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FOUNDATIONS OF OPERATIONS MANAGEMENT Fall Quarter 2016 – Room Jacobs 561

This version: Sep 2, 2016

Changes may be made.

Instructor:

Jan A. Van Mieghem

VanMieghem@northwestern.edu

Objective: This course will introduce PhD students to academic research of operations

management. As such, we will survey a broad array of “research content” (basic models and

approaches in the literature) as well as discuss the “process of conducting research” (how to write

a paper and deliver a talk).

The course can be divided along various dimensions:

1. Theory vs Data-driven approaches

2. Insight vs decision-support objectives

3. Single vs. multi dimensional models (e.g., single product, location, decision maker,

networks)

4. Make-to-stock material systems or “inventory models” vs. make-to-order service systems

or “queuing models.”

This is not intended to be a course in either inventory theory or queuing theory. Each of these

topics is broad and deep enough to be subject of several quarter long PhD courses. Rather, our

objective will be to understand the basic models of inventory and queuing and appreciate how they

can be used as building blocks to answer more complex research questions. Our primary focus

will be on getting a sense of how to develop research questions and we will introduce tools and

techniques wherever required.

In each part, we will start with the traditional approach to operations management, which considers

a single decision maker that has the complete information and absolute control over the entire

system. The main objective of most traditional models is to come up with the optimal design or

optimal control of various operational systems. We can call this the Operations Research (OR)

approach often with the objective to support decisions.

We will then consider modifications of the basic models by incorporating multiple self-interested

agents and investigate the impact of their strategic interactions on the performance of the

operational model under consideration. The objective of these models is (mostly) to present a

parsimonious theory of observed phenomenon and (occasionally) to provide qualitative

recommendations on designing better systems by aligning incentives of the agents. We can call

this the Economics approach often with the objective to generate insight.

We will also consider situations where the research objective is not to design optimal systems or

to build parsimonious theories but rather to test the theoretical predictions using data. We will

study recent empirical research in operations management, which entails either testing the

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appropriateness of the normative models of decision-making introduced earlier or estimating the

parameters of those models. We can call this the Empirical approach.

In particular, we will cover traditional reduced-form and structural estimation models in the OM

literature. Recently, various other fields (i.e. economics, finance, and marketing) have seen an

increasing trend of using machine learning methods to extract valuable information to either testify

or as an input to existing models. Therefore, we will also briefly scratch the surface of machine

learning (data science in general), and their potential usages in OM research.

The topics covered here represent only a slice of many well-researched OM topics. A non-

exhaustive list of excluded topics includes Project Management, Quality Management, New

Product Development, Production Planning and Scheduling, Facility Location etc.

COURSE REQUIREMENTS

Class grades will be based on the following components with the stated weights:

Class contribution 5%

Homework / Assignments 15%

Final exam 80%

Homework will consist of problem sets that will give you an opportunity to think about and apply

concepts covered in class. Some problems will require you to provide analytical proofs and some

others will involve computations. In addition, for some classes, you will be asked to write a

critique on research papers that will be covered in the class.

To prepare your research writing process: “You can submit the first 5 weeks in either Latex or

hand-written, but you are required to submit in Latex from week 6 on.” (Latex template on

Canvas.)

Honor code: The application of the honor code to this course is important and implies, among

others, that you should do all assignments without consulting any potential solutions sets from

whichever source.

All students are expected to actively contribute to class discussions, which can involve solving

problems on the blackboard and/or critically commenting on research papers.

The final exam will be based on all the material covered during the quarter and can include both

closed-ended analysis questions (like homework problems) and more open-ended modeling

questions.

Students auditing the course will be required to complete homework assignments and contribute

to the class discussion. All homework/assignments can be done in groups of preferably two but

maximally three students.

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BOOKS AND READINGS

The lectures will draw upon the following textbooks:

[PHZ] P.H. Zipkin. Foundations of Inventory Management, McGraw Hill, 2000.

[ELP] E.L. Porteus. Foundations of Stochastic Inventory Theory, Stanford Business Books,

2002.

[TK] Taylor, H. M., and S. Karlin. An Introduction to Stochastic Modeling, Academic Press,

Boston.

For advanced topics, specific research papers (classic and contemporary) will be assigned for

reading, which are mentioned in the class details below.

SYLLABUS OUTLINE1

Week Date Title and Description Textbook Chapters /

Papers2

1 Sep19 Introduction Overview of OPNS and of the course

Single Location Inventory Models (Deterministic) Stationary: EOQ model and variants (EPQ-finite

production rate, backorders (r,q) policies, quantity

discounts)

[JVM] Ch 1;

[PHZ] Ch 2;

Van Mieghem (2011)

[PHZ] Ch 3

2 Sep26 Dynamic: Wagner-Whitin model

Single Location Inventory Models (Stochastic)

Static: Newsvendor model

[PHZ] Ch 4; Wagner &

Whitin (1958)

[ELP] Sec 1.2

3 Oct 3 Dynamic: Discrete time models

Economics of Single Location Inventory Models

Quantity discount contracts; Buy back contracts

[ELP] Ch 4

Lee and Rosenblatt (1986);

Pasternack (1985);

4 Oct 10 Pricing in newsvendor models

Newsvendor Networks

Linear programs with recourse

Flexibility

Gradient descent and IPA

Petruzzi & Dada (1999)

Salinger & Ampudia (2011)

Van Mieghem & Rudi

(2002); Van Mieghem

(1998)

5 Oct 19

(WED

1300-

1600)

Operational Hedging

Risk Aversion

Van Mieghem (2010)

6 Oct 24 Risk Aversion in Newsvendor Networks

Empirics of Inventory Models

Schweitzer and Cachon

(2000) ; Olivares,

Terwiesch, Cassorla

1 Exact sequence of sessions is subject to change. 2 See below for more details

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Experimental evidence and behavioral biases

Structural estimation

(2008) ; Rudi & Drake

(2015)

7 Nov 3

(THU

1500-

1800)

Machine Learning and Online Experiments

What is machine learning?

Supervised Machine Learning Models

Online Field Experiments

Amazon Mechanical Turk

Chapter 1 – 3, Elements of

Statistical Learning

8 Nov 7 Single Server Queuing models and economics

Basic models; Three key questions:

1. capacity investment,

[TK] Ch 9;

Rubinovitch;

9 Nov 21

2. admission control/pricing

3. variability mgt.

Data-driven capacity estimation and staffing

Robust queuing

Naor (1969);

Hasija, Pinker, Shumsky

(2010)

10 Nov 28 Practice-Driven Research

Production-inventory models

Applications to Flexibility and Dual Sourcing

Bandi, Bertsimas and

Yousef (2015)

Allon and Van Mieghem

(2010); Boute and Van

Mieghem (2013)

For your interest:

On Canvas I have put some documents like:

- How to write and present well

- How to write a referee report

- How to write a literature review

- Latex templates to write a report or paper

Views on Research Tastes

Gérard P. Cachon What Is Interesting in Operations Management? MSOM Fellow Inaugural

Lecture. M&SOM Vol. 14, No. 2, Spring 2012, pp. 166–169

Van Mieghem, J. A. 3Rs of OM: Research, Relevance, and Rewards MSOM Fellow Inaugural

Lecture. M&SOM Vol. 15, No. 1, Winter 2013, pp. 2–5

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DETAILED DESCRIPTION OF CLASSES

Class 1: INTRODUCTION + Single Location Inventory Models (Deterministic)

We start the course with an overview of what typically falls under the umbrella of operations

management and what will be covered in this course.

Then we start our discussion of inventory models by focusing on deterministic models, i.e., cases

where demand is exactly known. The key decisions are: when to place an order and how much to

order each time. The latter is called the optimal “batch / lot size” that balances the trade-off

between fixed ordering cost (which forces you to order infrequently) and inventory holding cost

(which forces you to order infrequently). We will consider the basic version of the lot sizing model

with stationary and constant demand rate (called EOQ model) and its several variants such as finite

production rate, planned backordering and quantity discounts.

Readings:

[PHZ] Sections 3.1 to 3.5. This chapter also includes several variants of the EOQ model, such as

finite production rate, planned backordering, which we will not necessarily cover in the class but

are easy enough to follow on your own.

Class 2: Single Location Inventory Models (Dynamic, Stochastic)

Next, we extend the lot sizing model to a scenario where the demand is deterministic but can

change over time. We will build on some of the learnings from the EOQ model and develop

additional solution methods.

We will then move to the newsvendor model, where we relax the assumption of deterministic

demand. In many real applications the decision maker does not know the demand exactly but has

some information about the stochasticity, which is modeled using the distribution. We will begin

with a single period model (called newsvendor model) where the key tradeoff while deciding the

order quantity here is between holding cost (which forces you to order less) and shortage cost

(which forces you to order more).

Assignment Due:

1. Homework 1: (see below)

Readings:

[PHZ] Section 4.3. This section includes the lot-sizing model where demand rate is time-varying.

It is interesting to read the original paper mentioned below.

Wagner HM, Whitin TM. 1958. “Dynamic Version of the Optimal Lot Size Model,” Management

Science 5(1): 89-96

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[ELP] Section 1.2: This section contains all the basics of the newsvendor model.

Class 3: A: Multi-period Stochastic Inventory Model B: Economics of Single Location

Inventory models

In this class, we will extend our discussion of stochastic inventory models to multi-period setting.

For simplicity, we will consider models without fixed ordering costs, where the optimal policy is

characterized by a single threshold called the base stock. This will use some basic concepts of

finite horizon dynamic programming. We also briefly explore the notion of myopic policies and

conditions sufficient to ensure their optimality.

We will then begin our discussion of economic issues by extending the most basic single location

models (EOQ) to supply chain consisting of a buyer and a supplier. We will mostly focus on the

issue of designing appropriate contracting structures (pricing, discounts etc.) to align the incentives

of the two parties and “coordinate” the supply chain. Lee and Rosenblatt (1986) discuss this in

the context of EOQ model and Pasternack (1985) discusses this in the context of the newsvendor

model.

Assignment Due:

1. Submit a one page critique (written in Latex) on Lee and Rosenblatt (1986) and a one page

critique on Pasternack (1985);

Readings:

[ELP] Chapter 4: The section of primary interest is 4.2, which includes the base-stock model.

Section 4.1 provides basics of stochastic dynamic programming, which are required in the

subsequent analysis.

Lee HL, Rosenblatt M J. 1986. “A Generalized Quantity Discount Pricing Model to Increase

Supplier’s Profits,” Management Science 32(9): 1177-1185.

Pasternack BA. 1985. “Optimal Pricing and Return Policies for Perishable Commodities,” Marketing

Science 4(2): 166-176.

Class 4: Newsvendor Networks

We extend the newsvendor model by considering demand that depends on price and the decision

is to jointly optimize on price and order quantity (Petruzzi and Dada 1999). [The optional paper

by Salinger and Ampudia puts this in a general context.]

So far, we have restricted ourselves mostly to a single product, single resource setting. Here we

extend the classic newsvendor model to the multi-product, multi-resource setting. We begin with

Van Mieghem (1998) which examines the value of flexible resources. Van Mieghem and Rudi

(2002) present a rather general network formulation for the newsvendor model.

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(The optional Van Mieghem paper on subcontracting considers a decentralized supply chain using

this framework and specifically applies a bargaining model.)

Assignment Due:

1. Homework 2: (see below)

2. Read Petruzzi and Dada (1999) (Only Section 1)

Van Mieghem, J. A., “Investment Strategies for Flexible Resources”, Management Science 44 (8),

1998.

Van Mieghem, J. A., and Rudi, “Newsvendor Networks: inventory management and capacity

investment with discretionary activities”, Manufacturing & Service Operations Management, vol

4, winter, 2002.

Optional:

Petruzzi NC, Dada M. 1999. “Pricing and the Newsvendor Problem: A Review with Extensions,”

Operations Research 47(2): 183-194.

Salinger and Ampudia, 2011. “Simple Economics of the Price-setting Newsvendor Problem,”

Management Science 57(11)1996-1998.

Class 5: Operational Hedging and Risk Aversion

Nearly everything we have done to this point has assumed that all actors are risk neutral.

Obviously, this abstracts from reality. Eeckhoudt et al. looks at the implication of risk aversion in

the newsvendor model. Van Mieghem gives an overview of risk management and operational

hedging.

Assignment Due:

Homework 3: Newsvendor networks (see below)

Eeckhoudt L., C. Gollier, and H. Schlesinger, “The Risk Averse (and Prudent) Newsboy”

Management Science, 1995, 41, 786-794

Optional:

Van Mieghem, J.A., “Risk Management and Operational Hedging: An Overview,” Preliminary

Draft: December 30, 2009. This chapter will be reviewed for inclusion in the Handbook of

Integrated Risk Management in Global Supply Chains, co-edited by Panos Kouvelis, Onur

Boyabatli, Lingxiu Dong, and Rong Li, and to be published by John Wiley \& Sons, Inc.

Class 6: Risk Aversion in Newsvendor Networks; Empirics of Single Location Inventory

models

Here, we will return to the newsvendor model but rather than holding a normative perspective

(what should the decision maker do), we will hold a positive or descriptive perspective (what does

the decision maker do). Specifically, we will study two papers that analyze the decisions of

individuals when they are faced with the newsvendor model. Schweitzer and Cachon (2000)

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follow an experimental methodology while Corbett and Fransoo (2008) adopt a survey

methodology.

Assignment Due:

1. Pick one of the papers below, submit one page critique (Latex) and a 35min presentation

(Powerpoint).

2. Derive the first-order conditions for the newsvendor network from Homework 3 analytically

for a demand distribution that is uniform over the square [0, 600] x [0, 600]. Solve the 3

equations numerically to come up with the optimal capacity vector K.

3. Start working on Integrative Case (due Class 7)

Schweitzer ME, Cachon GP. 2000. “Decision Bias in the Newsvendor Model with a Known

Demand Distribtion: Experimental Evidence,” Management Science. 46(3): 404-420.

Olivares, Marcelo, and Christian Terwiesch and Lydia Cassorla. 2008. “Structural Estimation of

the Newsvendor Model: An Application to Reserving operating room time,” management science

54(1)41-55.

Rudi, Nils and Drake, David. 2010. Observation bias: The impact of demand censoring on

newsvendor level and adjustment behavior

Class 7: Machine Learning and Online Experiments

Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, “An Introduction to Statistical

Learning with Applications in R.” Springer.

Trevor Hastie, Robert Tibshirani and Jerome Friedman, “Elements of Statistical Learning: Data

Mining, Inference and Prediction.” Springer.

Larry Wasserman, “All of Statistics: A Concise Course in Statistical Inference.” Springer.

Assignment due: Integrative Case.

Class 8: Single Server Queuing Models and Economics

We start our discussion of queuing models to study stochastic flow systems. These models were

originally motivated by the study of the flow of “customers” queuing up in lines (“make-to-order”)

but they also link to make-to-stock inventory models. We start from Markov models and formulate

the famous M/M/1 queuing model. The Taylor and Karlin chapter provides some general

background reading. The Rubinovitch paper analyzes a simple but interesting system.

Taylor, H. M., and S. Karlin, “Queuing Systems,” Chapter 9 in An Introduction to Stochastic

Modeling, Academic Press, Boston.

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Rubinovitch, M., “The Slow Server Problem,” Journal of Applied Probability, 22 (1985), 205-

213.

Class 9: Single Server Queuing Models and Economics

We start addressing three important ways of managing queuing systems:

1. capacity investment,

2. admission control/pricing,

3. variability management. (This will be motivated by the simulation homework.)

If we have time, we discuss priority queues.

Finally, we discuss a data-driven method to estimate capacity and plan staffing.

Assignment Due:

1. Homework 4: single queue simulator + sequential queueing network (see below)

2. Read Hasja, Pinker and Shumsky (2010) and Robust Queuing.

Naor, P., “The Regulation of Queue Size by Levying Tolls,” Econometrica, Vol. 37, No. 1. (Jan.,

1969), pp. 15-24.

Hasja, Pinker and Shumsky (2010) “Work Expands to Fill the Time Available: Capacity

Estimation and Staffing under Parkinson’s Law,” MSOM, 12(1)1-18.

Optional papers:

Shiliang (John) Cui, Xuanming Su, Senthil Veeraraghavan (Working), 2013, A Model of Rational Retrials in

Queues.

Kakalik, James S. and Little, John D. (Sept 1971) Optimal Service Policy for the M/G/1 queue

with multiple classes and arrivals. Rand paper series, P-4525. Rand Corporation, Santa Monica,

CA.

Class 10: Practice-Driven Research: Smoothing and Sourcing

We finish the course by looking at research that were inspired by practice. First we consider global

dual sourcing with applications to offshoring.

Bandi, Bertsimas and Youssef. “Robust Queuing Theory”. Read first 11 pages

Background papers:

Global dual sourcing and order smoothing. With Robert Boute. To appear in Management

Science 2015.

Allon and Van Mieghem (Management Science 2010). This paper is also featured in Kellogg

Insight: Global Dual Sourcing Strategies: Should you source your carbon fiber bicycle from Mexico

or China?

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Assignment Due:

1. Homework 5: Mexico-China Simulation Game (see below)

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Homework 1: Single location deterministic inventory models

[PHZ] Problems 3.1; 3.2; 3.5; 3.8; (3.16; 3.17 – these last two only if we finished quantity

discounts in class)

Pooling benefits: Compare the total inventory, cost, and days-of-inventory of two configurations:

1. Decentralized: N identical EOQ retailers with parameters c, k, h,

2. Centralized/Pooled: 1 EOQ retailer (with same parameters c, k, h but serving the

aggregate demand N of the decentralized system).

What are the benefits of pooling in this setting? In reality, what may change those benefits?

Finite production rate: Consider a set up identical to the basic EOQ model, with constant

demand rate λ, holding cost h and fixed ordering cost k. In addition, suppose that the supplier can

either produce at a constant rate of μ>λ (supply is “on”) or idle (supply is “off”).

a. Calculate the optimal (economic) production quantity or EPQ in this situation.

b. If given a choice, what μ would you choose optimally? What is the EPQ in that case?

c. Comment on the physical relevance of your recommendation in b. What would you add to

the model to make it more meaningful?

d. How does the optimal policy and cost change if the supply process produces N different

products (which all have same constant demand rate ) in a cyclic production fashion

(meaning, produce a batch of product 1, then product 2, …, product N, and then cycle

repeats)?

Homework 2: Single location stochastic inventory models

[ELP] Exercises 1.18; 1.25; 4.7; 4.10; 4.11; 4.12; PHZ: 3.16; 3.17 (if not done earlier)

Only if we did not do this yet in class: Consider the newsvendor model with normally distributed

demand. Follow the notation that we used in the class and prove that the optimal profit function

is given by 𝑉(𝑆) = (𝑝 − 𝑐)𝜇 − 𝑝𝜎𝜑𝑁(𝑧∗) where 𝑧∗ = 𝑁

−1(𝑝−𝑐

𝑝).

Homework 3: Newsvendor Network Problem

Consider the 2-product, 3-resources newsvendor network model, as shown in Fig 1, in a single-

period setting, thereby dispensing with inventory dynamics and discounting (i.e., discount factor

= 1).

Final Assembly 1

Capacity K1

Product 1

Product 2

Final Test

Capacity K3

Product 1 (demand D1)

Product 2 (demand D2)Final Assembly 2

Capacity K2

Final Assembly 1

Capacity K1

Product 1

Product 2

Final Test

Capacity K3

Product 1 (demand D1)

Product 2 (demand D2)Final Assembly 2

Capacity K2

Figure 1 A newsvendor network capacity investment problem

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For concreteness, assume the following data: demand (in thousands) is uncertain and was

estimated for three discrete scenarios and shows high mix uncertainty:

1. a "pessimistic scenario" D = D¹ = (150,350) with probability 1/4,

2. the "expected scenario" D = D² = (300,300) with probability 1/2,

3. and an "optimistic scenario" of D = D³ = (450,250) with probability 1/4.

The capacity adjustment cost function is affine:

C(K) = cK,0 + cK′K = $40,000,000 + ($30, $20, $80) ′K.

The unit contribution margins are p – c = ($400, $300). Clearly, a 2-dimensional activity vector

x=(x₁,x₂), where xi is the production quantity of product i, is a sufficient descriptor. The relevant

network matrices are the demand routing matrix RD and capacity consumption matrix A:

Assignment questions:

1. A decision maker that only plans for expected quantities would choose a capacity K = (300,

300, 600). For that capacity vector, what is the feasible region, i.e., how do you draw the

capacity region? What is the expected operating profit, expected firm value, and ROI under

this investment? (Assume capacity will have zero salvage value.)

2. Analyze the impact of demand uncertainty (in the form of the three points): what capacity

plan do you recommend to hedge against uncertainty? Your answer should give the optimal

capacity vector. Verify financial attractiveness of your recommendation: What is the

expected profit and ROI now? Are both financial measures in agreement as to the

recommended course of action? If not, what do you recommend?

3. Interpret your recommended capacity portfolio in intuitive terms: what are you "hedging"

and why is your plan to be preferred?

4. What is the expected value of perfect information?

5. For the remainder of the homework, extend the demand forecast to a normally-distributed

random 2-vector with same mean and covariance matrix as the original 3-scenario demand

forecast.

a. Solve numerically for the optimal capacity plan now using optimization via

simulation. Hand-in a brief outline/copy of your code.

b. Now keep the 2 variances, but let the covariance vary. That is, investigate the role

of the correlation coefficient by letting it vary from =-1 to +1, and calculating the

associated optimal profit and capacity vector. How does your "hedging plan"

depend on the correlation?

c. (Extra credit:) Assume the decision maker is risk averse with constant absolute risk

aversion (CARA). What investment is optimal (as a function of the coefficient of

risk aversion and demand correlation ; you can pick a few values of these

parameters)? Interpret.

RD

1 0

0 1and A

1 0

0 1

1 1

.

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Come prepared to class with your results on some Powerpoint slides so you can discuss/show

your assignment as a group in class.

Homework 4: Single Queue Simulator

Part 4.1: Consider the following open acyclic network: Poisson arrivals feed into station 1 (a single

server with unlimited queue and independent, exponential service times with rate ). Departures

of station 1 feed into station 2 (a single server with unlimited queue and independent, exponential

service times with rate 2). Compute the limiting joint distribution of X = (X1, X2) where Xi is the

number of jobs at station i. Use the graphical approach from class, now applied into two

dimensions, and submit your diagram nicely drawn. Derive the balance equations and solve them

to its simplest form.

Part 4.2: Write a discrete event simulator of a single queue, single server system in your preferred

programming language (Matlab is easy). The program should be able to estimate the queue length

and waiting time distributions.

Simulate two systems:

1. An M/M/1 queue with service rate = 1 and utilization = .8

2. A GI/G/1 queue with independent normally distributed interarrival and service times, again

with = 1, = .8, and both distributions having coefficient of variation COV = .3

Assignment questions: hand in

1. A copy of your code (make it intelligible for grading purposes)

2. The simulated steady-state expected queue length and waiting time for both systems.

Explain how you determined the steady-state estimate.

3. For M/M/1: compare both expectations, as well as the simulated distributions, with the

analytic results to get a sense of your simulation errors. How do errors change if you

change the utilization ?

4. Simulate the expected waiting time of the GI/G/1 as a function of:

a. Utilization and plot the result against the M/M/1 analytic result. Report E(wait

in queue only for GI/G/1) / E(wait in queue only for M/M/1).

b. COV (assume both distributions have same COV) and plot the result in linear scale

as well as quadratic scale (meaning EW as a function of COV2).

Come prepared to class with your results on some Powerpoint slides so you can discuss/show

your assignment as a group in class.

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Homework 5: Due class 10

The Mexico-China Dual Sourcing assignment as described in the excel spreadsheet file (on

Blackboard or that I will email).

A. Please hand-in your analysis and solution (with explanation) to the two questions

contained in the spreadsheet.

B. What strategic allocation would the model by Boute and Van Mieghem suggest for the

simulation game? How does that compare with your proposed strategy and allocation?

C. Come prepared to class with one laptop per person. The laptop should have WiFi and a

browser like FireFox but NOT Internet Explorer installed, as well as the excel

spreadsheet. Be ready to start playing the global dual sourcing simulation in real-time.