Strategic and Tactical Urban Farm Design

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Strategic and Tactical Urban Farm Design

Nicolas Brulard, Van-Dat Cung, Nicolas Catusse

To cite this version:

Nicolas Brulard, Van-Dat Cung, Nicolas Catusse. Strategic and Tactical Urban Farm Design. FSD5 5th International Symposium for Farming Systems Design, Sep 2015, Montpellier, France. �hal- 01240450�

Graphical representation of the results

STRATEGIC AND TACTICAL URBAN FARM DESIGN

1 Univ. Grenoble Alpes, G-SCOP, F-38000 Grenoble, France CNRS, G-SCOP, F-38000 Grenoble, France

2 Jardins de Gally, 78870 Bailly, France

nicolas.brulard@grenoble-inp.org

Nicolas Brulard ^1,2 , Van-Dat Cung ¹ , Nicolas Catusse ¹

• Model to support decision in creating new urban farms and adapting existing peri-urban farms with viable business models

• Multi-techniques, multi-products and multi-clients systems producing perishable products on limited surfaces with expensive labor cost

• Considering fresh products perishability requires to include tactical scheduling decisions in our strategic sizing problem

Context and problem description

Data instances & computation times MILP model structure

Prospects

• Short-time perishability (some days)

• Response to daily demands/prices

 On-plot and cold room limited storages, loss functions, price reduction

Considering products perishability

Different management practices can be needed to match these demands

in fresh products

Objective :

Preprocessing and optimization

Sales

Amortization Tasks cost Labor cost

• 5 to 9 sets of management practices, 1 or 2 products, 4 to 9 plots max, 1 or 2 clients.

• Optimal solution reached in 8 to 1100s (Cplex 12.6, Intel Core i7- 4600U 2.10GHz proc, 8.0 Go of RAM).

Model tested on real farm data (lettuce, strawberry and tomato farm)

 New formulation of lot sizing constraints and better optimization algorithms to speed up resolution

 Integration of multi-year strategic sizing, robust solutions.

-1j << >> 3j 0 0 0

MP1 MP2 MP3 MP4 MP5 MP6 MP7 MP8 MP9

Total area affectation

0 m² 0 m² 0 m²

3000 m²

511 m² _{161 m²}

0 m²

1059 m²

667 m²

0 1000 2000 3000 4000

Surface (m²)

Production of each set of management practices

Cumulated production and stocks

Required labor

Demand _𝑐,𝑝 ∆_{𝑐,𝑝,𝑑}

On-plot stocks and picked quantities

Product 1 cold stock (Sets of MP 1 to 5)

Product 2 cold stock (Sets of MP 6 to 9)

𝑥𝐷𝐶_{𝑐,𝑝,𝑑}^𝜃,𝛽 𝑥𝐷𝐶𝐿^𝜃,𝛽_{𝑐,𝑝,𝑑}

𝑥𝐶𝐿^𝜃,𝛽_𝑝,𝑑 𝑥𝐶_𝑝,𝑑^𝜃,𝛽

Hired labor 𝐿𝑇_𝑑

Tasks time Picking time 𝐿𝑇𝑥𝑃_𝑖,𝑑^𝜃

Monitoring time

max 𝑅 =

𝑝,𝜃,𝛽,𝑑

𝑥𝐷𝐶

_{𝑐,𝑝,𝑑}^𝜃,𝛽

∗ 𝑃𝑅

_{𝑐,𝑝,𝑑}

∗ (1 − 𝜔

_𝑖,𝑝^𝜃,𝛽

)

−

𝑖

(𝐴𝑚𝑜𝑓

_𝑖

+ 𝑎

_𝑖

∗ 𝐴𝑚𝑜𝑣

_𝑖

) −

𝑖,𝑡

𝐴

_𝑖

∗ 𝐶

_𝑖^𝑡

−

𝑑

𝐿𝑇

_𝐷

∗ 𝐶𝐿𝑇 +

𝑑

𝐶𝐿𝑇

^±

∗ (𝐿𝑇

_𝑑⁺

+ 𝐿𝑇

_𝑑⁻

)

Production curve 𝑌_𝑖,𝑑

+ 2-period shift

- 2-period shift Av. on-plot stock 𝑥_𝑖,𝑑^𝜃

Picked quantities 𝑥𝑃_𝑖,𝑑^𝜃 MP1

MP2 MP3 MP4

MP5

MP6

MP7 MP8

MP9 PARAMETERS

VARIABLES

PREPROCESSING

OPTIMIZATION

Set of management practices i

𝑌

_𝑖,𝑑

0 25 50

1 2 3 4 5 6 7 8 9 10

0 25 50

1 2 3 4 5 6 7 8 9 10

0 25 50

1 2 3 4 5 6 7 8 9 10

0 25 50

1 2 3 4 5 6 7 8 9 10

0 1

ta1ta2

0 1

ta1ta2

0 1

ta1ta2

0 1

ta1ta2

0 1

ta1ta2 0 0.5 1

1 2 3 4 5 6 7 8 9 10

𝑌

_𝑖,𝑑

ta1 ta2

𝐴𝑃

_𝑖,𝑑 ^,𝑡

𝐷

_𝑖^𝑡

𝐷𝐷

_𝑖^𝑡

(kg/m²) Production curve

(periods) Tasks starting date

(periods) Tasks starting date

(kg/m²) Shifted prod curve

(periods) Shifted task avail.

Unauthorized shift, starting date lower than .𝐷𝑎 ^𝑖

𝑎

_,𝑑 ^,𝑡

𝑎

_,𝑑 ^,𝑡

𝑎

_,𝑑 ^,𝑡

𝑎

_,𝑑 ^,𝑡

𝑎

_,𝑑 ^,𝑡

(m²)

𝐴

_𝑖

= 𝑎

_𝑖

=

_𝑖,𝑑 ^,𝑡

,𝑑

𝑥

_𝑖,𝑑^𝜃

𝑥 _, 𝑥 _, 𝑥 _,

∆

_{𝑐,𝑝,𝑑}

0 2 4 6 8 10

1 2 3 4 5 6 7 8 9 10

𝐿𝑇_𝑑 = 𝐿𝑇𝑥𝐷𝐶_𝑝,𝑑^𝜃,𝛽

𝑝,𝜃,𝛽 + 𝐿𝑇𝑥𝑃_𝑖,𝑑^𝜃

𝑖,𝜃 + 𝐿𝑇 _𝑖,𝑑

𝑖 (m²/period)

Av. production (kg)

𝑥𝑃

_𝑖,𝑑^𝜃

Picked quantity (kg)

𝑥𝐶

_𝑝,𝑑^𝜃,𝛽

Avail. cold room stock (kg)

𝑥𝐷𝐶

_{𝑐,𝑝,𝑑}^𝜃,𝛽

Delivered quantity (kg)

Sets / products matrix

𝐿𝑇

_𝑑

Hired labor time (h/period)

Demand

Other sets of MPs picked quantities 𝑝,𝑖

𝑌

_𝑖,𝑑