an approximate dynamic programming approach

138 Pages·2015·0.62 MB·English

BLOOD PLATELET BANK INVENTORY MANAGEMENT: AN
APPROXIMATE DYNAMIC PROGRAMMING APPROACH
By
Usama S. Albdulwahab
Bachelor of System Engineering { KFUPM University, Dhahran, Saudi Arabia, 1987
Master of Industrial Engineering { KAA University, Jeddah, Saudi Arabia, 1996
A dissertation
presented to Ryerson University in partial
ful(cid:12)llment of the requirements for the degree
of Doctor of Philosophy in the Program of
Mechanical and Industrial Engineering
Toronto, Ontario, Canada, 2015
⃝c Usama Saleh Abdulwahab 2015
AUTHOR’S DECLARATION FOR ELECTRONIC SUBMISSION OF A DISSERTATION
IherebydeclarethatIamthesoleauthorofthisdissertation. Thisisatruecopyofthedissertation,
including any required (cid:12)nal revisions, as accepted by my examiners.
I authorize Ryerson University to lend this dissertation to other institutions or individuals for the
purpose of scholarly research.
I further authorize Ryerson University to reproduce this dissertation by photocopying or by other
means, in total or in part, at the request of other institutions or individuals for the purpose of
scholarly research.
I understand that my dissertation may be made electronically available to the public.
ii
Approximate Dynamic Programming Model for Blood Platelets Inventory Problems
Doctor of Philosophy in Mechanical and Industrial Engineering (2015)
Usama Saleh Alabdulwahab
Mechanical and Industrial Engineering
Ryerson University, Toronto, Canada
Abstract
Blood platelets are precious and highly perishable; their supply and demand suffer from signi(cid:12)cant
variation. Consequently, the inventory management of platelets is an actual, contemporary prob-
lem of considerable human interest. Although many researchers have solved a plethora of inventory
models, their solutions have faced various challenges. This dissertation models some of these chal-
lenges, alongside expenses and stock levels. This dissertation is based on four key objectives: (1) to
develop a blood platelet inventory model that can represent an actual blood bank inventory, while
overcoming the problem’s curse of dimensionality; (2) to look for the best issuing policy based on
the proposed model that can serve different incoming blood platelet demands; (3) to analyze the
effect of having a new, arti(cid:12)cial blood platelet alongside the existing natural eight blood types; and
(4) to enhance the proposed model for a dual-supplied regional blood platelet bank that serves a
network of hospitals. Blood platelet inventory management model is a multi-period, multi-product
model that considers the eight natural blood types with uncertain demand, and deterministic lead
times, alongside the arti(cid:12)cial platelet and patients right to refuse it.
The study is supported by both a review of literature and a testing data provided by the
Canadian Blood Service. The (cid:12)ndings show that modeling blood platelet inventory management,
including the eight blood types and their ages, represents the actual-life model without any need
for downsizing. It also leads to signi(cid:12)cantly reductions in shortages and outdates while increasing
reward gained and maintaining minimal inventory levels. Compared to a single supply model, the
dual supply model give less shortage and outdate rates. The regional blood bank inventory model
considers the fact that patients have the right to refuse transfusion using arti(cid:12)cial blood platelets.
Finally, if the percentage of arti(cid:12)cial supply in the inventory is more than 30% and the rate of
patient acceptance is more than 30%, then both outdate and shortage percentages are below 1%.
iii
Acknowledgements
Working as a PhD student at Ryerson University was a challenging and enthusiastic journey. Dur-
ing my PhD journey I met many brilliant and inspiring people who supported, encouraged and
in(cid:13)uenced me to reach my goals. I would like to thank those who helped me and made this part of
my life a pleasant and a rich experience for me.
First, I am grateful to Dr. Mohammed Wahab Mohammed Ismail for enthusiastically supporting
my work, sharing his knowledge, and guiding me throughout the program.
I am also thankful to the program director Dr. A. Ghasempoor for providing support, as well as
to the members of my internal defense committee; Dr. C. Searcy and Dr. L. Fang, for providing
valuable input to my research. I also thank the Ryerson MIE administrative staff for their valuable
assistance.
In addition, my gratitude goes to Maha Farsi, my better half, for wholeheartedly supporting me in
this endeavor. Special acknowledgments go to my brothers Dr. Sami and Dr. Ahmed, who were
catalysts to my completion of this program.
iv
Dedicated to the most wonderful people in my life:
Mom and Dad
Saleh Alabdulwahab
Fatima Mokhtar
v
Table of Contents
Author’s Declaration ii
Abstract iii
Acknowledgment iv
Table of Contents ix
List of Tables x
List of Figures xii
Nomenclature xiv
List of Acronyms xvi
Glossary of Terms xvii
1 INTRODUCTION 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Blood Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Blood Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Blood Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 Blood Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.4 Blood Donation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.5 Blood Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.6 Blood Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.7 Blood Transfusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.8 Crossmatching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
vi
1.5 Expected Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.7 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 LITERATURE REVIEW 12
2.1 Literature Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Blood Platelet Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Markov Chain Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Time Series Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Dynamic Programming (DP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Approximate Dynamic Programming (ADP) . . . . . . . . . . . . . . . . . . . . . . 17
2.8 Comparison between DP and ADP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.9 Arti(cid:12)cial Blood Platelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.10 Blood Bank Issuance and Replenishment Policies . . . . . . . . . . . . . . . . . . . . 21
2.11 Inventory Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.12 Newsvendor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.13 Inventory Models with Dual Supply Sources . . . . . . . . . . . . . . . . . . . . . . . 24
2.14 Inventory Network Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.15 Factors Affecting Blood Platelet Banks . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.15.1 Platelet Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.15.2 Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.15.3 Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.15.4 Shortage of Platelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.15.5 Outdating of Platelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.15.6 Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.16 Literature Summary and Research Gaps . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.17 Research Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.17.1 Developing an Inventory Model of a Typical Blood Platelet Bank Using Ap-
proximate Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . 33
2.17.2 Looking for the Best Issuing Policy for Different Incoming Blood Platelet
Demands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.17.3 AnalyzingtheEffectofHavinganAdditionalNew,Arti(cid:12)cial,UniversalPlatelet
alongside the Existing Natural Platelet Types . . . . . . . . . . . . . . . . . . 36
2.17.4 Developing a Network of One Regional Blood Bank and Different Hospitals . 37
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3 DATA ANALYSIS 39
3.1 Data Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Demand Stations Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 APPROXIMATE DYNAMIC PROGRAMMING MODELING FOR A TYPI-
CAL BLOOD PLATELET BANK 45
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.1 Linear Programming Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.2 Reward Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2.3 Approximate Dynamic Programming Model . . . . . . . . . . . . . . . . . . . 51
4.3 Algorithm Fine-tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3.1 Step-size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.2 Flow Limits of the Parallel Arcs . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.3 Optimal Policy Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.4 Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5 HOSPITAL BLOOD PLATELET INVENTORY CONTROL POLICIES 68
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2 Proposed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.4 Issuance Policies Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6 DUALSUPPLYSOURCEBLOODPLATELETBANKINVENTORYMODEL 78
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2 Problem De(cid:12)nition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.3.1 Linear Programming Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.3.2 ADP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3.3 Issuance Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
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6.4.1 Single or Dual Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.4.2 Arti(cid:12)cial Blood Platelet Percentage Variations . . . . . . . . . . . . . . . . . 85
6.4.3 Average Inventory Level and Age . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7 REGIONAL BLOOD BANK NETWORK MODEL WITH DUAL SUPPLY
SOURCE 91
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.3.1 Linear Programming Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.3.2 ADP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.4.1 Serving Demand Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.4.2 Average Inventory Level and Age . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.4.3 Arti(cid:12)cial Blood Platelet Percentages Variation . . . . . . . . . . . . . . . . . 98
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8 CONCLUSION AND FUTURE RESEARCH 103
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
8.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.5 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Bibliography 108
ix
List of Tables
1.1 Blood type percentage distributions in different countries . . . . . . . . . . . . . . . 5
1.2 Blood platelet substitution relationships (American Blood Organization 2013) . . . . 8
2.1 OutdatedcomponentsinCanada, asapercentageofthetotaloftransfusionplatelets
in 2011 (Canadian Blood Services 2012) . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 Sample raw CBS data for 2009-2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Kolmogorov test of the blood platelet bank data . . . . . . . . . . . . . . . . . . . . 41
3.3 Weekly demand data summary and (cid:12)tting distribution . . . . . . . . . . . . . . . . . 42
3.4 Weekly demand data summary and (cid:12)tting distribution for every station . . . . . . . 42
3.5 Sample blood platelet data issued, ordered by date and city . . . . . . . . . . . . . . 42
3.6 Blood platelet data issued, ordered by city and by day of week . . . . . . . . . . . . 43
3.7 Blood bank shipment distribution in Ontario . . . . . . . . . . . . . . . . . . . . . . 44
3.8 Blood type issue distribution percentages in Ontario . . . . . . . . . . . . . . . . . . 44
4.1 Blood type percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Set of rewards for different demand types . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Circular policy reward function for blood type AB+ . . . . . . . . . . . . . . . . . . 58
4.4 Comparison of the three policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5 Blood type inventories and policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1 CRF policy reward function for blood type AB+ . . . . . . . . . . . . . . . . . . . . 70
5.2 CRFR policy reward function for blood type O{ . . . . . . . . . . . . . . . . . . . . 71
5.3 CRFR policy reward function for blood type O+ . . . . . . . . . . . . . . . . . . . . 71
5.4 CRN policy reward function for blood type AB+ . . . . . . . . . . . . . . . . . . . . 71
5.5 FIFO policy reward function for blood type O{ . . . . . . . . . . . . . . . . . . . . . 72
5.6 Comparison between the four policies . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.7 Inventory levels median for CRFR policy . . . . . . . . . . . . . . . . . . . . . . . . 75
x