Modeling Uncertain Demand in Wood Pellet Supply Chains: A Case Study from Northern Ontario By: Natalie Hughes, MScF Candidate Dr. Chander Shahi Dr. Reino Pulkki Dr. Kevin Crowe

Introduction VCO Network Theme 4: – Value Optimizing Scheduling and Control

• Operational decision-making level – Short-term scheduling/production decisions

• How to handle uncertain demand for wood pellet manufacturers • Agile model using real information • Using the case study of Industries Lacwood (ILW), a wood pellet manufacturer in Hearst, Ontario

Project Objectives 1)

Create three dynamic, user-friendly optimization models using Mathematical Programming Language (MPL®).

2)

Produce 100 demand datasets for pellets and run these through each of the three models created for objective 1. Compare the gross margin (GM) results of the three models and select the model with the best overall performance for further analysis.

3)

Generate stochastic demand schedules for pellets from the 100 demand datasets produced for objective 2. Use this stochastic demand schedule as a benchmark to illustrate how the model chosen from objective 2 is a comprehensive, operational-level DST that wood pellet producers may utilize to achieve optimal GMs under uncertain demand conditions and with other variable input factors.

Methods - Case Study • Industries Lacwood – Hearst, ON

• Normand Lacroix – Founder and owner

• Forest products company – Spruce and pine – EZ n’Organized line, core boxes

• Zero-waste policy – Make wood pellets from processing waste – Heating pellets and horse bedding pellets

Methods - Case Study • Real information about: – Overhead costs – Raw material procurement – Processing costs – Employment costs – Throughput rates – Retailer locations and historical demand data

• Wood pellet creation only in recent years • Rapid expansion of heating pellet market • Bedding pellet market still developing

Methods – Objective 1 • Three optimization models – Created in MPL® – Maximize the GM of pellet manufacturer

• Model 1: – No inventory, variable production

• Model 2: – Demand flow inventory, variable production

• Model 3: – Demand flow inventory, constant production

Objective Function • Maximize GM: Z = Max (Revenue – fixed overhead costs – pellet storage cost – residue storage cost – pellet manufacturing cost – residue transportation cost – pellet transportation cost – unfulfilled demand penalty cost)

Objective Function 2

40 12

𝑍 = 𝑀𝑎𝑥

12

𝑊𝑗𝑙𝑡 𝑅𝑗𝑙𝑡 − 𝑗 =1 𝑙=1 𝑡=1

2

12

−

2

2

𝑗 =1 𝑡=1

2

12

2

12

𝑖=1 𝑘=1 𝑡=1

2

2

12

𝑖=1 𝑘=1 𝑡=1

𝑈𝐹𝐷𝑗𝑙𝑡 𝑁𝑗𝑙𝑡 𝑗 =1 𝑙=1 𝑡=1

2

40 1

𝑉𝑖𝑘𝑡 𝐶𝑖𝑘𝑡 −

40 12

𝑊𝑗𝑙𝑡 𝐴𝑗𝑙𝑡 − 𝑗 =1 𝑙=1 𝑡=1

12

𝑈𝑖𝑘𝑡 𝐹𝑖𝑘𝑡 −

𝑌𝑗𝑡 𝐷𝑗𝑡 − 2

2

𝑍𝑗𝑡 𝐸𝑗𝑡 −

𝑗 =1 𝑡=1

40 12

2

𝑗 =1 𝑡=1

𝑈𝑖𝑘𝑡 𝐹𝑖𝑘𝑡 −

𝑉𝑖𝑘𝑡 𝐶𝑖𝑘𝑡 − 𝑘=1 𝑡=1

2

𝑖=1 𝑘=1 𝑡=1

12

𝑂𝐶𝑡 − 𝑡=1

12

𝑍𝑗𝑡 𝐸𝑗𝑡 −

2

𝑗 =1 𝑙=1 𝑡

Indices • • • • •

i = 1, 2 (Residue types) j = 1, 2 (Pellet types) k = 1, 2 (Suppliers) l = 1 to 40 (Retailers) t = 1 to 12 (One-month time periods)

Parameters o 𝑅𝑗𝑙𝑡 = Revenue from sale of pellet type j to retailer l in period t ($/tonne) o 𝑂𝐶𝑡 = Overhead costs for pellet facility in period t ($) o 𝐷𝑗𝑡 = Cost of manufacturing pellet j in period t ($/tonne) o 𝐶𝑖𝑘𝑡 = Cost of shipping residue type i, from supplier k, to pellet producer in period t ($/tonne) o 𝐴𝑗𝑙𝑡 = Cost of shipping pellet j to retailer l in period t ($/tonne) o o o o

𝐸𝑗𝑡 = Cost of storing pellet j in period t ($/tonne) 𝐹𝑖𝑘𝑡 = Cost of storing residue type i, from supplier k, in period t ($/tonne) 𝐺𝑗𝑙𝑡 = Demand for pellet type j from retailer l in period t (tonnes) 𝐻𝑖𝑘𝑡 = Supply of residue type i from supplier k in period t (tonnes)

o 𝑁𝑗𝑙𝑡 = Penalty cost for not meeting demand for pellet type j demanded by retailer l in period t ($/tonne)

Variables •

𝑋𝑖𝑗𝑡 = Amount of residue type i used for pellet type j in period t (tonnes)

• • •

𝑈𝑖𝑘𝑡 = Amount of residue type i, from supplier k, stored in period t (tonnes) 𝑉𝑖𝑘𝑡 = Amount of residue type i purchased from supplier k in period t (tonnes) 𝑌𝑗𝑡 = Amount of pellet type j produced in period t (tonnes)

•

𝑍𝑗𝑡 = Amount of pellet type j stored in period t (tonnes)

•

𝑈𝐹𝐷𝑗𝑙𝑡 = Amount of unfulfilled demand of pellet type j demanded by retailer l in period t (tonnes) 𝑊𝑗𝑙𝑡 = Amount of pellet type j sold and shipped to retailer l in period t (tonnes)

•

Constraints • Inventory – Residue and pellets

• • • • •

Pellet yield from residue Supply purchase Composition of pellet 2 Capacity Non-negativity

Model 1 • No inventory with variable production o Residue inventory must be equal to 0: 𝑈𝑖𝑘𝑡 = 0 o Pellet inventory must be equal to 0: 𝑍𝑗𝑡 = 0

Model 2 • Demand flow inventory with variable production

• Same formulation as model 1 except: o Residue inventory must be greater than or equal to 0: 𝑈𝑖𝑘𝑡 ≥ 0 o Pellet inventory must be greater than or equal to 0: 𝑍𝑗𝑡 ≥ 0

Model 3 • Demand flow inventory with constant production • Same formulation as model 1 except: o Pellet production is equal to 500 tonnes (maximum amount given supply availability): 2

𝑌𝑗𝑡 = 500 𝑗=1

o Residue inventory must be greater than or equal to 0:

𝑈𝑖𝑘𝑡 ≥ 0

o Pellet inventory must be greater than or equal to 0:

𝑍𝑗𝑡 ≥ 0

Methods – Objective 2 • Pellet 1 – Forecasting • Exponential smoothing based on historical demand data • Over 24 periods

– Demand fluctuations • Average values from 24 periods for a starting per-period demand schedule • 100 demand sets generated from these average values – Random number generation between the possible maximum and minimum values for each period’s total demand output with a 95% confidence interval

– Allocation to retailers • Average proportions calculated from the distribution of the original observed demand dataset

Methods – Objective 2 • Pellet 2 – Retailers within 20km radius of equestrian centre – Random number generation between 0 and 5 tonnes for each retailer identified • 100 datasets created

Methods – Objective 2 • Model Selection – 100 datasets run through each of the three models to determine how the GM is affected with fluctuating demand – Model with best performance based on GM results chosen for further analysis

Methods – Objective 3 • Stochastic demand schedule – Average values from 100 datasets for both pellet types – Pellet 1 demand applied to retailers based on proportional distribution

• Scenarios – 11 applied to the chosen model – Using stochastic demand set as base demand input values – Scenarios contain altered input values for: • • • •

Demand Supply Costs Revenue

– Results compared with stochastic demand set output to determine model sensitivity

Results – Objective 1 • Three optimization models created in MPL® using formulation described in methods for objective 1

Results – Objective 2

Historical demand data for ILW

Results – Objective 2

GM output comparisons from the three optimization models

Results – Objective 2 • Selected model: o Model 2 – demand flow inventory with variable production o Consistently higher GM o Less fluctuation between values

Results – Objective 3 Period

Corresponding month

Stochastic demand for pellet 1 (tonnes)

Stochastic demand for pellet 2 (tonnes)

1

Jan

359

44

2

Feb

368

55

3

Mar

296

33

4

Apr

207

56

5

May

239

49

6

Jun

278

38

7

Jul

218

43

8

Aug

376

41

9

Sep

664

61

10

Oct

493

48

11

Nov

377

54

12

Dec

327

62

Stochastic demand schedule

Results – Objective 3

(1)

Scenario

GM

Scenario factor test

Sensitivity

1

$444,035

pellet 1 demand

high

2

$404,807

pellet 2 demand

3

$362,455

residue supply decrease

high

4

$519,075

residue supply increase

high

unlimited residue supply

high until production capacity (2) reached

pellet 1 inventory, pellet 1 production, pellet 1 unfulfilled demand

low

pellet 1 inventory

5

$519,945

6

$447,384

7

$445,540

8

$405,220

9

$311,404

10

$445,354

11

$326,846

residue inventory holding costs increase pellet inventory costs increase transportation cost increase production cost increase unfulfilled demand penalty increase revenue from pellet 1 decrease

moderate low

What changed? pellet 1 inventory, pellet 1 unfulfilled demand (1) pellet 2 production pellet 1 inventory, pellet 1 production, pellet 1 unfulfilled demand pellet 1 inventory, pellet 1 production, pellet 1 unfulfilled demand

pellet 1 inventory, pellet 1 unfulfilled demand pellet 1 inventory, pellet 1 unfulfilled demand

Production decreased in tandem with the change in scenario 2 and is therefore not considered a sensitivity indicator in this case. The sensitivity to the supply increase was high until the production capacity was reached. Then, supply availability increases to the magnitude of 999,999 tonnes had no effect on the model’s output. Therefore, model 2 is considered to be insensitive to an unlimited supply of residue. (2)

Conclusions • Illustrative model – Implications of uncertain demand combined with other variable input factors

• Practical, user-friendly • Agile; easy modification – Can be applied to other manufacturers

• Further studies should be done – More scenarios – Pairing with Visual Basic® interface – Different forecasting methods

Project Significance • Optimized operational efficiency/minimized expenditures for companies • Lower retail costs for consumers • Minimized environmental impact • Case study is foundation for general, practical application to other pellet producers • Promotes ‘green energy’ in Ontario and Canada

THANK YOU!