Certainty Equivalent Planning for Multi-Product Batch Differentiation: Analysis and Bounds

51 Pages Posted: 18 Dec 2015 Last revised: 7 Jan 2016

See all articles by Hyun-Soo Ahn

Hyun-Soo Ahn

University of Michigan, Stephen M. Ross School of Business

Stefanus Jasin

University of Michigan, Stephen M. Ross School of Business

Philip Kaminsky

University of California, Berkeley - Department of Industrial Engineering & Operations Research (IEOR)

Yang Wang

University of California, Berkeley - Department of Industrial Engineering and Operations Research

Date Written: December 16, 2015

Abstract

We consider a multi-period planning problem faced by a firm that must coordinate the production and allocations of batches to end products for multiple markets. Motivated by a problem faced by a biopharmaceutical firm, we model this as a discrete-time inventory planning problem where in each period the firm must decide how many batches to produce and how to differentiate batches to meet demands for different end products. This is a challenging problem to solve optimally, so we derive a theoretical bound on the performance of a Certainty Equivalent (CE) control for this model, in which all random variables are replaced by their expected values and the corresponding deterministic optimization problem is solved. This is a variant of an approach that is widely used in practice. We show that while a CE control can perform very poorly in certain instances, a simple re-optimization of the CE control in each period can substantially improve both the theoretical and computational performance of the heuristic, and we bound the performance of this re-optimization. To address the limitations of CE control and provide guidance for heuristic design, we also derive performance bounds for two additional heuristic controls -- (1) Re-optimized Stochastic Programming (RSP), which utilizes full demand distribution but limits the adaptive nature of decision dynamics, and (2) Multi-Point Approximation (MPA), which uses limited demand information to model uncertainty but fully capture the adaptive nature of decision dynamics. We show that although RSP in general outperforms the re-optimized CE control, the improvement is limited. On the other hand, with a carefully chosen demand approximation in each period, MPA can significantly outperform RSP. This suggests that, in our setting, explicitly capturing decision dynamics adds more value than simply capturing full demand information.

Keywords: certainty equivalent, heuristics

Suggested Citation

Ahn, Hyun-Soo and Jasin, Stefanus and Kaminsky, Philip and Wang, Yang, Certainty Equivalent Planning for Multi-Product Batch Differentiation: Analysis and Bounds (December 16, 2015). Ross School of Business Paper No. 1296. Available at SSRN: https://ssrn.com/abstract=2704595 or http://dx.doi.org/10.2139/ssrn.2704595

Hyun-Soo Ahn

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan St
R5456
Ann Arbor, MI 48109-1234
United States

Stefanus Jasin (Contact Author)

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Philip Kaminsky

University of California, Berkeley - Department of Industrial Engineering & Operations Research (IEOR) ( email )

IEOR Department
4135 Etcheverry Hall
Berkeley, CA 94720
United States

Yang Wang

University of California, Berkeley - Department of Industrial Engineering and Operations Research ( email )

4141 Etcheverry Hall
Berkeley, CA 94720-1777
United States

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