Capacitated plant location - case study P1

Supply Chain Analytics in Python

Aaren Stubberfield

Supply Chain Analytics Mgr.

Context

Multiple options to meet regional product demand

Option	Pro	Con
Small manufacturing facilities within region	Low transportation costs, few to no tariffs or duties	Overall network may have excess capacity, cannot take advantage economies of scale
A few large manufacturing plants and ship product to region	Economies of scale	Higher transportation, higher tariffs and duties

Capacitated plant location model

Capacitated Plant Location Model$^{1}$
The goal is to optimize global Supply Chain network
- Meet regional demand at the lowest cost
- Determine regional production of a product

¹ Chopra, Sunil, and Peter Meindl. _Supply Chain Management: Strategy, Planning, and Operations._ Pearson Prentice-Hall, 2007.

Capacitated plant location model

Modeling

Production at regional facilities
- Two plant sizes (low / high)
Exporting production to other regions
Production facilities open / close

image of globe with regional production

Decision variables

What we can control:

$x_{ij}$ = quantity produced at location _i_ and shipped to _j_
$y_{is}$ = 1 if the plant at location _i_ of capacity _s_ is open, 0 if closed
- $s$ = low or high capacity plant

Objective function

Minimize $z = \sum_{i=1}^{n}(f_{is} y_{is}) + \sum_{i=1}^{n} \sum_{i=1}^{m} (c_{ij} x_{ij})$

$c_{ij}$ = cost of producing and shipping from plant _i_ to region _j_
$f_{is}$ = fixed cost of keeping plant _i_ of capacity _s_ open
$n$ = number of production facilities
$m$ = number of markets or regional demand points

from pulp import *

# Initialize Class
model = LpProblem("Capacitated Plant Location Model", LpMinimize)

# Define Decision Variables
loc = ['A', 'B', 'C', 'D', 'E']
size = ['Low_Cap','High_Cap']
x = LpVariable.dicts("production",[(i,j) for i in loc for j in loc], 
                      lowBound=0, upBound=None, cat='Continous')
y = LpVariable.dicts("plant",[(i,s) for s in size for i in loc], cat='Binary')

# Define objective function
model += (lpSum([fix_cost.loc[i,s]*y[(i,s)] for s in size for i in loc])
          + lpSum([var_cost.loc[i,j]*x[(i,j)] for i in loc for j in loc]))

Summary

Capacitated Plant Location Model:

Finds a balance between the number of production facilities
Model decision variables:
- Quantity of production in a region and exported
- High or low capacity facilities open or closed
Reviewed objective function
- Sums variable and fixed production costs
Reviewed code example

Review time

Supply Chain Analytics in Python