Master Thesis Exposé Stimulating Additional …...Master Thesis Exposé Stimulating Additional Demand in Dynamic Lot-Sizing Models at Neutral Costs in Online Retailing An inventory

Master Thesis Exposé

Stimulating Additional Demand in Dynamic Lot-

Sizing Models at Neutral Costs in Online

Retailing

An inventory management model for perishable goods

Submitted by:

Frédéric N. P. Nicolas

Kassel, 21.10.2018

I

Abstract

Keywords

MILP, E-Commerce, Dynamic Lot-Sizing, Additional Demand, Dynamic Price Scheduling,

Replenishment, Order Quantity Planning, Internet Marketing, Flash Sales, Supply Chain

Integration

Background

Frequently it can be observed that customer’s demand is not in harmony with a retailer’s optimal

replenishment policy. Many methods therefore focus on smoothing the customer’s demand for

an increased predictability. These methods use the joint leverage of marketing methods and

supply chain management techniques to stimulate, shift, or offset the customer’s demand to

flatten the demand curve. Oppositely, it can also be used to emphasize demand at peaks and

reduce demand in troughs. Assuming the peaks overlap with the replenishment policy a retailer

could therefore drastically reduce inventory holding costs.

Purpose

This study attempts to combine common marketing practices to grow consumer market share

with traditional supply chain management processes to optimize batch sizes in order to subsidize

marketing efforts by incorporating and determining the stimulated demand inside the lot-sizing

process. It aims to do so by 1.) detecting the underlying synergies between the marketing and

supply chain operations, 2.) examine the mathematical foundations, 3.) define a linear mixed-

integer problem for a practical application and 4.) conduct a numerical experiment to confirm the

assumptions.

Methods

The quantitative data will be collected by formulating a linear mixed-integer problem, which

incorporates the additional demand generation under marketing constraints, to represent the new

batch size optimization and submitting it to a numerical study composed of exemplary data from

a fictional online retailer specialized on perishable goods. The received data will then in a second

step be tested against a set of data collected by a standardized model. By this means the

hypothesis that an increasing amount of orders can lead to a higher market coverage without

causing additional costs will be tested.

Stimulating Additional Demand in Dynamic Lot-Sizing Models at Neutral Costs in Online Retailing

II

Table of Contents

Abstract ............................................................................................................................................ I

Table of Contents ............................................................................................................................ II

List of Figures ................................................................................................................................. III

List of Tables ................................................................................................................................. IV

List of Abbreviations ........................................................................................................................V

List of Symbols .............................................................................................................................. VI

1. Introduction .............................................................................................................................. 1

1.1 Background ..................................................................................................................... 1

1.2 Problem Statement ......................................................................................................... 2

1.3 Purpose ........................................................................................................................... 2

1.4 Structure .......................................................................................................................... 3

2. Theoretical Framework ........................................................................................................... 4

2.1 Literature Review ............................................................................................................ 4

2.2 E-Commerce Marketing with Flash Sales ...................................................................... 6

2.3 DLS applied to E-Commerce .......................................................................................... 8

2.4 Implementation of Additional Demand into Inventory Management ............................ 10

3. Study Framework .................................................................................................................. 13

3.1 Research Question ....................................................................................................... 13

3.2 Hypothesis ..................................................................................................................... 13

4. Methodology .......................................................................................................................... 14

4.1 MILP for Inventory Management with Additional Demand ........................................... 14

4.2 Numerical Experiment ................................................................................................... 16

5. Plan of Work .......................................................................................................................... 18

List of References ......................................................................................................................... 19


III

List of Figures

Figure 1: Demand Curves for Flash Sales ..................................................................................... 7

Figure 3: Optimized Cost Structure .............................................................................................. 11

Figure 2. Normal Cost Structure ................................................................................................... 11

Figure 4: Optimized Cost Structure with Additional Demand ....................................................... 12

Figure 5: Sample Demand Structure ............................................................................................ 17


IV

List of Tables

Table 1: Normal Replenishment Schedule ................................................................................... 10

Table 2: Replenishment Schedule under Additional Demand ..................................................... 12

Table 3: Decision Variables for Sample Data ............................................................................... 17


V

List of Abbreviations

ADI Advanced demand information

B2C Business to consumer

CP Constraint programming

DLS Dynamic lot-sizing

FTL Full truck load

LTL Less then truckload

MILP Mixed-integer linear problem

SCI Supply chain integration

SCM Supply chain management

SLULSP Single level uncapacitated lot-sizing problem

USD United states dollar


VI

List of Symbols

dt demand in period t

h inventory holding costs

ht inventory holding costs in period t

p price

pt period price

qt order quantity in period t

s fixed ordering costs

st fixed replenishment costs in period t

vkt shipping costs per unit in period t

yt inventory at the end of period t

v binary additional demand condition

z additional demand

t binary replenishment condition in period t

N total allowed periods with additional demand

M sizable number

T periodic time frame


1

1. Introduction

1.1 Background

For 2020 Statista’s Digital Market Outlook (2017) expects the total turnover of E-Commerce

worldwide is expected to grow from 1.35 trillion USD in 2016 to over 2,2 trillion USD. Other

forecasts, such as eMarketer (2016) even predict the total turnover to rise to over 4 trillion

USD. In Europe alone, the market is expected to grow by over 120 billion USD in the same

time frame (Striapunina, 2018). But whilst the overall revenue and the average revenue per

user see a steady increase, the proportion of online shoppers under the internet users in highly

industrialized countries, such as Germany and Great Britain, seem to have reached a

saturation level (Ipsos, 2016). Consequently, “E-Commerce has gradually become an integral

part of people’s life” (Zhou, Sun, Ma & Chen, 2018). In view of these developments online

retailers have to face fierce competition. To gain a competitive advantage many online

retailers seek to optimize their cost structure and try to find new ways to generate additional

value with their existing assets.

An important share in the cost structure of every retailer falls to the inventory holding costs

and can be reduced by an effective inventory management. When the ECC Köln (2014) asked

online retailers in a survey where they see potential to save costs, 62% of them identified the

reduction of inventory as having great potential.

Inside the E-Commerce market, the market for perishable goods is growing at a dramatic rate.

According to Zhou et al., “[r]esearch suggest that the sale of fruits is the highest in [the] fresh

products e-commerce” (p. 209). When it comes to perishable goods, the consumers’

willingness to purchase perishable products decreases depending on the expiration date and

subsequently along the products shelf lifetime (Tsiros & Heilman, 2005; Li & Teng, 2018).

Fujiwara and Perera (1993) developed an economic order quantity model that applies penalty

costs to deteriorating products over their lifetime, which effectively increases the inventory

holding costs of the products. Due to the high growth rate of the perishable goods market

and the peculiar characteristics of perishable goods, in particular their elevated inventory costs

and time sensitive storage capabilities, this research focuses on online retailers specialized in

fresh fruits.

Besides the rise of E-Commerce platform, the development of new social media platforms

makes online retailers face new challenges in the “in making their websites socially rich by

implementing the features that address their customers’ needs” (Huang & Benyoucef, 2015).


2

With those challenges also come chances for the online retailers to embrace the technology

and create new marketing techniques to stimulate further demand.

Combining these marketing techniques and supply chain management (SCM) challenges is

the task of supply chain integration (SCI). SCI refers to “the extent to which a firm coordinates

its strategic supply chain activities (such as planning and forecasting) with its channel

members (such as customers and suppliers)” (Yu, Jacobs, Chavez & Feng, 2016, p. 4196).

When examining the integration of marketing and supply chain activities, Mollenkopf, Gibson

and Ozanne (2000) found that “[f]irms that are integrated can expect to provide higher levels

of customer service, at lower costs, as well as create more satisfies customers and increase

profits over the long term” (p. 89). This study attempts to build on these effects to optimize the

upstream supply chains of online retailers.

1.2 Problem Statement

This research aspires to shed light on the prospective gains that an online retailer can achieve

by combining marketing and supply chain management processes. By considering marketing

efforts and taking their effects on the demand into account, the supply chain management can

use that information to adjust their inventory replenishment schedule. Furthermore, when

deeply embedding marketing constraints into the supply chain management processes,

decisions on the optimal scope and timing of those marketing activities can be made. Those

decisions are driven by the joint effort to gain a competitive edge and allow the online retailer

to increase the overall market share. This study aims to indicate the potential of a decision-

making process that helps to create additional value and reduce costs by leveraging the

strength of a collaboration between the two departments. It intends to do so by defining a

linear programming model for the inventory management of an online retailer with additional

constraints of the marketing department. In return the model should define the scope and

timing of marketing activities, which are aiming to stimulate demand.

The in this research suggested approach focuses on applying traditional dynamic lot-sizing

methods to online retailing and expanding it with parameters simulating additionally stimulated

demand. Further constraints must then be defined to simulate marketing restrictions, such as

the maximal demand and discount budget constraints.

1.3 Purpose

Building on previous research and the abovementioned problem statement, the purpose of

this study is to investigate the synergies between marketing practices to grow consumer

market share and traditional supply chain management processes for inventory replenishment


3

problems. Specifically, the intention is to contribute to the current development of linear

programming models for determined dynamic demand lot-sizing problems in the context of

online retailing. It aims to do so by detecting the underlying synergies between the marketing

and supply chain operations inside a typical online retailer and defining a mixed-integer linear

problem to suggest an alternative replenishment schedule and therefore allowing the online

retailer to determine the additionally stimulated demand inside the lot-sizing process.

Moreover, this research addresses the potential cost savings which can be achieved by

emphasizing local peaks instead of smoothing the demand throughout the periodic time frame.

In a more practical context, the formulated MILP can be exploited by online retailers, in order

to optimize their replenishment schedule and align it with their marketing activities. The

outcome of this study can therefore help the online retailers to gain a competitive advantage

in today’s vigorous environment in E-Commerce.

1.4 Structure

In order to introduce the research question in depth, the theoretical framework of the study is

presented. Starting off with a short review of the most important literature on the supply chain

management for online retailers, demand stimulating marketing methods in E-Commerce, and

especially of the current use of MILP models for postponing lead times and modifying batch

sizes is presented. Subsequently the use of flash sales in E-Commerce, the use of dynamic

lo-sizing solutions in E-Commerce, and lastly the implementation of additional demand into

the inventory management are presented in depth. The following segment is dedicated to the

research question, leading to the detailed explanation of the hypotheses. The next segment

will present the methodology. It includes the approach used to obtain a set of sample data,

the method used to run the numerical study and the analysis and interpretation of the results.

Finally, a segment will be dedicated to the conclusion of the research, consisting of the

theoretical and managerial implications, the limitations of the suggested models and

suggestions for further research.


4

2. Theoretical Framework

2.1 Literature Review

The following table identifies some of the key resources that are going to be used in this study.

Title Author Source (Year) Content

Why and how do

branders sell new

products on flash sale

platforms

Zhang,

Mingyang;

Zhang,

Juliang;

Cheng, T.C.E.;

Hua, Guowei

European Journal of

Research

Operations (2018)

Provides a definition of

flash sales and details

on their use by online

retailers.

User preferences of

social features on

social commerce

websites: An empirical

study

Huang, Zhao;

Benyoucef,

Morad

Technological

Forecasting and

Social Change

(2015)

This study examines the

benefits and drawbacks

of marketing methods

such as flash sales.

A supply chain under

limited-time promotion:

The effect of customer

sensitivity

Kogan,

Konstantin;

Herbon, Avi

European Journal of

Operational

Research (2008)

A study on the effects of

limited time promotions

on the consumers’

purchase behavior.

The impacts of IT

capability and

marketing capability

on supply chain

integration: a

resource-based

perspective

Yu, Wantao;

Jacobs, Mark

A.; Chavez,

Roberto;

Feng,

Mengying

International Journal

of Production

Research (2016)

Conceptual view of the

impact of marketing

capabilities on the

supply chain integration.

Coordinated

deterministic dynamic

demand lot-sizing

problem: review of

models and algorithms

Robinson,

Powell;

Narayanan,

Arunachalam;

Sahin, Funda

Omega (2009) Provides a review of

existing solutions for

determined dynamic

demand lot-sizing

problems.

Produktionsplanung in

Supply Chains

Tempelmeier,

Horst

3. Edition

Nordestedt: BoD

(2015)

Definition of the single

level uncapacitated lot-

sizing problem.


5

Ressourcenorientierte

Bestellmengenplanung

und

Lieferantenauswahl

Reith-

Ahlemeier,

Gabriele

Nordestedt: BoD

(2002)

Multiple mathematical

formulations of the

dynamic lot-sizing

problems with variability

of downstream

discounts by suppliers.

Dynamic lot-sizing

models for retailers

with online channels

Xu, Hanon International Journal

of Production

Economics (2017)

Application of dynamic

lot-sizing problems to

replenishment problem’s

in E-Commerce

Technical Note-On

Optimal Policies for

Inventory Systems

with Batch Ordering

Huh,

Woonghee T.;

Janakiraman,

Ganesh

Operations

Research (2012)

Use of multiechelon

system to determine

batch sizes in interaction

with expected discount

sums. Study shows the

downstream example on

modifying order

quantities to leverage

price advantages.

Dynamic Lot Sizing

with Batch Ordering

and Truckload

Discounts

Li, Chung-Lun;

Hsu, Vernon

H.; Xiao, Wen-

Quiang

Operations

Research (2004)

The paper studies the

implementation

Truckload discounts into

the batch ordering

through backlogging. It

distinguishes FLT and

LTL to optimize freight

costs on inbound

logistics.

The-Multi-Item Joint

Replenishment

Problem with

Transportation and

Container Effects

Ben-Kheder,

Nejib; Yano,

Candance A.

Transportation

Science (1884)

Considers a multi-item

joint replenishment

problem, where multiple

items share a joint

container/FTL. The

study develops a

heuristic method to

solve that problem.

Coordinating

Replenishment of

Items under Time-

Varying Demand:

Dynamic programming

Formulation

Silver, Edward

A.

Naval Research

Logistics Quarterly

(1979)

Shows how to define an

inventory-control

problem under time-

varying demand

conditions.


6

Joint dynamic pricing

and capacity control

for hotels and rentals

with advanced

demand information

Zhuang,

Weigen; Chen,

Jiguang; Fu,

Xiaowen

Operations

Research Letters

(2017)

Study about the

implementation of

dynamic pricing and

capacity control for

hotels. Creates a joint

model for ADI and non-

ADI customers inside a

stochastic dynamic

programming model.

Dynamic lot-sizing in

sequential online retail

auctions

Chen, Xi;

Ghate, Archis;

Tripathi,

Arvind

European Journal of

Operational

Research (2011)

Displays optimal lot-

sizing policies under

second order conditions.

Serves as an example

for the use of a

stochastic dynamic

programming model and

numerical experiment

Efficient formulation

and heuristics for

multi-item single

source ordering

problem with

transportation cost

Venkatachalm,

Saravanan;

Narayanan,

Arunachalam

International Journal

of Production

Research (2016)

Linear programming

relaxation of a dynamic

demand multi-item

single source

replenishment problem

to achieve performance

gains.

2.2 E-Commerce Marketing with Flash Sales

Online retailers have developed many techniques to draw customers onto their web pages

and increase market share (Svatošová, 2015). The marketing management in the space of

E-commerce is often referred to as E-marketing and defined “as the concentration of all efforts

in the sense of adapting and developing marketing strategies into the web environment”

(Gerrikagoitiaa, Castandera, Rebona & Alzua-Sorzabala, 2014). Next to traditional marketing

methods such as mail and banner advertisement, new forms of advertisement to stimulate

additional demand has emerged in E-marketing (Blagcia & Damnjan, 2011). Those

techniques to grant customers discounts for a short period as well as more settled short-term

discount campaigns have gained in popularity and proven to effectively stimulate customer

demand (Abington, 2005). Such new forms include recommendations (Jannach, Ludewig &

Lerche, 2017), flash sales (Zhang, Zhang, Cheng & Hua; 2018), or “early-bird-discounts” (Lo

& Salant, 2016, p. 97).


7

It has been shown that even small reductions of pricing can have a positive and significant

impact on the customer’s price perception (Thomas & Morwitz, 2005; Wagner & Beinke, 2006).

Building on the impact of price reductions shown in the previous studies, this research

concentrates on so called sale promotions, which “represent an activity taking place from time

to time and targets short term sale increase” (Ion, Sorin & Ion, 2009, p. 148), are of interest,

as they enable the online retailer to stimulate additional demand in key periods. A method

named flash sales has emerged in this field as one of the most effective and popular e-

commerce marketing method through which brander firms sell limited numbers of products

and services at discounted prices within a specified time frame (Zhang et al., 2018). Like

many other methods, flash sales find their origin in traditional bricks-and-mortar retailers.

Those are retailers who carry costs for physical structures such as retail shops (Business &

Management Dictionary, 2007, p. 1084). The main target of flash sales is to spread the word-

of-mouth in order to accelerate the product diffusion and attract additional customers (Rosario,

Sotgiu, De Valkck & Bijmolt, 2016). In an empirical study Huang and Benyoucef (2015)

showed that flash sales prove to be a feature that “is beneficial for building brand loyalty,

increasing sales and quickly moving surplus inventory”. In the context of this rapidly

progressing ecosystem, Ferreira, Lee, and Simchi-Levi (2016) have used machine learning

techniques to predict future demands and define and optimize product pricing. Figure 1 shows

their findings on the demand curves for flash sales. It underlines the potential that flash sales

have on moving limited amounts of inventory within a short time frame. Therefore, this

research assumes that the marketing department can use existing methods to stimulate the

customer demand according to the scope defined by a joint replenishment model.

Figure 1: Demand Curves for Flash Sales (percentage of total sales by hour) (Ferreira et al., 2016)


8

2.3 DLS applied to E-Commerce

When considering the normal demand for an online retailer, it can be observed that the

demand of the customer is not necessarily harmony with a retailer’s optimal replenishment

policy (Boute, Disney, Lambrecht & van Houdt, 2007). To serve the demand and reduce his

costs the online retailer must order the products in batches from his supplier and hold a certain

inventory to serve the demand. Therefore, every retailer must perform some sort of inventory

management to determine replenishment schedule. Over the years many methods have been

developed to facilitate the management process. The Economic-Order-Quantity model is

seen as the root of all inventory management or production scheduling models and addresses

the problem of the optimal order volume under the consideration of the inventory holding costs

(Piasecki, 2001). In attempt to optimize the processing time of the inventory management

process, many heuristics have been developed to solve the order quantity problem through

determining the optimal cost point with heuristics (Bastos, Mendes, Nunes, Melo & Carneiro,

2017; Bijvanik, 2013). Most prominently, the Silver-Meal heuristic attempts to determine the

optimal amount above which it becomes more economical to order a new batch, rather than

hold inventory (Tempelmeier, 2015). To achieve an exact result and to solve more

sophisticated problems the inventory management can often be solved through dynamic

programming (Tempelmeier, 2015). Accordingly, a problem needs to be described as a

mixed-integer linear problem and solved by a corresponding software. This method also

allows for the implementation of further restrictions to the replenishment plan. Due to the

many advantages that dynamic programming offers, this study will concentrate on the dynamic

programing approach for its inventory management.

Independent of the inventory management method used it is essential to hold on to the

determined replenishment schedule to optimize the process in regard to the decision relevant

costs (Reith-Ahlemeier, 2002). In the context of online retailing, these costs typically arise

from the fixed ordering costs, the variable ordering costs and the inventory holding costs.

Considering that the main objective of the inventory management is the reduction of the total

costs, one can observe parallel to dynamic lot sizing (DLS) approaches. In DLS the optimal

lot-size for each period is determined in dependence of the total quantity of material under the

objective of minimal total costs (Wagner & Within, 2004). Those total costs are made up out

of the set-up costs, the inventory holding costs and the variable production costs

(Tempelmeier, 2015). Due to these parallels it is feasible to apply an existing DLS model to

the inventory management of an online retailer.


9

This research uses a single-level uncapacitated lot sizing problem analogous to the Wagner-

Within model (Tempelmeier, 2015, p. 30), which is defined as followed:

Objective:

𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑍 = ∑(𝑠 ∙ 𝛾𝑡 + 𝑝𝑡 ∙ 𝑞𝑡 + ℎ ∙ 𝑦𝑡)

𝑇

𝑡=1

(1.0)

under the constraints:

𝑦𝑡−1 + 𝑞𝑡 − 𝑦𝑡 = 𝑑𝑡; 𝑡 = 1, … , 𝑇 (1.1)

𝑞𝑡 ≤ 𝑀 ∙ 𝛾𝑡 ; 𝑡 = 1, … , 𝑇 (1.2)

𝑦𝑡 ≥ 0 𝑡 = 1, … , 𝑇 (1.3)

𝑞𝑡 ≥ 0; 𝑡 = 1, … , 𝑇 (1.4)

𝑦0, 𝑦𝑇 = 0; (1.5)

𝛾𝑡 ∈ {0,1}; 𝑡 = 1, … , 𝑇 (1.6)

The symbols of the model can be interpreted as:

s = fixed ordering costs;

yT = inventory at the end of the period;

pt = period price;

qt = lot size;

h = inventory holding costs;

dt = demand;

𝛾t = replenishment condition;

M = big number;

The model follows the assumption and restrictions:

1. The total demand quantity dt, as well as the period price pt of the the periodic time

frame of T periods (t = 1,2,…,T) are determined at the beginning of the periodic time

frame.

2. Shortfalls are not allowed, meaning that the demand of each period must be fulfilled

in its entirety and on time (Reith-Ahlemeier, 2002).

3. The inventory of all products is null at the beginning of the periodic timeframe y0 as

well as at the end of the periodic time frame yT (cf. constraint (1.6).

4. The order quantity qt and the inventory yt have to be equal or bigger zero at any time

(cf. constraints (1.4) and (1.5)).


10

2.4 Implementation of Additional Demand into Inventory Management

Considering that, as mentioned in the section 2.3, the demand of the customers is not

necessarily aligned with the optimal replenishment schedule of the retailer many approaches

have aimed at smoothing that demand through various methods in traditional bricks-and-

mortar structures as well as in online retailing. In section 2.2 we discussed the methods that

have merged to stimulate additional demand in the B2C E-Commerce. The easy

implementation of such discounts and increased digitalization make it possible to

automatically implement such marketing campaigns and reveal the opportunity to stimulate

additional demand in predefined periods to guide the customer demand in order to optimize

the replenishment schedule.

This research aims to emphasize demand in periods with peak demand. Assuming that a

peak will trigger replenishment periods anteriorly, consequently more peaks will lead to more

replenishment periods and could therefore allow the retailer to drastically reduce his

inventory. In order for this statement to be true in regard to the total cost, the additional peaks

and replenishment periods must occur in strategic periods to enable the cost saving potential.

To clarify the problem the fictional online retailer FreshBerry will be guiding as a reference

throughout this study. FreshBerry sells perishable goods over its own webstore to end

customers. It relies on one uncapacitated supplier, which can always serve the orders in a

timely and in full. The supplier does not require a specific lead time. On the other side the

customer demand is assumed to be deterministic, without seasonal influences and to have a

repeating structure over the weeks. Table 1 displays the typical replenishment schedule of a

normal 5 day working week for FreshBerry. As it can be seen FreshBerry traditionally has to

fulfill a high demand at the start of the week, due to cumulated demand from the weekend that

is added to the demand of Monday (here period 1), and a relatively high demand in periods

4 and 5, which represent Thursday and Friday. The retailer faces fixed costs for each batch

order and inventory costs per item. FreshBerry has determined that the optimal point at which

Period 1 2 3 4 5

Demand 130 10 0 40 40

Batch Size 220 0 0 0 0

Inventory 90 80 80 40 0

Table 1: Normal Replenishment Schedule


11

placing an additional order over holding inventory lies at a cumulated demand of 100 items.

Table 1 shows that the cumulated demand from period 2 to 5 only reaches 90 units and is not

sufficient to justify a second order.

Furthermore, it is estimated that the fixed ordering cost amount to 240 USD and that the

inventory holding cost are 1 USD / day / item. Using the replenishment problem in its MILP

form, as presented in section 2.3, an optimal solution can be identified. The resulting cost

structure is illustrated in Figure 3. The example data in Table 1 shows a special case, where

multiple optimal solutions are possible. Due to the limitation of Branch & Bound methods for

linear programs, most problem solvers will end their calculations when one optimal solution is

identified. Therefore, a solution as depicted in Figure 2, which reduces the inventory holding

costs as a trade of for higher fixed ordering costs will in most cases not be found.

Table 2 on the other hand shows an example of how additionally stimulated demand in period

4 can change the replenishment schedule of FreshBerry. As Figure 4 illustrates, the overall

higher demand leads FreshBerry to place a second order in period 4 and makes it drastically

reduce the

inventory and all associated costs. The cost structure in Figure 4 is similar to Figure 2. This

due to the special characteristics of the example data shown. To ensure that the optimal

solution for the lowest inventory costs is always preferred, a gratification system needs to be

implemented into the MILP, which will reward the use of additional demand and lowers total

costs. As discussed earlier this assumes that the determined additional orders will serve the

stimulated demand of the customers. In order for this new replenishment policy to also be

economically successful it has always to be assumed that the average costs per item will be

lower in the scenario with added demand. A second criteria to consider is the costs caused

to the retailer incurred through loss of revenue by granting the discounts. To keep the added

0

100

200

300

400

500

600

1 2 3 4 5

Co

sts

Period

Total Costs Fixed Costs

Inventory Costs

0

100

200

300

400

500

600

1 2 3 4 5

Co

sts

Period

Normal Costs Total Costs

Fixed Costs Inventory Costs

Figure 3. Normal Cost Structure Figure 2: Optimized Cost Structure


12

demand at a cost neutral level the granted discounts should therefore not exceed the total

savings achieved. To estimate a base cost and appropriate margins, this research assumes

that the full cost pricing is determined with a progressive calculation method, such as the

“Cost-Plus-Pricing” or “Target-Return-Pricing” methods (Decker, Kroll, Meißner & Wagner,

2015). The granted discount for each item of the added demand should therefore not exceed

the sum of the unit margin and its share on the total savings.

Table 2: Replenishment Schedule under Additional Demand

Period 1 2 3 4 5

Demand 130 10 0 40 40

Additional

Demand 0 0 0 20 0

Batch Size 140 0 0 100 0

Inventory 10 0 0 40 0

0

100

200

300

400

500

600

1 2 3 4 5

Co

sts

Period

Normal Costs

Total Costs

Optimized Costs

Fixed Costs

Inventory Costs

Additional Demand

Figure 4: Optimized Cost Structure with Additional Demand


13

3. Study Framework

3.1 Research Question

This study attempts to combine common marketing practices to grow consumer market share

with traditional supply chain management processes to optimize batch sizes in order to

subsidize marketing efforts by incorporating and determining the stimulated demand inside

the lot-sizing process. Previous research has found that integrating marketing capabilities into

the supply chain management can yield a competitive advantage (Agan, 2011). It aims to do

so by aligning marketing and supply chain management constraints inside the inventory

management. More particularly, this research studies the effects of stimulating additional

demand through short term sales in the form of flash sales on the batch sizes and order

intervals, by integrating marketing constraints into a dynamic lot-sizing model, that has been

adapted for the inventory management of an online retailer. This study aspires to determine

whether implementing marketing constraints, which emphasize peaks in the customer

demand, into the inventory management can increase consumer market at neutral costs?

Whether stimulating additional demand in key periods can change the replenishment schedule

and whether those additional orders can be cost efficient? And whether it is possible to define

the scope of the marketing activities, especially their order and discount volume, can be

determined within a dynamic lot-sizing model adapted for inventory management.

3.2 Hypothesis

Following the research question presented in section 3.1, the following hypothesis can be

defined:

H1: Embedding marketing constraints into the inventory management leads to reduced

inventory holding costs.

At a conceptual level, integrating marketing and SCM activities can lead improved efficiencies

and lower costs (Mollenkopf et al., 2000). This study aims to show on a more specific level

how embedding the marketing activities inside a dynamic lot-sizing model adapted for

inventory management can lead to reduced inventory holding costs. It intends to accentuate

the trade-off between fixed ordering costs and inventory holding costs in an environment

where shorter ordering intervals are favorable.


14

H2: Strategically important periods with additional demand, which lead to changes in the

replenishment schedule, are identified.

Reorder intervals have frequently been used as performance measurement for lot-sizing

techniques (Sánchez, Triantaphyllou, Webster & Liao, 2001). In a perishable goods market a

lower ordering interval and therefore tighter replenishment schedule is desirable. This

research attempts to identify strategic periods, in which additional demand can be stimulated

to trigger additional reorders, inside the dynamic lot-sizing model. Triggering additional

reorders will shorten the replenishment schedule and hence reduce inventory costs, as

established in H1.

H3: The scope of granted discounts to consumers is determined by the replenishment model.

After establishing the potential for a reduction of the inventory holding costs in H1 and

identifying the important periods where additional demand is raised in and subsequently

defining a new replenishment schedule in H2, this information can now be combined to

determine a budget that can be allocated for the marketing activities. This budget therefore

equals to the savings achieved through the previous steps. Using flash sales as the main

marketing technique, the budget is equivalent with further discounts that are granted to the

customers to make the pricing of the products more attractive.

4. Methodology

4.1 MILP for Inventory Management with Additional Demand

This segment will show on how to combine the dynamic lot sizing model presented in section

2.3 with the implementation of additional demand into a replenishment schedule, as presented

in section 2.4.

The main objective of the MILP is to create additional demand in periods in which currently no

ordering is occurring, in order to modify the replenishment schedule. The most fundamental

approach to restrict the added demand replenishment condition to non-order periods is by

running the model in a sequential format. Meaning that a base model as presented in section

2.3 first determines an optimal solution. In a second step, the here formulated problem will

determine whether there are additional periods that apply for additional demand. This two-

step process allows for an optimal approximation to determine strategic periods. On the

downside this approach requires significantly higher processing times than non-sequential

methods.


15

In a second step, this research will attempt to reduce the processing time by relaxing the

added demand replenishment condition. This leads to a simplified model, which does not

require sequential formulation. Such a linear problem, using the constraints programming

feature in IBM ILOG CPLEX Optimization Studios could resemble to the following model:

Objective:

𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑍 = ∑(𝑠 ∙ 𝛾𝑡 + 𝑝𝑡 ∙ 𝑞𝑡 + ℎ ∙ 𝑦𝑡)

𝑑𝑡 + 𝑧𝑡

𝑇

𝑡=1

(2.0)

under the constraints:

𝑦𝑡−1 + 𝑞𝑡 − 𝑦𝑡 = 𝑑𝑡 + 𝑧𝑡; 𝑡 = 1, … , 𝑇 (2.1)

𝑞𝑡 ≤ 𝑀 ∙ 𝛾𝑡 ; 𝑡 = 1, … , 𝑇 (2.2)

𝑧𝑡 ≤ 𝑀 ∙ 𝑣𝑡; 𝑡 = 1, … , 𝑇 (2.3)

𝑣𝑡 ≤ 𝑧𝑡; 𝑡 = 1, … , 𝑇 (2.4)

∑ 𝑣𝑡

𝑧𝑡

𝑡≤ 𝑛; 𝑡 = 1, … , 𝑇 (2.5)

𝑦𝑡 , 𝑧𝑡 , 𝑞𝑡 ≥ 0; 𝑡 = 1, … , 𝑇 (2.6)

𝑦0, 𝑦𝑇 = 0; (2.7)

𝛾𝑡 ∈ {0,1}; 𝑡 = 1, … , 𝑇 (2.8)

This model introduces the following new variables:

z = additional demand;

v = added demand replenishment condition;

n = max number of periods in which additional demand is allowed;

The above presented MILP follows the assumptions and symbolism of the section 2.3 and 2.4.

As the presented MILP is currently not in a linear form it can be reformulated to be linearized

(even though this leads to the need of post processing to interpret the concrete batch sizes

and inventory). Furthermore, the formulation in the above state does not contain a factor to

represent granted discounts.


16

An objective including granted discounts containing a secondary condition inside the main

objective might be formulated in the following way:

Objective:

𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑍 = ∑(𝑠 ∙ 𝛾𝑡 + 𝑝𝑡 ∙ 𝑞𝑡 + ℎ ∙ 𝑦𝑡 + 𝑀𝑎𝑥(𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡𝑡 ∙ 𝑧𝑡))

𝑑𝑡 + 𝑧𝑡

𝑇

𝑡=1

(3.0)

On the downside this condition furthermore jeopardizes the linearity of the model as it leads

to additional non-linear terms.

4.2 Numerical Experiment

The quantitative data will be collected by formulating a linear mixed-integer problem, which

incorporates the additional demand generation under marketing constraints, to represent the

new batch size optimization and submitting it to a numerical study composed of exemplary

data from a fictional online retailer specialized on perishable goods. The received data will

then in a second step be tested against a set of data collected by a standardized model. By

this means the hypothesis that an increasing amount of orders can lead to a higher market

coverage without causing additional costs will be tested.

This research creates a set of sample data based on assumptions for an online retailer

specialized in perishable goods, whose critical challenges are among others the “time

pressure due to perishability, the need for cooling and the related waste management

challenge” (Petljak, Zulauf, Stulec, Seuring-Stella & Wagner, 2018, p. 2). As such the fictional

retailer FreshBerry, as presented in section 2.4, serves as the foundation for the sample data.

To further simplify the experiment, the only product that FreshBerry offers are strawberries. A

good that in its nature decays rapidly. To reflect this the inventory costs, need to be set at an

elevated level and the ratio of inventory holding costs to fixed ordering costs will decrease. In

this example it is favorable to have lower inventory holding costs to fixed ordering costs ratio

as it increases it makes additional replenishments more likely.

Taking a closer look at the demand structure described in section 2.4 and at Table 1, one can

assume that the higher demand in period 1 is due to a cumulated demand. It implies that the

online retailer has a normal working schedule of 5 days a week. Traditionally such a working

schedule indicates that the retailer is working form Monday till Friday and takes the weekend

of. Plotting that demand into Figure 5, the blue line shows the example data of Table 1. The

red line is the actual customer demand. It assumes that demand will rise over the weekend

and therefore spreads the peaks of the blue line out over the period of Saturday to Monday.

Analyzing the customer demand curve over period of multiple weeks, one can discover a


17

repeating behavior. The green line shows a simplification of the customer demand into a sinus

curve. As it can be observed the green line follows the shape of the red line. Most noticeably,

the demand prediction on Thursdays seems to fall outside the scope of the sinus demand

curve.

As the previous visual analysis shows, a scenario with a high demand on and towards the

weekend and a lower demand throughout the week can be predicted accurately by a sinus

wave with the shape of 𝑦 = 𝑎 ∙ 𝑠𝑖𝑛(

(𝑥−ℎ)

𝑏)+𝑘

𝜋. The sample data will therefore follow this shape.

Using an offset z defined Gaussian distribution, the demand in each period will be further

randomized resulting in a variety of demand curves (Thisleton, Marsh, Nelson & Tsallis, 2007).

In a second step the previously generated sample data can be solved in the MILP model

described in section 4.1. The model and the data will then be translated into the open

programming language (OPL) and solved with the help of the IBM CPLEX Optimization

Solution’s linear problem solver on Linux Cluster.

Table 3: Decision Variables for Sample Data

Symbol Range Meaning

a To be defined Amplitude of the curve

b To be defined Horizontal offset of the curve

h To be defined Horizontal stretch of the curve

k To be defined Vertical offset of the curve

z [0, to be defined] Randomized offset according to Gaussian distribution

N 10.000 Sample data size

-20

0

20

40

60

80

100

120

140

Mo Tu We Th Fr Sa So Mo2 Tu2 We2 Th2 Fr2 Sa2 So2

Dem

and

Day

Perceived Demand Customer Demand Sinus Demand Curve

Figure 5: Sample Demand Structure


18

5. Plan of Work

Period Activity Description

1.09. – 20.10. Exposé Topic selection, research gap and

literature review

21.10. – 1.11. Research Design Development of MILP and creation

of sample data

1.10. – 3.11 Numerical Study Run model with sample data

4.11. – 8.11. Data Analysis Data analysis

9.11 – 9.12. Writing basis of the thesis Introduction, Literature Review and

Methodology

10.12. – 20.1. Final thesis Results, conclusion & revision


19

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