Valuing supply‐chain responsiveness under demand jumps

• Published date: 01 July 2018
• DOI: http://doi.org/10.1016/j.jom.2018.06.002
• Date: 01 July 2018

RESEARCH ARTICLE

Valuing supply-chain responsiveness under demand jumps

Is¸ık Biçer

1

| Verena Hagspiel

2

| Suzanne de Treville

3

1

Schulich School of Business, York

University, Toronto, Canada

2

Department of Industrial Economics and

Technology Management, Norwegian

University of Science and Technology,

Trondheim, Norway

3

Faculty of Economics and Business,

Swiss Finance Institute, University of

Lausanne, Lausanne, Switzerland

Correspondence

Suzanne de Treville, Faculty of Economics

and Business, Swiss Finance Institute,

University of Lausanne, 1015 Lausanne,

Switzerland.

Email: suzanne.detreville@unil.ch

Handling Editor: Daniel Guide

Abstract

Asthetimebetweenthedecisionaboutwhattoproduceandthemomentwhen

demand is observed (the decision lead time) increases, the demand forecast becomes

more uncertain. Uncertainty can increase gradually in decision lead time, or can

increase as a dramatic change in median demand. Whether the forecast evolves

gradually or in jumps has important implications for the value of responsiveness,

whichwemodelasthecostpremiumworthpayingtoreducethedecisionleadtime

(the justified cost premium). Demand uncertainty arising from jumps rather than

from constant volatility increases the justified cost premium when an average jump

increases median demand, but decreases the justified cost premium when an aver-

age jump decreases median demand. We fit our model to two data sets, first publicly

available demand data from Reebok, then point-of-sale data from a supermarket

chain. Finally, we present two special cases of the model, one covering a sudden loss

of demand, and the other a one-time adjustment to median demand.

KEYWORDS

cost-differential frontier, demand modeling, fourier analysis, jump-diffusion process, lead-time

reduction

1|INTRODUCTION

Postponing an order quantity decision until demand is

known—thus reducing the decision lead time to zero—

eliminates demand-risk exposure.

1

Conversely, demand-

risk exposure tends to increase in the decision lead time,

resulting in stockouts or overstocks that generate mismatch

costs. The ability to postpone the decision about what to

order so that the order quantity can be based on better

demand information can be conceptualized as a real option

(de Treville & Trigeorgis, 2010), and that option's value can

be estimated using quantitative-finance methods. Being

able to quantify the value of reducing demand-uncertainty

exposure that arises from an increase in the decision lead

time transforms time into a decision variable.

The first step in estimating option value is to specify the

forecast-evolution process: how demand uncertainty increases

in decision lead time.

2

The simplest case is the random-walk

assumption that underlies the Black-Scholes option-pricing

model (Black & Scholes, 1973). Each instant that the deci-

sion lead time increases, demand uncertainty increases by a

minute amount following a geometric Brownian motion.

When this constant-instantaneous-volatility process holds,

demand is lognormally distributed with volatility increasing

in the square root of the decision lead time. This assumption

underlies the Cost-Differential Frontier decision tool pro-

posed by de Treville, Schurhoff, Trigeorgis, and Avanzi

(2014) that estimates the cost differential that must be

offered by a long-lead-time supplier to compensate for the

increase in demand-uncertainty exposure resulting from an

increase in decision lead time.

3

In practice, changes in demand may occur suddenly

as a change in median demand ( jump) rather than as an

instantaneous increase in volatility. Demand is frequently

subject to jumps: The World Economic Forum in its 2012

[Note: This article was retypeset after publication in an issue. Due to a

difference in final page count, this PDF has been left unpaginated.

Please refer to the How to Cite box following the references for correct

citation information.]

DOI: 10.1016/j.jom.2018.06.002

J Oper Manag. 2018;46–67. wileyonlinelibrary.com/journal/joom © 2018 APICS 1

report on supply-chain risk attributed 44% of supply-

chain disruptions to demand shocks (World Economic

Forum, 2012).

4

In finance, the limitations of the Black-

Scholes model are well known, but the model is generally

used as a reasonable approximation (e.g., Bakshi, Cao, &

Chen, 1997). When the true forecast-evolution process is

subject to jumps but the mismatch cost is estimated

assuming that all demand uncertainty emerges from a

constant-volatility process, how bad is the error? Does

the constant-volatility version of the model give a good

enough approximation of the mismatch cost for practical

purposes, or does the error impact decision making

enough to warrant the use of a more complex model?

To address this question, we extend the Cost-

Differential Frontier decision tool to include jumps fol-

lowing the classic model proposed by Merton (1976). We

use publicly available demand data from Reebok to gain

insight into how the choice of model impacts supply-

chain decision making. Parsons (2004) studied the cost of

demand-risk exposure faced by Reebok in the context of

the exclusive license held during the period 2000–2010 to

produce replica jerseys with the National Football League

(NFL, see also Graves & Parsons, 2005).

5

Available publi-

shed Reebok data include the mean and SD of annual

demand for replica jerseys for New England Patriots fans;

price, cost, and residual value; and a qualitative descrip-

tion of the many types of demand jumps observed by

Reebok. Parsons (2004, pp. 74–75) concluded his analysis

of Reebok data by proposing that “perhaps the single

greatest opportunity for Reebok is to improve its ability

to respond to shifts in demand through shorter lead

times.”These data are used by Parsons (2004), Graves

and Parsons (2005), and Parsons and Graves (2005) to

demonstrate the value of postponement. Cattani, Dahan,

and Schmidt (2008) cited this work as exemplifying the

importance of analyzing the value of responsiveness (see

also Uppala, 2016). The decision by the authors of the

Reebok study to make their data and analysis publicly

available made it possible for us to build directly on their

work and use our model to extend their analysis.

Our first result is that the impact of jumps on the cost

premium worth paying to reduce decision lead time

depends on whether a jump is expected to increase or

decrease median demand. If a jump is expected to

increase median demand, then treating demand uncer-

tainty as though it came from a constant-volatility pro-

cess results in an understatement of the justified cost

premium. If, however, a jump is expected to reduce

median demand, then assuming a constant-volatility pro-

cess will lead to an overstatement of that cost premium.

This result arises from how the jump changes the skew-

ness of the marginal demand density. Jumps that are

expected to increase median demand will increase skew-

ness as long as they occur relatively rarely.

6

The resulting

increase in right-tail weight increases the value of the

option to postpone the production commitment. A

jump that reduces median demand reduces skewness,

making the postponement option less valuable. Man-

agers with whom we have reviewed this result have

found it counterintuitive, as they experience more con-

cern about being stuck with excess inventory if a nega-

tive jump occurs than about stocking out following a

positive jump.

In order to make the analysis as useful as possible to

practitioners, we explore two special cases of jumps that

are frequently encountered in practice. The first special

case models the risk that demand would be completely

lost. In the Reebok case, this corresponds to a change of

team jersey that reduces demand for the old model to

zero. We show that adding any reasonable risk of

demand loss to a constant-volatility process substantially

increases the justified cost premium. The second special

case models a one-time update of median demand such

as occurs when decision makers obtain early-sales data,

which we use to quantify the impact of a possible Super-

Bowl win on the cost premium worth paying to reduce

decision lead time. These results are not surprising in

their direction, but they are striking in their magnitude.

When the jumps that everyone knows to exist are explic-

itly considered in setting the decision lead time, the com-

pany is likely to much more aggressively reduce decision

lead time.

A question that arose during the research project

was whether demand jumps are experienced in supply

chains. To address this question, we randomly selected

two products from a supermarket chain and analyzed

100 observations of daily demand from point-of-sale

data, then counted how many observations had stan-

dardized residuals more than three SDsfromzero.The

first product had four such outliers, indicative of

demand jumps, and the second had none. We then con-

sidered what would happen if we forced a jump model

on a product where it seemed like a constant-volatility

assumption would suffice. By moving the threshold

defining outliers from the usual three down to 2.52

SDs, the number of outliers for the second product

increased from zero to four. Interestingly, treating

these four points as jumps rather than normal varia-

tion for the second product substantially increased the

cost-premium frontier. Which representation is correct?

Our model cannot say. But, the fact that the option value

of responsiveness is quite sensitive to when outliers are

assumed to represent demand jumps indicates that this is

an area that managers should be pondering.

2BIÇER ET AL.