14].

#### 3.3. Indices and Sets

$\mathcal{B}$ | set of levels of battery capacity |

$i$ | index of places in job sequences ($i\in \mathcal{J}$) |

$\mathcal{J}$ | set of places in the job sequence addressed by forklifts $\left\{1,\dots ,i,\dots ,K\right\}$ |

$k$ | identifier of jobs ($k\in \mathcal{K}$) |

$\mathcal{K}$ | set of jobs $\left\{1,\dots ,k,\dots ,K\right\}$ |

m | identifier of forklifts ($m\in \mathcal{M}$) |

$\mathcal{M}$ | set of forklifts $\left\{1,\dots ,m,\dots ,M\right\}$ |

$n$ | identifier of battery charging stations ($n\in \mathcal{N}$) |

$\mathcal{N}$ | set of charging stations $\left\{1,\dots ,n,\dots ,N\right\}$ |

$t$ | index of time slots ($t\in \mathcal{T}$) |

$\mathcal{T}$ | planning horizon $\left\{1,\dots ,t,\dots T\right\}$. |

#### 3.4. Parameters

${a}_{nt}$ | 1 if charging station $n$ is available at time $t$; 0 otherwise |

${b}_{min}$ | minimum battery capacity |

${b}_{max}$ | fully charged battery capacity |

${b}_{0}^{m}$ | capacity of the battery in forklift $m$ at the beginning of the planning horizon |

${b}_{f}^{m}$ | capacity of the battery on forklift $m$ at the end of final setup |

${c}_{0}^{m}$ | setup completion time of forklift $m$ |

${e}_{t}$ | energy unitary cost at time slot $t$ |

$K$ | number of jobs |

${l}_{k}$ | processing duration of job $k$ |

$L$ | a large number |

$M$ | number of electric forklift |

$N$ | number of charging stations |

${p}_{k}$ | processing priority of job $k$ |

${q}_{m}$ | penalty unitary cost related to the job makespan |

${q}_{p}$ | penalty unitary cost related to the job ordering |

${q}_{r}$ | penalty unitary cost related to the battery recharging completion time |

$T$ | number of time slots |

$\u03f5$ | amount of energy required to charge one battery in one time slot |

${\mu}^{I}$ | weighting factor of the makespan penalty term in the objective function of the first-step optimization |

${\mu}^{II}$ | weighting factor of the job ordering penalty term in the objective function of the first-step optimization |

${\pi}^{I}$ | weighting factor of the makespan penalty term in the objective function of the second-step optimization |

${\pi}^{II}$ | weighting factor of the recharging completion time penalty term in the objective function of the second-step optimization |

${\pi}^{III}$ | weighting factor of the energy cost term in the objective function of the second-step optimization. |

#### 3.5. Decision Variables

${b}_{i}^{m}$ | capacity of battery on forklift $m\in \mathcal{M}$ at the beginning of activity $i\in \left[1,{I}_{m}+1\right]$ taking into account the potential battery replacement |

${c}_{max}$ | maximum completion time over all the jobs (makespan) |

${c}_{max,id}$ | maximum completion time over all the jobs and forklifts (makespan), assuming that battery capacity is infinite |

${c}_{i}^{m}$ | completion time of job $i\in \left[1,{I}_{m}\right]$ on forklift $m\in \mathcal{M}$ |

${c}_{max,id}^{m}$ | maximum completion time of forklift $m\in \mathcal{M}$, assuming that battery capacity is infinite |

${d}_{i}^{m}$ | idling time before processing job $i\in \left[1,{I}_{m}\right]$ on forklift $m\in \mathcal{M}$ |

$EC$ | energy cost for the overall charging of forklift batteries over the planning horizon |

${E}_{t}$ | energy for charging batteries of forklifts at time slot $t$ |

${I}_{m}$ | number of jobs allocated to forklift $m$ |

${j}_{i}^{m}$ | identifier of the $i$-th activity—including jobs (${j}_{i}^{m}\in \mathcal{K}$), forklift initial setup (${j}_{i}^{m}=0$), and final setup (${j}_{i}^{m}={I}_{m}+1$)—related to the $m$-th forklift |

$MC$ | penalty cost related to makespan |

$PC$ | penalty cost related to job ordering |

$RC$ | penalty cost related to overall completion times of battery recharging processes |

${r}_{i}^{m}$ | completion time of recharging process related to the battery replaced at the beginning of activity $i\in \left[1,{I}_{m}+1\right]$ on forklift $m\in \mathcal{M}$ |

${r}_{max}^{n}$ | overall completion time of recharging processes related to charging station $n\in \mathcal{N}$ |

${s}_{i}^{m}$ | starting time of activity $i\in \left[1,{I}_{m}+1\right]$ on forklift $m\in \mathcal{M}$ |

${x}_{ik}^{m}$ | 1 if job $k$ is the $i$-th activity executed by forklift $m$; 0 otherwise |

${z}_{i}^{mn}$ | 1 if forklift $m\in \mathcal{M}$ replaces its battery with a fully-charged one at the beginning of activity $i\in \left[1,{I}_{m}+1\right]$ at charging station $n\in \mathcal{N}$; 0 otherwise |

${\beta}_{i}^{m}$ | capacity of battery on forklift $m\in \mathcal{M}$ at the beginning of activity $i\in \left[1,{I}_{m}+1\right]$ |

${\gamma}_{i}^{mt}$ | 1 if $t$ is the completion time of the recharging window for the battery replaced at the beginning of activity $i\in \left[1,{I}_{m}+1\right]$ on forklift $m\in \mathcal{M}$; 0 otherwise |

${\delta}_{i}^{mt}$ | 1 if $t$ is within the recharging window for the battery replaced at the beginning of activity $i\in \left[1,{I}_{m}+1\right]$ on forklift $m\in \mathcal{M}$; 0 otherwise |

${\rho}_{i}^{mt}$ | 1 if the battery replaced at the beginning of activity $i\in \left[1,{I}_{m}+1\right]$ is actually recharged in time slot $t$ on forklift $m\in \mathcal{M}$; 0 otherwise |

${\sigma}_{i}^{mt}$ | 1 if $t$ is the starting time of the recharging window for the battery replaced at the beginning of activity $i\in \left[1,{I}_{m}+1\right]$ on forklift $m\in \mathcal{M}$; 0 otherwise. |

#### 3.6. Optimization Model

#### 3.6.1. First-Step Optimization

#### 3.6.2. Second-Step Optimization

## 4. Numerical Experiments

#### 4.1. Setup of Experiments

- Scenario I: We analyze in detail the optimal job scheduling, battery replacement strategies, and charging station energy scheduling when $K=15$ jobs are handled using $M=2$ forklifts and $N=3$ charging stations under two different model set-ups:
- Case I.a: With energy scheduling, i.e., ${\mu}^{I}={\mu}^{II}=$1/2 and ${\pi}^{I}={\pi}^{II}={\pi}^{III}=$1/3;
- Case I.b: Without energy scheduling, i.e., ${\mu}^{I}=1,{\mu}^{II}=0$ and ${\pi}^{I}=1,{\pi}^{II}={\pi}^{III}=$0.

- Scenario II: We compare the optimal job scheduling, battery replacement strategies, and charging station energy scheduling obtained in scenario I.a (i.e., $K=15$ jobs, $M=2$ forklifts and $N=3$ charging stations) with the results obtained under two different configurations:
- Case II.a: $M=3$ forklifts and $N=3$ charging stations;
- Case II.b: $M=3$ forklifts and $N=4$ charging stations.

- Scenario III: We analyze how the results in terms of makespan, total completion time of recharging process, and energy cost are affected by variations in the number of jobs $K$ (changed in the range 15 ÷ 30), while varying the number of forklifts $M$ (changed in the range 2 ÷ 8), and the number of charging stations $N$ (changed in the range 2 ÷ 11).

#### 4.2. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Scopus-indexed papers on sustainable logistics classified in the research topics “Transport” and “Warehouse”.

**Figure 2.**End-use worldwide energy consumption by sector, observed (until 2018) and predicted (until 2050). Source: U.S. Energy Information Administration (EIA) [10].

**Figure 12.**Scheduling of recharging operations and charging diagram of batteries on each charging station.

**Figure 15.**Contour plot of the makespan as a function of the number of forklifts and charging stations for different numbers of jobs.

**Figure 16.**Contour plot of the recharging process completion time as a function of the number of forklifts and charging stations for different numbers of jobs.

**Figure 17.**Contour plot of energy cost as a function of the number of forklifts and charging stations for different numbers of jobs.

**Figure 18.**Contour plot of the run time as a function of the number of forklifts and charging stations for different numbers of jobs.

**Table 1.**Energy consumption in warehouses by end-use category (1976–2017). Source: https://www.fem-eur.com/.

Time [year] | Energy consumed [MWh per year] | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MHE | Δ [%] | HVAC | Δ [%] | Lighting | Δ [%] | Plug Load | Δ [%] | |||||

1976 | 500 | 6300 | 1100 | 300 | ||||||||

1979 | 400 | −20 | 2850 | −55 | 2600 | +136 | 200 | −33 | ||||

1991 | 800 | +100 | 1400 | −51 | 900 | −65 | 600 | +20 | ||||

2000 | 2200 | +175 | 2600 | +86 | 1300 | +44 | 300 | −50 | ||||

2010 | 3000 | +36 | 2400 | −8 | 1000 | −23 | 350 | +17 | ||||

2017 | 3900 | +30 | +680 | 2600 | +8 | −59 | 800 | −20 | −27 | 600 | +71 | +100 |

Description | Symbol | Value |
---|---|---|

Job index | $k$ | [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] |

Job priority | ${p}_{k}$ | [ 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] |

Job processing duration | ${l}_{k}$ | [ 9, 9, 9, 6, 3, 4, 8, 1, 3, 2, 5, 2, 9, 2, 2, 1, 4, 3, 4, 4, 1, 3, 8, 4, 4, 9, 5, 1, 9, 3 ] |

Description | Symbol | Value |
---|---|---|

Setup completion time slot for each forklift | ${c}_{0}^{m}$ | [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] |

Initial state of charge of the on-board battery for each forklift | ${b}_{0}^{m}$ | [ 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 ] |

Final state of charge of the on-board battery for each forklift | ${b}_{f}^{m}$ | [ 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 ] |

Initial availability of a fully charged battery in charging stations | ${a}_{nt}$ | 1, $\forall n\in \mathcal{N}$, $\forall t\in \mathcal{T}$ |

Description | Symbol | Value |
---|---|---|

Fully charged battery capacity | ${b}_{max}$ | 10 |

Minimum battery capacity | ${b}_{min}$ | 1 |

Penalty unitary cost related to the job makespan | ${q}_{m}$ | 1 |

Penalty unitary cost related to the job ordering | ${q}_{p}$ | 1 |

Penalty unitary cost related to the battery recharging completion time | ${q}_{r}$ | 1 |

Weighting factors of the objective function terms in the first-step optimization | ${\mu}^{I}$, ${\mu}^{II}$ | 1/2, 1/2 in case I.a, scenario II and III 1, 0 in case I.b |

Weighting factors of the objective function terms in the second-step optimization | ${\pi}^{I},{\pi}^{II},{\pi}^{III}$ | 1/3, 1/3, 1/3 in case I.a, scenario II and III 1, 0, 0 in case I.b |

Case I.a | Case I.b | Case II.a | Case II.b | |
---|---|---|---|---|

Makespan: ${c}_{max}$ | 34 | 35 | 24 | 24 |

Recharging process completion time: ${r}_{max}$ | 44 | 46 | 34 | 33 |

Normalized energy cost: $EC/\left(\u03f5{\mathrm{min}}_{t}{e}_{t}\right)$ | 69 | 77 | 74 | 67 |

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## Share and Cite

**MDPI and ACS Style**

Carli, R.; Dotoli, M.; Digiesi, S.; Facchini, F.; Mossa, G.
Sustainable Scheduling of Material Handling Activities in Labor-Intensive Warehouses: A Decision and Control Model. *Sustainability* **2020**, *12*, 3111.
https://doi.org/10.3390/su12083111

**AMA Style**

Carli R, Dotoli M, Digiesi S, Facchini F, Mossa G.
Sustainable Scheduling of Material Handling Activities in Labor-Intensive Warehouses: A Decision and Control Model. *Sustainability*. 2020; 12(8):3111.
https://doi.org/10.3390/su12083111

**Chicago/Turabian Style**

Carli, Raffaele, Mariagrazia Dotoli, Salvatore Digiesi, Francesco Facchini, and Giorgio Mossa.
2020. "Sustainable Scheduling of Material Handling Activities in Labor-Intensive Warehouses: A Decision and Control Model" *Sustainability* 12, no. 8: 3111.
https://doi.org/10.3390/su12083111