Production Planning and Inventory Control in Pharmaceutical

Production Planning and Inventory Control in Pharmaceutical Manufacturing Process
By Dan Bu
A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in
Engineering – Industrial Engineering and Operations Research in the
Graduate Division of the
University of California, Berkeley
Committee in charge: Professor Philip M Kaminsky, Chair
Professor Ilan Adler Assistant Professor Allan M Sly
Fall 2015

Abstract
Production Planning and Inventory Control in Pharmaceutical Manufacturing Process
by
Dan Bu
Doctor of Philosophy in Industrial Engineering and Operations Research
University of California, Berkeley
Professor Philip M Kaminsky, Chair
Motivated by a specific type of semi-batch biotechnology manufacturing, perfusion, we develop insights into biopharmaceutical production planning and inventory control in two areas. First, at the production site, we consider a continuous time infinite horizon lot-sizing model where a single product is manufactured on a single machine. Each time manufacturing restarts, a random production rate is realized, and production continues at this rate until the machine is shut down. Although the rate is random and chosen from an arbitrary set of random rates, it is known as soon as production starts, so this information could be used to determine when to stop production. Based on the production planning models, we show that given the objective of minimizing either average cost per unit time or total discounted cost, it is optimal to produce up to the same inventory level regardless of the realized production rate; even when backorder allowed, it is optimal to keep the same maximum backorder position. We also develop heuristics for the multi-product version of this production model. Next, for two-stage manufacturing supply chains, we extend this model to consider a specific characteristic of biopharmaceutical inventory planning – both intermediates and finished goods expire, but the expiration “clock” is restarted at each stage. We propose a two-stage production-inventory integrated model for this setting and develop two heuristics for this model – fixed size and fixed ratio shipment policies.
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Contents

1 Introduction

1

2 Literature Review

4

2.1 Supply Chain Operations in Biotech Industry . . . . . . . . . . . . . . 4

2.2 Production Planning & Inventory Control Models . . . . . . . . . . . . 6

2.2.1 Economic Lot Scheduling . . . . . . . . . . . . . . . . . . . . . . 6

2.2.2 Production Models with Random Yield . . . . . . . . . . . . . . 7

2.2.3 Integrated Production-Inventory Models . . . . . . . . . . . . . 9

2.2.4 Perishable Inventory Models . . . . . . . . . . . . . . . . . . . . 13

2.3 Solution Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.1 Dynamic Programming in Markov Decision Process . . . . . . . 15

2.3.2 Block Coordinate Descent . . . . . . . . . . . . . . . . . . . . . 17

2.3.3 Fractional Programming . . . . . . . . . . . . . . . . . . . . . . 18

2.3.4 Quadratically Constrained Quadratic Ratio Problems . . . . . . 20

2.3.5 Semidefinite Relaxation . . . . . . . . . . . . . . . . . . . . . . 21

2.3.6 Harmony Search . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Production Planning Models under Perfusion Process

25

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 The Single-Product Model . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Minimizing Average Cost . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.1 No Backorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.2 Some production rates smaller than the demand D . . . . . . . 30

3.3.3 Backorder Allowed . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4 Discounted Infinite Horizon . . . . . . . . . . . . . . . . . . . . . . . . 39

3.4.1 No Backorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4.2 Backorder Allowed . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.5 Markov Decision Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.5.1 Computational Examples . . . . . . . . . . . . . . . . . . . . . . 47

3.6 Multiple Products Model . . . . . . . . . . . . . . . . . . . . . . . . . . 52

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3.6.1 Adapted Common Cycle Approach (ACC) . . . . . . . . . . . . 53 3.6.2 Adapted Basic Period Approach (ABP) . . . . . . . . . . . . . . 53 3.6.3 Produce-up-to the Same Level . . . . . . . . . . . . . . . . . . . 54 3.6.4 Computational Experiments . . . . . . . . . . . . . . . . . . . . 59

4 Perfusion Production and Multi-stage Perishable Inventory Integrated

Models

63

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.2 Model Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.3 Fixed Size Shipment / Non-perishable Inventory at the Vendor . . . . . 66

4.3.1 Feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.3.2 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.3.3 Solution Procedure: Block Coordinate Descent . . . . . . . . . . 72

4.4 Fixed Ratio Shipment Policy / Non-perishable Inventory at the Vendor 79

4.4.1 Feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.4.2 Solution Procedure: Block Coordinate Descent . . . . . . . . . . 81

4.5 Fixed Size Shipment / Perishable Inventory at the Vendor . . . . . . . 82

4.6 Numerical Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5 Concluding Remarks and Future Work

94

Appendix A

103

A.1 Proof of Theorem 3.3 (Section 3.3.2) . . . . . . . . . . . . . . . . . . . 103

A.2 Theorems for Section 3.4.2 . . . . . . . . . . . . . . . . . . . . . . . . . 105

Appendix B

108

B.1 Feasibility of the FIT Class of Heuristics . . . . . . . . . . . . . . . . . 108

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List of Figures
2.1 EOQ policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 EPQ policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 General shipping strategy introduced by Hoque (2011a) . . . . . . . . 11
3.1 Sample inventory levels for optimal policies with J = ∅ (on the left) and J = ∅ (on the right). A circle at the zero inventory level means using rates µi, i = 1, . . . , L, a square at the maximum inventory level means using a subset of rates less than D. . . . . . . . . . . . . . . . . . . . . 34
3.2 Generic perfusion production process. Three possible production batches with stochastic production rates are presented. . . . . . . . . . . . . . . 45
3.3 Discretized perfusion production process . . . . . . . . . . . . . . . . . 46 3.4 K = 20, D = 2, c = 1, λ = 0.9 . . . . . . . . . . . . . . . . . . . . . . . 49 3.5 K = 100, d = 2, c = 1, λ = 0.9 . . . . . . . . . . . . . . . . . . . . . . . 50 3.6 K = 20, d = 2, c = 5, λ = 0.9 . . . . . . . . . . . . . . . . . . . . . . . 51 3.7 K = 20, d = 5, c = 1, λ = 0.9 . . . . . . . . . . . . . . . . . . . . . . . 51 3.8 Sample production schedule of ACC and FIT . . . . . . . . . . . . . . 57 3.9 Sample production schedule of ABP-H and FIT . . . . . . . . . . . . . 58
4.1 General shipping strategy introduced by Hoque (2011a) . . . . . . . . 65 4.2 Equal-sized batch shipment with l = 0, n = 4 . . . . . . . . . . . . . . 67 4.3 Equal-sized Batch shipment with l = 0, n = 4 . . . . . . . . . . . . . . 68 4.4 Inventory lifetime after m − 1th shipment . . . . . . . . . . . . . . . . 70 4.5 Fixed Ratio Batch Shipment, n = 3 in this example . . . . . . . . . . . 80 4.6 Production policy for nd = 1 . . . . . . . . . . . . . . . . . . . . . . . . 83 4.7 Production policy for nd = 1 . . . . . . . . . . . . . . . . . . . . . . . . 85 4.8 Objectives under different policies when varying K1. LB denotes the
solution from the relaxed problem (n ∈ RL) with FS and FR policies respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.9 Objectives under different policies when varying h1 . . . . . . . . . . . 92 4.10 Objectives under different policies when varying µ3 . . . . . . . . . . . 93 4.11 Objectives under different policies when varying p2 . . . . . . . . . . . 93
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A.1 Sample possible cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 A.2 Sample path starting with zero inventory . . . . . . . . . . . . . . . . . 105 B.1 An example of R2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
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List of Tables
3.1 Probability Distributions gτt . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2 Overall Performance of ACC, ABP-H and FIT . . . . . . . . . . . . . . 60 3.3 Statistics of η value under various fixed cost . . . . . . . . . . . . . . . 60 3.4 Statistics of η value under various holding costs . . . . . . . . . . . . . 60 3.5 Statistics of η under various production rates . . . . . . . . . . . . . . . 61 3.6 Statistics of η under various B values . . . . . . . . . . . . . . . . . . . 62 4.1 Results of fixed size (FS) and fixed ratio (FR) policy. Note that every
iteration starts with an initialized vector n = (1, 1, · · ·) . . . . . . . . . 87 4.2 Lower bounds of fixed size (FS) and fixed ratio (FR) policy . . . . . . . 88 4.3 Harmony search in the FS policy . . . . . . . . . . . . . . . . . . . . . 89 4.4 Harmony search in FR policy . . . . . . . . . . . . . . . . . . . . . . . 90
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Acknowledgements I would never have been able to finish my dissertation without the guidance from my advisor, committee members, help from friends, and support from my family. Foremost, I would like to express my deepest gratitude to my advisor Professor Phil Kaminsky, without whom I can not finish my research and Ph.D. thesis. He is the one of the smartest, nicest people I know at UC Berkeley. He has always been supportive and available to advise me in the past five years. I’m very grateful for his patience, encouragement, valuable advice and scholarly inputs. I would like to thank my co-author, Professor Ilan Adler, who has been a truly dedicated mentor. His thoughtful insights and profound expertise have provided tremendous help in our research. I would also like to thank professor Allan Sly, for serving as my committee members. I would like to thank my friends at Cal: my roommate Kelly and Xunxun, their accompany have been keeping me warm and giving me courage and persistence to finish my Ph.D. study. LZ, who have taught me a lot on friendship and have made a significant impact on my life in the US. My loved one, Steven, who has been unconditionally supporting me both mentally and physically. Special mention goes to Chuandao, Guming, Stewart, Connie, Ying, for their great support. I would like to thank my family, dad, mom and younger brother. They have always been the source of motivation throughout my graduate study. I would like to thank myself for getting through all those difficult times.
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Chapter 1
Introduction
Over the past several years, the CELDi Biopharmaceutical Operations Initiative at UC Berkeley has worked with a variety of biopharmaceutical firms to optimize production planning and supply chain management. Production and supply chain operations in the biopharmaceutical industry feature a variety of characteristics that make production and inventory planning challenging. For instance,
• Bulk production has significant economies of scale, and capacity is shared, leading to campaign-style production.
• Bulk production is either in batches, with significant levels of random yield, or semi-continuous (known as a perfusion process), with random production rates (although rates are known soon after production starts).
• There is significant region-specific differentiation between bulk production and finished goods production (filling/finishing/labeling).
• There is an expiration period for bulk drugs, and a new, non-cumulative expiration period for finished drugs.
• In some cases, bulk production batches must be entirely differentiated (that is, processed into finished goods for specific markets), even if it would be more efficient to partially differentiate them.
• Quality analysis can take significantly more time than production, with a very high variability in the required amount of time.
• In many cases, some but not all production steps are outsourced, so: – Utilization of this outsourced capacity must be “scheduled” in advance.
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