Determining an optimal warehouse location, capacity, and product allocations in a multi product 4 echelon distribution network

This study addresses the distribution network design problem in a complex 4-echelon supply chain system, which includes production factories, internal warehouses, external warehouses, an

DETERMINING AN OPTIMAL WAREHOUSE

LOCATION, CAPACITY, AND PRODUCT

ALLOCATIONS IN A MULTI-PRODUCT 4-ECHELON

DISTRIBUTION NETWORK

BY

LE THI DIEM CHAU

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF MASTER OF

ENGINEERING (LOGISTICS AND SUPPLY CHAIN SYSTEMS

ENGINEERING) SIRINDHORN INTERNATIONAL INSTITUTE OF TECHNOLOGY

THAMMASAT UNIVERSITY ACADEMIC YEAR 2017

DETERMINING AN OPTIMAL WAREHOUSE

LOCATION, CAPACITY, AND PRODUCT

ALLOCATIONS IN A MULT-PRODUCT 4-ECHELON

DISTRIBUTION NETWORK

BY

LE THI DIEM CHAU

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF MASTER OF

ENGINEERING (LOGISTICS AND SUPPLY CHAIN SYSTEMS

ENGINEERING) SIRINDHORN INTERNATIONAL INSTITUTE OF TECHNOLOGY

THAMMASAT UNIVERSITY ACADEMIC YEAR 2017

ABSTRACT

DETERMINING AN OPTIMAL WAREHOUSE LOCATION, CAPACITY, AND

PRODUCT ALLOCATIONS IN A MULTI-PRODUCT 4-ECHELON

DISTRIBUTION NETWORK

by

LE THI DIEM CHAU

Bachelor of Engineering (Industrial Engineering), Ho Chi Minh City University of Technology, Vietnam, 2014

Master of Engineering (Logistics and Supply Chain Systems Engineering), Sirindhorn International Institute of Technology, Thammasat University, Thailand, 2017

This study addresses the distribution network design problem in a complex 4-echelon supply chain system, which includes production factories, internal warehouses, external warehouses, and customers Furthermore, the problem considers multiple products, multiple periods, and two shipment methods to customers with deterministic demands Eleven factories with capacities ranging from 20,000 tons to over 700,000 tons per year produce various products Each product has many different quality grade and is packed in many package sizes and types, resulting in 696 different forms of finished products All products are shipped to internal warehouses first for initial packaging Then, it is either stored and shipped directly to customers (i.e direct shipment) or transferred to one of the external warehouses for storage and shipping to customers (i.e through distribution center) Customers include two groups that are domestic customers in 44 provicens of Thailand and oversea customers Domestic and oversea customers may receive products from both internal and external warehouses

In this network, all factories and internal warehouses are under a single ownership, whereas external warehouses are non-corporate-own Therefore, logistics cost regarding all product transfers are paid to other logistics service providers (transportation and warehouse) The company considers constructing a new external

warehouse that would be shared among the 11 factories for overflow products that are currently transferred to external warehouses Thus, the objective is to determine an optimal warehouse location and its capacity in order to minimize the total logistics cost, including transportation and warehouse costs Transportation costs are the total cost of transporting all products from factories to warehouses, and from warehouses to customers Warehouse costs consist of twelve warehousing activities at the warehouses and five activities for transferring from internal warehouses to external warehouses A mixed integer linear programming (MILP) model is developed to seek the best location and capacity for the new external warehouse A sensitivity analysis of important input parameters, including demand, unit warehouse cost, and unit transportation cost, is performed to gain a more robust optimal solution Finally, a cost comparison is made

to assess potential cost savings from the new warehouse based on the robust solution

Keywords: Warehouse location, Warehouse capacity, Distribution network design,

Mixed integer linear programming

ACKNOWLEDGEMENTS

First and foremost, I would like to express my deep gratitude to my advisor, Assoc.Prof Jirachai Buddhakulsomsiri, for his dedicated support of my study This research would have not been completed without him His patience, motivation, enthusiansm, and immense knowledge helped me overcome many obstacles and finish

my thesis timely Besides my advisor, I would like to thank the rest of my thesis committee: Assoc.Prof Chawalit Jeenanunta and Assoc.Prof Thananya Wasusri, for their constructive comments and overhelming encouragement, but also for the challenged questions leading to significant refinement of my wok Moreover, I also appreciate financial support via EFS scholarship program provided by Sirindhorn International Insititute of Technology (SIIT), Thammasat University Last but not least,

I would like to thank my parents for supporting me spiritually throughout the course of writing this thesis

Table of Contents

Signature Page ii

Abstract ii

Acknowledgements iv

List of Tables vii

List of Figures viii

1 Introduction 1

2 Literature Review 3

2.1 Number of supply chain echelons 4

2.2 Facility decision 5

2.3 Problem characteristucs 7

2.4 Most relevant studies and research gap 7

3 Problem Description 9

3.1 Distribution network 9

3.2 Supply chain members 10

3.3 Products 12

3.4 Demand 12

3.5 Product movements 13

3.6 Warehouse operations 14

3.7 Storage type 14

3.8 Transportation mode 14

3.9 Potential locations and capacities of the new warehouse 15

3.10 Cost structure 15

3.11 Assumptions 16

3.12 Input data 16

4 Mathematical model 17

4.1 Sets 17

4.2 Parameters 19

4.3 Decision variables 20

4.4 Objective function 21

4.5 Constraints 21

5 Result and discussion 26

5.1 Examples of input data and output 26

5.1.1 Example of input data 26

5.1.2 Example of output 29

5.2 Base case 37

5.2.1 Optimal logistics cost 37

5.2.2 Example of product flows in the current and future networks 37

5.2.3 Optimal product movements and allocations 38

5.3 Sensitivity analysis 41

5.4 Cost comparisons 42

5.4.1 The total cost comparison 42

5.4.1.1 The current and future network with 20,000 Tons 42

5.4.1.2 The current and future network with 60,000 Tons 43

5.4.2 Cost comparison of each factory 43

6 Conclusion and Recommendation 45

Reference 46

Appendices 50

Appendix A Input Data 51

Appendix B GAMs Model 307

Appendix C Output 320

List of Tables

2.1 Characteristics of the recent relevant studies 3

3.1 Information of plants 10

3.2 Number of products of each factory 12

3.3 Average inventory day of fast and slow moving products 13

5.1 Product master data 26

5.2 Customer demand 27

5.3 Warehouse cost 27

5.4 Transportation cost from factory to internal warehouses 28

5.5 Transportation cost from internal warehouse to external warehouse 28

5.6 Transportation cost from warehouses to customers 29

5.7 Amount of products from factory to internal warehouse 29

5.8 Amount of products from internal warehouse to external warehouse 30

5.9 Amount of products from internal warehouse to oversea customer 31

5.10 Amount of products from external warehouse to oversea customer 31

5.11 Amount of products from internal warehouse to domestic customer 32

5.12 Amount of products from external warehouse to domestic customer 33

5.13 Amount of products at internal warehouse 34

5.14 Amount of products at external warehouse 34

5.15 Amount of products transferred from internal warehouse 35

5.16 Opening new external warehouse 36

5.17 Total storage space of storage type at internal warehouse 36

5.18 Total storage space of storage type at external warehouse 36

5.19 The cost of each location 37

5.20 “Fast moving” and “ Slow moving” products 40

5.21 The total cost of the current and future networks 42

5.2 Cost comparison 44

List of Figures

3.1 The existing network 10

3.2 Forecast demand from 2018 to 2037 13

3.3 Activities at warehouses 14

3.4 Cost structure in the operation process 16

5.1 A case of the optimal distribution network 38

5.2 Optimal new warehouse location and capacity 41

Chapter 1 Introduction

Today businesses have to pay much attention to both investment and management of their supply chain The goal is to satisfy customer demand in the most efficient way, while maintaining acceptable level of responsiveness Strategic supply chain decisions regarding supply chain’s physical network structure are important factors affecting its competiviveness (Chopra, 2003) These decisions include location, capacity, and function of each facility in the network

Warehouses are an essential component of a distribution network because of their direct impact on the total logistics costs and customer services Warehouses are used as consolidated storage points that help to reduce the total network distribution cost, specifically, transportation cost Location of a warehouse directly determines distance from customers, as well as suppliers, both of which in turn affect the outbound and inbound transportation cost Warehouse size indicates the amount of inventory that

it can keep, and therefore, the inventory holding cost, material handing cost, utility cost, and other costs associated with inventory level Therefore, determining an optimal number of warehouses, their locations, and sizes in a distribution network is not only significant in terms of costs and customer service level, but also majorly influence the success and failure of many supply chains (Frazelle, 2002a)

This study involves a case study of determining an optimal location and size of

a new warehouse of one of the largest polymer distribution network in Thailand It consists of factories, internal warehouses (dedicated and shared), external warehouses and many customers, domestic and oversea The factories produce hundreds of products that are immediately transported to the respective internal warehouse for packaging Then, the products are either kept at the internal warehouse or transferred to be kept at external rent warehouses due to limited capacity of internal warehouse Thus, customer demand can be satisfied by both internal warehouse and external warehouse In the other hand, Factories and internal warehouses in this network, although operate independently, are under a single ownership, a large corporation However, external warehouse spaces are rented on a per storage unit per period basis Currently, the logistics costs of transporting to the external warehouses and storage rental are very

high Management has decided to build a new external warehouse that can be shared among factories Important decisions are the new warehouse location, its size, and product allocation The objective is to minimize the total logistics cost of the distribution network over a period of planning horizon A mixed integer linear programming (MILP) model is developed to find an optimal solution In addition, a sensitivity analysis on important input parameters including demand, unit transportation cost, and unit warehousing cost is performed to find a robust solution

The remaining contents of this thesis are as follows Chapter 2 contains a literature review that provides a synopsis about the characteristics and contributions of previous relevant research studies, which help identifying the research gap that our study aims to fill Capter 3 presents a comprehensive problem description, problem characteristics, data, and assumptions Next, chapter 4 shows a mixed integer linear program formulation Then, chapter 5 provides results and discussions, as well as sensitivity analysis Finally, conclusions are given in chapter 6

Chapter 2 Literature Review

Facility location problem is a critical aspect of a long term strategic planning in

a distribution network This is because it directly affects performance of a network, especially the total cost of satisfying customer demand The problem involves facility related decisions, such as location of warehouse, distribution center, or manufacturing plant that help to meet customer demand quickly ( Guha and Khuller,1999) The facility location problem has challenged many researchers in the past few decades, and there also are numerous dedications relating to facility location proble This chapter reviews relevant studies to give an overview of previous and more recent contributions

Approximately 30 studies are reported in the literature between 2006 and 2017 The problem characteristics are summarized to identify a research gap that is filled by our study These characteristics include the number of supply chain echelons, decisions, and other problem characteristics, as summarized in Table 2.1

Table 2.1 Characteristics of the recent relevant studies

2.1 Number of supply chain echelons

In the previous studies, the number of supply chain echelons ranges from two echelons to four echelons

 Two-echolon network structure: suppliers  customers (Wu and Zhang, 2006)

 Three-echelon network structure can be categorized as follows:

o An external supplier  wholesaler  retailer (Shu et al., 2015)

o Suppliers  wholesaler  retailer (Farahani et al., 2008; Zhuge et al., 2016)

o Suppliers  manufacturing plants  customers (Tuzkaya et al., 2009)

o Central warehouses  regional warehouses  customers (Afshari et al., 2010)

o Manufacturing plants  warehouses  customers (Sourirajan et al., 2009; Conceição et al., 2012; Kılıç et al., 2015; Sadeghi et al., 2017)

o Manufacturing plants  warehouses  retailers (Sadjady et al., 2012; Askin et al., 2014; Manatkar et al., 2016),

o Seaports  warehouses  stores (Hlayl et al., 2015)

o Suppliers  distribution centers  customers (Hamedania et al., 2013)

 Four-echelon network structure:

o Suppliers  manufacturing plants  warehouses  customers (Thanh et al., 2008; Bidhandi et al., 2009; Shankar et al., 2013; Shahabi et al., 2013; Izadi et al., 2014; Cortinhal et al., 2015)

o Suppliers  manufacturing plants  distribution centers  retailers (Serdar et al., 2016; Munasinghe et al., 2016; Loaizaa et al., 2017)

o Manufacturing plants  central distribution centers  regional distribution centers  customers (Hiremath et al., 2013)

2.2 Facility decision

Decisions related to facilities may include one to three of the followings: determining the facility location(s), capacity, and product-facility-market allocations For facility locations, all studies have a list of candidate facility locations, and the decision is to find either a single location or multiple locations to open

Among them, a single decision involves:

 Product allocation

o Tuzkaya et al (2009) used linear programming

o Shahabi et al.(2013) implemented mixed integer nonlinear programming

o Manatkar et al.(2016) applied multi-objective non-linear integer programming

 Facility location(s) and production allocation

o Wu and Zhang (2006) considered a single product problem using mixed integer programming

o Sourirajan et al (2009) and Hlayl et al (2015) implemented genetic algorithm for a single product problem

o Loaizaa et al (2017) used mixed-integer nonlinear programming for a single product

o Conceição et al (2012), Hiremath et al.(2013), and Sadeghi and Nookabadi (2017) applied mixed integer programming for multiple-product problem

o Kılıç et al (2015) considered multiple-product problem using two-stage stochastic mixed integer programming

o Hamedania et al.(2013) used mixed integer nonlinear programming for multiple-product problem

o Izadi et al.(2014) developed genetic algorithms for multiple-product problem

 Facility location(s) and capacity

o A multiple-product problem was considered by Amiri (2006), Sadjady et al (2012), Thanh et al (2008) These studies used mixed integer linear programming

o Zhuge et al (2016) used stochastic programming for multiple products problem

 Facility capacity and product allocation

o Bidhandi et al.(2009) and Serdar et al.(2016) applied mixed integer linear programming for multiple product problem

There are three previous studies that considered all three decisions: Shankar et

al (2013) and Askin et al (2014), which considered a single product problem using multi-objective hybrid particle swarm optimization algorithm, and genetic algorithms, respectively; and Cortinhal et al (2015), which considered multiple product problem using mixed integer linear programming

 Uncertain demand in a single period (Wu and Zhang, 2006; Amiri, 2006; Sourirajan

et al., 2009; Afshari et al., 2010; Sadjady et al., 2012; Shahabi et al., 2013; Hiremath

et al., 2013; Hamedania et al., 2013; Askin et al., 2014; Izadi et al., 2014; Shua et al., 2015; Loaizaa et al., 2017; Sadeghi and Nookabadi, 2017)

 Uncertain demand in a multiple period (Farahani et al., 2008; Tuzkaya et al., 2009; Kılıç et al., 2015; Zhuge et al., 2016; Manatkar et al., 2016)

2.4 Most relevant studies and research gap

The most related studies to this thesis are Shankar et al., 2013 and Cortinhal et

al (2015) with the main difference in the number of facilities to open However, there are other distinct differences in the structure of the supply chain Shankar et al., 2013 and Cortinhal et al (2015) considered a supplier  manufacturing plants  warehouses  customers; where our study considers manufacturing plants  internal warehouses (shared and dedicated)  external warehouses (shared)  customers An important aspect of our problem is that the ownership of the facilities, where manufacturing plants and internal warehouses, although operate independently, are under a single ownership, i.e a large corporation, while all existed, shared external warehouses are of different ownerships Thus, in this study, the corporate plans to open its own shared external warehouse to reduce the total logistics cost that it has to pay to other external warehouses Also, this problem is based on a real problem faced by the

industrial user, which contains 636 products in 20 periods of planning horizon This makes the number of variables in the model very large

Chapter 3 Problem Description

The problem under study is motivated by a real distribution network desgin problem of one of the largest polymer distribution networks in Thailand This chapter contains details of the problem characteristics and related input data These include distribution network, supply chain members, products, demand, product movement, warehouse operations, storage types, transportation modes, potential locations and capacity of new warehouse, assumptions, and transportation and warehouse costs

3.1 Distribution network

The polymer distribution network, is shown in Figure 1.1 The network contains four groups of members They are 11 factories, eight internal warehouses, six existing external warehouses, and geographically scatterred domestic customers in 44 provinces and oversea customers Firstly, the factories produce many different polymer products, all of which are supplied to their internal warehouses for packaging and potentially storage Due to limited capacity of the internal warehouses, excessive products are transferred, after packaging, to be stored at one or more external lease warehouses Thus, customer demand can be satisfied either from inventories at the internal warehouse or external warehouses The factories and internal warehouses, although operate independently, are under the same corporation Each year the cost that all factories pay to the external warehouses is significant Top executives at the headquarter have decided to build a new warehouse that will serve as an external warehouse to store some of the excessive items to save this cost Important decisions are location, its capacity, and the product assortment to be stored at the new warehouse

Note: F denotes factory, I denotes internal warehouse, E denotes external warehouse,

D denotes a set of domestic customers, and O denotes a set of oversea customers

Figure 3.1 The existing network

3.2 Supply chain members

This section introduces detail information of supply chain members The first two members are factories and their internal warehouses (Table 3.1)

Table 3.1 Information of plants Facility Characteristic Capacity

(Ton)

Int.W/H

& capacity (sqm) F1 High density polyethylene 250,000 I1 20,000

E6

D

O

Customer Factory

Internal warehouse

External warehouse

E3

Facility Characteristic Capacity

(Ton)

Int.W/H

& capacity (sqm) F6 Poly MethyMethacrylate 40,000 I6 2,500

F8 High density polyethylene 300,000

I8* 84,000

F9 Low density Polyethylene 700,000

F10 Linear low density Polyethylene 700,000

F11 Linear low density Polyethylene Expanded

capacity Note: F denotes factory, I denotes internal warehouse, and I8 denotes shared external warehouses among four factories (F8 to F11)

The 11 factories produce over 600 polymer products, which can be categorized

as high density polyethylene, low density polyethylene, linear low density polyethylene polypropylene, poly methymethacrylate, refined fatty alcohol and fatty alcohols, and bio-based material, with capacities ranging from 20,000 tons to 780,000 tons per year There are eight internal warehouse in which seven factories have their dedicated warehouses, and four others share one warehouse together Seven own internal warehouses have storage capacities from only 178 square meter (sqm) for small factory

to 20,000 sqm for large factory

In addition, one shared internal warehouse has a capacity of 84,000 sqm The next is external warehouses Three of the six external lease warehouses are small with range of capacity from 1,400 sqm to 7,000 sqm and dedicated to two factories due to their locations And the other three warehouses are one small with capacity of 15,000 sqm and two large with range of capacity from 20,000 sqm to 242,000 sqm They are shared among factories according to their locations Note that the three dedicated and one small shared warehouse have limited capacities, whereas the two large shared warehouses are assumed to always have storage space available These external warehouses charge storage cost on a per unit per period basis Finally, the customers can be separated into domestic customers in 44 provinces of Thailand and oversea customers, whose delivery destination is the largest seaport of Thailand

3.3 Products

Each of the 11 factories produces one type of polymer product Each polymer product has many different quality grades (over 100 product grades in total) These products are packed in more than 30 different package sizes and types, e.g 20-kg bag, 25-kg bag, 500-kg big bag, 1,000-kg big bag, drum, slab, etc These packages required different modes of storage and transportation For example, some products need to be packed and transported in specialized modes, e.g sea bulk, bulk truck, that are requested by the customers In total, there are 696 products resulting from unique combinations of the production factory, its quality grade and package type (Table 3.2)

Table 3.2 Number of products of each factory Factory Quality grade Type of

Future customer demands are forecasted for the period of planning horizon of

20 years, from 2018 to 2037 These include domestic and oversea demands Domestic demands are expected to continuously increase for the next few years (2018-2020), slowly grow for approximately five years (2021-2025), and become stabilized from

2026 to 2037 Oversea demands remain relatively the same between 2018 and 2019, slowly drop from 2020 to 2025, and stabilize in later years The forecast demand patterns are as showed in Figure 3.1

Figure 3.2 Forecast demand from 2018 to 2037

3.5 Product movements

Product movement are simply classified as fast moving and slow moving Among eleven factories, factories 5, 6, and 7 do not have slow moving products For the factories with both product movements, the number of SKUs and average inventory days are as shown in Table 3.1

Table 3.3 Average inventory day of fast and slow moving products

in terms of their product movements

3.6 Warehouse operations

The warehouse operations, both internal and external, include bagging, inbound loading and unloading with either forklift or labor, loading and unloading of various special packages (which required different material handling equipment), putting away, storage, retrieving, wrappings, and loading and unloading on the outbound

At internal warehouses (Figure 3.3), all products that are delivered from factories are bagged, and either put away and stored or transferred to one or more external warehouses For transferred products, they will be put in a bag in bagging area, then wrapped, moved, and loaded to be transferred to the external warehouses For products that are shipped to customers, activities at internal and external warehouse are similar The products are bagged before they are kept in storage When the products are ready to be delivered to the customers, at both internal and external warehouses, they are retrieved from storage, picked, palletized (if needed), wrapped, load and unload on

to delivery trucks (or other transportaion modes)

Figure 3.3 Activities at warehouses

3.7 Storage type

There are four types of storages that require different storage areas in the warehouses: normal bag and big bag storage (block stack) in conventional storage areas, rack, and tent Products and storage areas are preassigned according to the product grade, package, and value For example, normal and big bag storage mainly stored common products, storage on rack is for small products, and tent storage is for high value products These storage types must be taken into account, when considering the warehouse capacity

3.8 Transportation mode

There are 12 modes of transportation, which are two types of 10-wheel trucks, three types/sizes of 18-wheel trucks, bulk truck, two sizes of trailer trucks for container,

Move in Holding Move out Loading

Direct transfer Direct sale

pipe, barge, train, and customer pick-up They are used to deliver products from factories to warehouses (i.e pipe, 10-wheel trucks, 18-wheel trucks, bulk truck), and from warehouses to domestic customers (i.e 10-wheel trucks, 18-wheel trucks, bulk truck, and customer pick-up), and from warehouses to the seaport (18-wheel trucks, trailer trucks)

3.9 Potential locations and capacities of the new warehouse

There are four candidate locations for the new warehouse Locations 1 and 2 are close to the production factories, and locations 3 and 4 are close to the seaport For location 1, 2, and 3, the new warehouse can be built with one of the three capacity levels, which are 20,000 tons, 40,000 tons, and 60,000 tons In location 4, the new warehouse capacity is only 13,000 tons due to the limited land area

3.10 Cost structure

The total logistics cost has the cost structure as illustrated in Figure 3.4 using the flows that occur in the network, from factories to customers Each time that the products arae transported from factories to internal warehouse, internal warehouse to external warehouse, or from external warehouse to customers, the costs would incur according to the logistics activities or operations required These can be separated into transportation cost and warehouse cost, including operation cost and storage cost at internal warehouses, external warehouses, and the transferring product from internal warehouses

Mathematical formulation of transportation cost is showed as follows: transportation cost between two nodes is computed by multiplying unit transportation cost and an amount of product flow between two nodes Mathematical formulation of warehouse cost is built for each type of warehouse operation, whose cost is computed

by multiplying warehouse cost factors of an operation, unit operation cost of a product, and amount of products For example, bagging cost is computed from unit bagging cost and an amount of bagged products Storage cost is displayed by multiplying unit storage cost of a product and amount of stored product, and adjusted by number of product inventory day

Note: Int.W/H denotes internal warehouse and Ext.W/H denotes external warehouse

Figure 3.4 Cost structure in the operation process

 The new external warehouse uses the same warehouse costs in terms of cost structure and storage cost per unit as the existing external warehouses

 The period of planning horizon is 20 years, from 2018-2037

3.12 Input data

The input data that are used as input paramesters to the mathematical formulation of the problem consists of the following information: product property, warehouse property, and transportation property The detailed data are given in Appendix A

Transportation cost (THB/ton)

Operation cost (THB/ton):

loading, bagging, …

Storage cost (THB/ton) Storage cost (THB/ton)

Chapter 4 Mathematical model

In this chapter, mathematical formulation of the distribution network is described The mathematical model includes sets, parameters, decision variables, an objective function, and constraints Set, parameter, and decision variable, are declared

in section 4.1, 4.2, and 4.3, respectively They are used in the objective function and constraints, as described in section 4.4 and 4.5

4.1 Sets

Set notations are divided into two groups, one-dimensional sets and

multi-dimentional sets One-dimensional sets are the main indices that represent factories, warehouses, customers, periods, storages, and activities of warehouses Multi-

dimentional sets represent sets and parameters that require more than one index to specify the relationship For example, pairs of factory and warehouse are specified in a two-dimentional sets, sets of products and warehouse, set of transportation modes, and

so on All notations are presented as follow:

p : a product which is defined uniquely by factory, quality grade and package type

opi : operations in internal warehouse

ope : operations in external warehouse

opt : operations for transferring product from internal warehouses to external

warehouses

k : storage type

FI : a set of factory f and internal warehouse i ; with   f i ,  FI

FP : a set of factory f and product p ; with  f p ,   FP

IP : a set of product p and internal warehouse i ; with   i p ,  IP

I = {1, 2, 3, ,8} : Internal warehouse set

T = {1, 2, 3, , 20} : Time period set

E = {1, 2, 3, , 16} : External warehouse set, include existing six external warehouses

and 10 potential new external warehouses

'

E = {7, 8, 9, , 16} : potential new external warehouse set with E'  E The seventh,

eighth and nineth warehouses belong to location 1 with a capacity of 20 KTons, 40 KTons, and 60 KTons, respectively The tenth, eleventh and twelfth warehouses belong

to location 2 with a capacity of 20 KTons, 40 KTons, and 60 KTons, respectively The thirteenth, fourteenth and fiveteenth warehouses belong to location 3 with a capacity of

20 KTons, 40 KTons, and 60 KTons, respectively The sixteenth warehouse belong to location 4 with a capacity of 13 KTons

O = {1} : oversea customer set

D = {1, 2, 3, , 44} : domestic customer set

A = {1, 2, 4, , 13} : all warehousing operation set at internal warehouse

B = {3, 4, 8, 9, 10, 11} : all warehousing operation set at external warehouse

C = {1, 4, 5, 6, 10} : all warehousing operation set of transferring from internal

warehouses to external warehouses

K = {1, 2, 3, 4} : storage type set

4.2 Parameters

Parameters are divided into seven categories, which are transportation cost, warehouse operation cost, warehouse capacity, inventory day, customer demand, the production capacity, and number of allowed external warehouse Each category reflects

a dimension from which distribution network operation is affected Transportation costs are unit cost of transportation by mode per ton between two nodes They consist of cost from factory to internal warehouse, from internal warehouse to external warehouse, from internal and external warehouse to domestic and oversea customer Warehouse operation costs are unit cost of performing all warehousing operations for products stored and products transferred at warehouses Warehouse capacity is capacity of each storage type of warehouse Inventory day is the average number of days that a product

is kept in stock Customer demand provides annual required amount of products The production capacity is the annual amount provided of product provided by each factory The number of allowed external warehouse is required by each factory All notations are as described below:

C : Unit cost of performing all warehousing operations of for products transferred

from internal warehouse i to external warehouse e

There are four sets of decision variables consisting of product flow, total amount

of products stored in each warehouse, facility-to-open, and capacity

constraint (19-21) relate to keeping or expanding new warehouse capacity at multiple periods

Constraints (2) relate the flow balance between factory production capacity and product flow coming out of the factory The amount of each product flow from a factory

to its internal warehouse must not exceed the total amount of factory production capacity for that product In this network all products must be conveyed to the internal warehouse of factory first for bagging Subsequently, it is either stored at the internal warehouse or transferred to be kept at an external warehouse before being shipped to customers

Constraints (4) narrate the flow balance of stored products on the outbound of

an internal warehouse that amount of stored products must be shipped to either domestic

Constraints (8) display the flow balances from internal and external warehouses

to oversea customers The demand of oversea customers must be satisfied by the shipped products from all external warehouses and internal warehouse in each period

Constraints (9) display the flow balances from internal and external warehouses

to domestic customers that the total amount shipped must satisfy the domestic customers’ demand in each period

p E

Contraints (14) force that the total storage areas at external warehouse must not exceed its capacity by storage type

e, , k t CAPe, k, e E, k K, t T

Contraints (15) force that the total the flow from internal warehouses to external warehouse that is adjusted by inventory day must not exceed the capacity of external warehouse by storage type

programming (MILP) that has 14,265,161variables, 4,600 of them are binary, and 2,615,942 constraints The model is solved to optimality using IBM ILOG CPLEX with version 12.6.3.0 in General Algenraic Modeling System with version 24.7.3 (Appendix B  Open CD-B )

Chapter 5 Result and discussion

This chapter contains examples of input data and output, i.e values of decision variales from solving the mathematical model to optimality, and summary of the results These include base case, sensitity analysis, and cost comparisons Examples of input and output are given in section 5.1 Summary of the base case results including an optimal solution of the new warehouse location and its capacity are shown in section 5.2 Sensitivity analysis, given in section 5.3, is performed to evaluate the robustness

of the optimal solution Finally, cost comparison, which provides impact of the new warehouse on the current network in terms of the total logistics cost, is presented in section 5.4

5.1 Examples of input data and output

5.1.1 Example of input data

Product master data includes product p, storage type k, product inventory day I,

product movement (Table 5.1)

Table 5.1 Product master data

O1 F11 G91 P 14 M2 51 55 … 55 Warehouse cost includes the cost of activities at warehouses (Table 5.3)

Table 5.3 Warehouse cost W/H f Unloading

Cost

Bagging Cost … Loadingcost

W/H f Unloading

Cost

Bagging Cost … Loadingcost

Table 5.4 Transportation cost from factory to internal warehouses

2018 2019 … 2037 I1 E1 60 60 … 64

I8 E6 60 60 … 64

Table 5.6 Transportation cost from warehouses to customers

f i m p t

2018 2019 … 2037 F7 I7 M7 F7 G13 P 22 1555 2685 … 2678

XIE : Flow of product p from internal warehouse i to external warehouse

e using mode m in period t (Table 5.2)

Table 5.8 Amount of products from internal warehouse to external warehouse