Multi-echelon Inventory Models

11

Abstract
This chapter describes a hierarchical, multilocation inventory system called
“multi-echelon” inventory system in which the stock is located at multiple
locations but belongs to the same system. In such a case an integrated approach
is necessary instead of treating each location of inventory in an autonomous
manner. Multi-echelon systems are complex in nature and will require to address
the strategic, tactical, and operational issues, which may be difficult to be
incorporated in a single model. Nested models combining a number of models
might become necessary. A base stock control policy with simultaneous trans-
mission of demand data to higher echelon can effectively handle the situation.
A multi-echelon repair-inventory system has been described for recoverable
items called as METRIC and MOD-METRIC.

Keywords
Hierarchical • Multilocation • Multi-echelon • Base stock control policy •
Repair-inventory system • METRIC • MOD-METRIC

11.1 Introduction to Multi-echelon Inventory Systems

Inventory models discussed so far assumed that the inventory is located at a single
stocking point from where demands are met and to which the replenishments are
added. In many large-scale problems, this assumption may not be valid as the
inventory is located at different storage points belonging to the same system. There
is often a hierarchy of location points among these inventory locations as a higher
location (echelon) supplies to lower locations (echelons). Since the inventory at all
locations is owned by the same system, it is more logical to treat all echelons and
each location at each echelon together rather than take an isolated view of the
system by treating each inventory location as an autonomous inventory. Taking a

# Springer India 2014 195

P. Vrat, Materials Management, Springer Texts in Business and Economics,
DOI 10.1007/978-81-322-1970-5_11
196 11 Multi-echelon Inventory Models

holistic view of the entire hierarchical locations and optimizing the entire inventory
in the system calls for modeling it as a “multi-echelon” inventory system. This
concept eventually led to developing the concepts of an integrated supply chain.
Alternative terminologies such as “multistage” inventory, “multilevel” inventory
system, “multilocation” inventory model, and hierarchical inventory problems have
been also used. Other terminologies such as “inventory-distribution” system,
“repair-inventory” system, multi-station system, and “arborescence” systems have
also been used. However, the term “multi-echelon” inventory system is more
commonly used and hence adopted in this work. The need to take an integrated
view of inventory problems also justifies the concept of “multi-echelon” inventory
models.

11.2 Structure of Multi-echelon Inventory Systems

Figure 11.1a–e shows some typical “multi-echelon” inventory systems. Figure 11.1a
shows a single-echelon, two installation system, where a source supplies to two
depots subjected to external demands. Figure 11.1b shows a two-echelon, three
installation system, where the central warehouse receives stock from some exogenous
source and supplies the same to second-level depots experiencing external system
demands. Figure 11.1c shows a series (in tandem) structure where preceding stage
supplies to succeeding stage and demands occur at the lowest level only. Figure 11.1d
shows a single source, multi-echelon arborescence inventory system, while Fig. 11.1e
shows a multi-source, multi-echelon system with transshipments. In general, the
structure of any multi-echelon inventory system depends upon the configuration
and arrangement of various echelons of the system with respect to each other and
can be portrayed as a directed network (Subash Babu 1980).
If the commodity flows are acyclic, i.e., can flow only in one direction, the
structure is called as “arborescence” or an “inverted tree” structure. In real-life
situations, the systems are quite complex and may involve transshipments among
various locations at the same echelon or in between any two echelons.

11.3 Need for a Multi-echelon Inventory System:

Concept of Supply Chain

In multi-echelon inventory systems, the items are stocked nearer the point of
consumption, rather than meeting the customer’s requirements directly from the
same source. Obviously, multi-echelon inventory systems are characterized by
higher levels of average inventory in the system but as a trade-off have lower
transportation costs, lower pipeline inventory, and faster response in meeting the
demand at the end-customer level. Single-echelon inventory systems have lower
inventory but higher transportation costs and are much simpler to analyze as
compared to complexity in modeling multi-echelon inventory systems. However,
11.3 Need for a Multi-echelon Inventory System: Concept of Supply Chain 197

a b Exogenous
Source
Exogenous
Source
Central
Warehouse

Depot 1 Depot 2

Depot 1 Depot 2 Depot 3

Demand Demand

Demand Demand Demand

c d
Exogenous
Source
Exogenous
Source

Depot 1
Central
Warehouse

Depot 2
Regional Regional Regional
Warehouse 1 Warehouse 2 Warehouse 3

Depot 3 1 2 1 2 1 2

Demand

Fig. 11.1 (a–e) Various structures of multi-echelon inventory systems

198 11 Multi-echelon Inventory Models

e
Production Production
Centre 1 Centre 2

Stocking Point Stocking Point

1 2

Regional Regional Regional Regional

Warehouse 1 Warehouse 2 Warehouse 3 Warehouses

1 2 3 4 5 6 Wholesales
whereohouse

1 2 3 4 5 6 7 8 9 10 11 12 Retail
Outlets
Demand Points

Fig. 11.1 (continued)

there are clear advantages associated with such centrally controlled hierarchical
inventory systems as follows:

1. It is possible to control understocking or overstocking at the individual locations

by means of redistribution, transshipment, returns, and disposals. A system’s
view is possible for inventory control.
2. Since information is centrally available for the entire system, a more effective
and efficient handling of emergencies is possible.
3. Since stock is located closer to point of consumption, a faster response to meet
the demand is possible.

A multi-echelon inventory system has to be viewed as a part of total logistics

planning to enable supply of goods from source to customer at the lowest overall
cost. In that context, what was earlier known as multi-echelon inventory system is
now contained in the concept of “supply chain management,” which will be
discussed later in detail in Chap. 20 in system-wide integration of flow of materials,
information, and money from the supplier to the customer.
In the design of multi-echelon inventory systems, the various decisions required
to be made include the design of the distribution network, number of echelons,
number of installation at each echelon, optimal location of each installation, size
11.4 Strategic, Tactical, and Operational Issues Involved 199

(capacity) of each installation, mode of transportation, design of inventory control,

and replenishment policies and procedures including the mechanism for meeting
emergencies, inventory rationing policies, inventory transshipment and redistribu-
tion, stock returns, and disposal policies. Hollier and Vrat (1976) have reviewed
these aspects extensively and compiled inventory models and policies to address
many such aspects in a very elaborate review report.

11.4 Strategic, Tactical, and Operational Issues Involved

Decisions concerning multi-echelon inventory systems can be categorized into

three types:

(a) Strategic – having long-term impact, wider scope, and high cost of error
(b) Tactical – in between the strategic and operational decisions
(c) Operational – having short-term impact, local scope, and errors easy to rectify

Strategic decisions include the design of network configuration such as the number
of echelons, number of installations, etc. Tactical decisions may include inventory
policies in the multi-echelon distribution network with the following decision variables:

(a) Inventory replenishment decisions involving procurement at the highest eche-

lon and production or repair at any level
(b) Mode of allocation, transshipment, and rationing of stock received from highest
echelon among lower echelon in order to meet the customer demands at the
lowest level

Operational decisions include day-to-day activities like routing and handling

routine problems such as priorities, breakdowns, queries and complaints, commu-
nication, expediting, progress follow-up, etc.
Hollier and Vrat (1976) classified various parameters required for design, oper-
ation, and control of multi-echelon inventory systems into four categories – uncon-
trollable parameters, structural parameters, controllable decision variables, and
measures of system performance as follows:

1. Uncontrollable parameters:
Demand characteristics
Supply source characteristics
Product characteristics
Lead time characteristics
Cost parameters
2. Structural parameters:
Echelon structures
Nature of control
Inventory policy
200 11 Multi-echelon Inventory Models

3. Controllable decision variables:

Strategic and tactical decisions outlined earlier in the section
4. Measures of system performance:
Total system cost
Customer service level
Average investment in inventories
Average system shortages
Average pipeline inventories

Figure 11.2 describes in a very elaborate manner the details in each of these
categories.

Multi-Echelon Inventory Systems

3. Controllable (Decision) 4. Measures of System

1. Uncontrollable Parameters 2. Structural Parameters
Parameters Performance

A. Demand Characteristics A. Echelon Structures A. Strategic Level Decisions A. Total System Cost

a. Deterministic demand a. Single-echelon-multi-installations a. Number of echelons/activities in

(i) Dynamic, (ii) Dynamic (time variant) b. Multi-echelon each echelon
b. Stochastic demand (i) Series structure-demand at lowest B. Customers Service
(i) Stationary demand distribution with known echelon, demand at any echelon; b. Optimal location of installation Level
mean, variance and nature of distribution, (ii) Parallel structure – single
(ii) Stationary unknown demand distribution, installation, multiple installation; c. Mode of transportation
(iii) Non-stationary demand. (iii) Hybrid structure – demand at lowest C. Average Investment
c. Nature of demand d. Central or individual control in Inventories.
echelon, demand at any echelon.
(i) Discrete of continuous,
(ii) slow moving or fast moving B. Nature of Control
D. Average system
B. Supply Source Characteristics Shortages
a. Centralized control B. Tactical Level Decisions
(a) Single source,
(b) Multiple source b. Individual control
a. Optimal procurement rules for E. Average number
the highest echelon of orders
C. Product Characteristics
processed/unit time
(a) Number of items b. Stock allocation rules
(i) Single , (ii) Multiple C. Inventory Policy Structures
(b) Nature of items c. Stock redistribution rules
a. with or without redistribution – F. Average Pipeline
(i) Recoverable,
within/between echelons d. Rules for meeting emergency stock
(ii) Consumable – Perishable or Non-perishable b. Return of excess stock to higher echelons supplies.
D. Replenishment Time c. Unmet demand
Characteristics (i) Lost sales, (ii) Back logging
d. Review
a. Types of lead times (i) Periodic (ii) Continuous
(i) Procurement lead time / resupply time e. Planning period
(ii) Redistribution lead time. (i) One period-myopic
b. Nature of lead times (ii) N-period-discounted, undiscounted,
(i) Zero, (ii) Significant – deterministic with state (iii) Infinite period-discounted,
dependence or state independence; negotiable; undiscounted.
stochastic with known or unknown distributions – f. Realization of stock ordered
dependent or independent of the state of the (i) Full (ii) Partial
system g. Replenishment of items
(i) Individual (ii) Co-ordinated
E. Cost Characteristics h. Type of inventory policy used
(i) Lot size reorder point (ii) (s, S)
a. Inventory holding costs (iii) (s, S) and (S-1, S)
(i) Linear, (ii) Concave, (iii) Convex i. Type of rationing/redistribution policy
b. Shortage costs j. Inventory location
(i) Infinite, (ii) Linear, (iii) Concave, (iv) Convex (i) Centralized, (ii) Distributed
c. Ordering costs
(i) Zero, (ii) Constant, (iii) Complex,
(iv) Time-variation set-up costs.
d. Depot holding costs
(i) Fixed, (ii) Operational
e. Transportation Costs
(i) Bulk quantity, small quantity, (ii) Constant,
quality dependent (iii) Trucking and local delivery
f. Costs trends
(i) Stationary costs, (ii) Time variant and
inflationary trend.

Fig. 11.2 Relevant parameters for multi-echelon inventory systems

11.5 A Simple Multi-echelon Inventory System: The Base Stock Control System 201

11.5 A Simple Multi-echelon Inventory System: The Base Stock

Control System

One of the earliest attempts to demonstrate the effect of concurrent sharing of

demand information at customer’s level with higher echelon was given in the
concept of “the base stock control system.” It indeed was precursor to what is
now called the “bullwhip” effect in supply chain management or what Forrester
called as “amplification effect” in production-inventory-distribution systems.
Figure 11.3a shows a simplified multi-echelon situation comprising of a central
warehouse supplying to a branch warehouse which in turn supplies to a retailer
which meets the customer demand. Each of these levels is treated independently
and takes its own decisions based on cost factors and service levels, predicted
demand based on information received from the next stocking point, and replenish-
ment lead time from the higher echelon.
Single stage information flow in Fig. 11.3a suffers from the information distor-
tion about demand as the forecasts are made at higher echelon resulting in small
changes in end-item demand leading to large oscillations in replenishment sizes and
inventory levels upstream. This phenomenon is now very popularly called “bull-
whip” effect in supply chains. The base stock control system addresses this by
making end-item demand information available at all stocking points as shown in
Fig. 11.3b. This enables each stocking point to make replenishment decisions based

a b
Supplier Supplier
Replenishment Information Replenishment Orders
2 weeks 2 weeks
(orders)

Central Central
Warehouse Warehouse

Information Replenishment 1 week

Replenishment 1 week Orders
(orders)

Branch Branch
Warehouse Wherehouse Demands
information
Replenishment 1 week Information Replenishment 1 week Orders
(orders)

Retailer Retailer

Sales Demands Sales Demands

Customers Customers

Fig. 11.3 (a) Information flow in sequential manner. (b) Information flow in base stock control
system
202 11 Multi-echelon Inventory Models

on actual end-item demand rather than replenishment orders from the next-level
downstream. With this, each stocking point can use single-echelon inventory
control policies with actual end-item demand information. If an (s, S) policy is
used, then S is called the base stock level, s is the reorder point, and Q is the order
quantity such that S ¼ s + Q.
In terms of physical operation, the stock status at each level is monitored as per
the following relation:

Inventory level ¼ ðon hand inventoryÞ þ ðorder on quantityÞ  committed supply:

In this, “on hand inventory” at a particular stocking point includes all of the on
hand stock at that point and at all stocking points closer to the customer as well as
any stock in transit beyond the stocking point closer to the customer. The
“committed” supply includes all customer demands received but not yet satisfied
at the end-item point. “Echelon stock” for stage j is defined “as the number of units
in the system which are in or have passed through stage j but have not yet been
sold.” From this, we can get the following:
Inventory level ¼ echelon stock + quantity in order. Once the inventory level is
known, then as per (s, S) policy, the ordering decisions are taken. It can be seen that
the base stock control policy is “pull”-type inventory control. However, in multi-
echelon inventory control, a push system can also be used in which, from the stock
received from external source at the central warehouse, a portion is kept and the
remainder is “pushed” down the echelon. How much to push to each level depends
upon the stock status at the central warehouse as well as at each branch warehouse.
Thus, a base stock control system, through concurrent information flow from retailer
to higher echelons, is an effective way to contain order fluctuations. More of it will be
discussed in Chap. 20 under “bullwhip” effect in supply chain management.

11.6 Multi-echelon Repair: Inventory System

The RAND Corporation conducted one of the most notable researches in the area of
multi-echelon repair-inventory system for the recoverable (rotable) items discussed
in Chap. 10. Sherbrooke (1966) developed a model called “METRIC” (Multi-
Echelon Technique for Recoverable Item Control). METRIC represented a
two-level parallel system with a depot and a number of bases, assumed (S  1, S)
policy, and employed stationary process approach.
The objective function of METRIC is to minimize the sum of expected back
orders on all items at lower echelon subject to a budget constraint. Mathematically
it can be stated as

X
n X
m  
Minimize Z ¼ B Sij ; Sio i ¼ 1 . . . n, j ¼ 1 . . . m
i¼1 j¼1
11.6 Multi-echelon Repair: Inventory System 203

X
n X
m
subject to Ci  Sij  C
i¼1 j¼0

where

Sij ¼ spare stock of item i at location j

Ci ¼ unit cost of item i (Ci > o)
C ¼ budget constraint
Xn X m  
Z¼ B Sij ; Sio ¼ sum of the expected back orders on all items at the lower
i¼1 j¼1

echelon.

The purpose of METRIC is to optimize system performance for specified level

of system investment. Muckstadt (1973) modified METRIC to develop
MOD-METRIC, which was an important extension of METRIC, where repair-
maintenance is done on modular basis. The problem of recoverable items was
considered important because Sherbrooke observed that recoverable (rotable)
items, though 8 % in number, were responsible for 58 % investment in
inventories.
Subash Babu (1980) studied a two-level repair-inventory system for a transport
corporation where the system structure is like any multi-echelon system but has a
feature of repairing internally a failed item, which in a way becomes an internal
source of supply. Chapter 10 had discussed problems of rotable spare provisioning
for a single location case. In this section a multi-echelon version of the rotable
spares provisioning is being presented.
Figure 11.4 depicts the structure of a two-level repair-inventory system studied
by Subash Babu in the context of a road transport corporation for determining the
optimal inventory of rotable spares (bus engine) at the central depot as well as at the
subdepots.
As a multi-echelon extension of rotable spares provisioning, the decision
variables are So, the optimal number of spare rotable engines at the central
depot, and Sj, the rotable spares inventory at the jth subdepot ( j ¼ 1. . ..n). When
a failed rotable is removed from the equipment (bus), a spare unit from the
subdepot’s own stock is fitted into it, if available. Otherwise, a requisition for a
spare is placed at the central depot. The central depot supplies a serviceable spare
to the subdepot, if available; otherwise, the demand remains backlogged till a
repairable, serviceable spare is made available from the central workshop. The
back orders result in downtime of the facility at the subdepot adversely affecting
the fleet availability.
Subash Babu (1980) assumed (S  1, S) inventory policy at all levels and major
repairs/overhauls to be done at the central workshop (repair facility). In case of
emergency, he considered expedited lead time at a higher cost of transportation to
204 11 Multi-echelon Inventory Models

= Storage points

Central depot

Serviceable
items

1 2 3 n-2 n-1 n
Sub-depots

Customer
service

Failed
items

Fig. 11.4 Structure of a 2-level repair-inventory system

reduce resupply lead time. The model minimized total expected system cost at both
echelons and each subdepot of the lower echelon. The costs included:

A. At the subdepot level:

1. Expected cost of removal and replacement per day
2. Expected cost of transportation under normal and emergency situations/day
3. Expected shortage cost/day
4. Expected holding cost/day
B. At the central depot level:
1. The expected holding cost
2. The expected repair cost

He developed an optimization model to minimize the expected total system cost

comprising of costs at the central as well as all the subdepots. The model was
illustrated with a case study with one central depot with a repair workshop and
20 subdepots serving a fleet of 2,000 buses in a metropolitan city in India.
Multi-echelon repair-inventory systems are too complex to be handled mathe-
matically if uncertainties of demand, repair, and lead times are incorporated. In
such a case, computer simulation such as the one developed by Subash Babu (1980)
can be employed for determining optimal rotable stock at central and subdepot
level. Further analysis involving optimal location of central depot, reduction of
repair turnaround time by increasing maintenance capacity, etc., can be studied.
11.8 Conceptual/Review Questions 205

Two-level system structure can be extended to a 3-level system structure which

may become necessary if the geographical territory being served is across a larger
area. Of course the model complexity will increase as the number of echelons
increase.

11.7 Chapter Summary/Concluding Remarks

This chapter described a hierarchical, multilocation inventory system called

“multi-echelon” inventory system in which the stock is located at multiple
locations but belongs to the same system. In such a case an integrated approach
is necessary instead of treating each location of inventory in an autonomous
manner. This concept of multi-echelon inventory system can be considered as a
precursor to a very topical subject of supply chain management which will be
discussed in Chap. 20 toward the concluding chapters of this book. Multi-echelon
systems are complex in nature and will require to address the strategic, tactical,
and operational issues, which may be difficult to be incorporated in a single
model. Nested models combining a number of models might become necessary.
Only elementary exposition of the subject has been included in this chapter.
Readers interested in more detailed work can follow up through the references
included. Two types of multi-echelon inventory situations are discussed in detail.
First a simple series structure comprising of a central warehouse – branch
warehouse – retailer supplying to meet customer demands is considered. The
risk of treating each location separately with sequentially transmitted information
is explained leading to amplification effect. A base stock control policy with
simultaneous transmission of demand data to higher echelon can effectively
handle the situation. The second situation of multi-echelon repair-inventory
system has been described for recoverable (rotable) items, and various cost
parameters relevant to modeling a repair-inventory system are listed. METRIC
and MOD-METRIC models are briefly described. A repair-inventory system of
transport corporation having 2-level system structure has been described in order
to determine optimal number of spare bus engines to be kept at the central depot
and each of the subdepots to minimize total expected system costs. Such models
being complex in nature may have to be simulated. The impact of optimizing the
location of central depot and compressing the repair time on inventory reduction
can also be studied with the help of such models.

11.8 Conceptual/Review Questions

1. Why are multi-echelon inventory systems important? What are the limitations
of treating each inventory location in isolation?
2. Describe different types of structures in multi-echelon inventory control. What
is an arborescence structure?
206 11 Multi-echelon Inventory Models

3. Discuss a base stock control policy. How does it prevent or reduce information
distortion of customer demand getting magnified as it moves upstream?
4. List strategic decisions relevant to multi-echelon inventory systems.
5. Compare “pull” and “push” strategies in the context of multi-echelon inventory
systems.
6. “Multi-echelon inventory systems” are forerunner to the concept of “supply
chain management” – critically examine this statement.
7. What is a repair-inventory system? Discuss a repair-inventory system structure
for recoverable spares in a road transportation system in a 2-level system
structure.
8. Discuss the trade-off in locating inventory in central depot vs. subdepots in the
context of a repair-inventory system.
9. What is the impact of expedited overhaul turnaround time on the inventory of
rotable spares in a repair-inventory system?
10. How does location of central workshop/central depot influence the total system
cost? Where should this location be?
11. What is METRIC? What is the objective function and constraint in METRIC
model?

11.9 Numerical Problems

1. Consider a serial structure of a 3-stage inventory system with the following

configuration:

Orders Orders Orders Demand

Central Branch
QS QC QB Retailer
Warehouse Warehouse Sales
Supplier Customers
4 Weeks 1.5 Week 1 Week

At present the demand occurs at retailer level, which puts orders to branch
warehouse, which in turn places orders to central warehouse. Central warehouse
places order to external vendor. The lead times are shown on the diagram above.
It has been suggested that a base stock control policy should be followed instead
which simultaneously transmits demand information to higher-level stages. It has
been estimated that the customer demand is normally distributed with mean of
25 units/week and standard deviation of 8 units/week. The order quantity for each
of these levels has been prescribed as QBranch ¼ 50 units, QCentral ¼ 100 units, and
QSupplier ¼ 300 units. Determine reorder points and base stock levels at each of the
three stocking points for a 0.05 probability of stockout in a replenishment cycle at
each level. If lead times are taken to be zero, does it change the situation?
11.9 Numerical Problems 207

2. Consider a two-level inventory system where both levels are owned by the same
organization with the following structure:

Supplier

Q1

Central Level 1
Warehouse

Q2 Q2 Q2

Branch Branch Branch

1 2 3 Level 2

Demand is assumed to be deterministic at 90,000 units/year and is equally

divided at the three branch warehouses supplied by the central warehouse.
Ordering cost from central warehouse to the supplier is `5,000/order, while
from branch warehouse to central warehouse it is `100/order. Item costs
`100 at level 1 and is imputed to cost `200/unit at branch warehouse. Fraction
of carrying charge is 25 % of the unit price/year. Analyze this situation to
determine Q1 and Q2 if there is zero lead time. If lead times are nonzero
(as normally the case is), how will your analysis change?
3. Consider a repair-inventory system in the context of a state road transportation
pertaining to a rotable item – gear box fitted into a bus. There are five depot
workshops and a central workshop with central store attached to it. A minor
repair of gear box can be done at the depot workshop, but a major repair/
overhaul can only be done at the central workshop. After major repair/overhaul,
the gear box is treated as good as new. After overhaul, it is deposited in the
central store to be shipped to the depot whenever a request is received. Minor
repair at a depot level takes 0.5 days on an average, but a major repair/overhaul
at central workshop takes on an average 5 days. Average lead time to send a
failed gear box to central workshop and receive a rotable gear box in working
condition from central store to a depot store takes on an average 1 day on each
leg of transportation. Repair time at central workshop as well as depot workshop
follows an exponential distribution. Failed gear box arrives at each depot at an
average rate of 2/day at the depot level and 5/day at central workshop. If a gear
box costs `25,000/per unit and carrying cost is 20 % of its value/year, find
reasonable stocking policy at the central as well as depot stores to improve
208 11 Multi-echelon Inventory Models

overall system performance. Assume any missing data. System structure is as

follows:

Depot

Depot

Central Spare Store

Depot
Workshop Central

Repaired
Gearbox Depot

Depot
Failed Gearbox

11.10 Case Study

SKIC Ltd. is a market leader in the kraft paper industry. It had been doing well
earlier, but in recent times, the company’s performance has taken a downturn.
A preliminary investigation indicated that the firm is incurring high inventory
holding cost, high transportation cost, and yet low service levels resulting in
frequent stockout occasions due to uncertainty of demand.
Initial diagnosis attributed this to the following causes:

1. SKIC Ltd. does not have a rational scientific inventory control policy and relies
on intuitive, manual procedures based on manager’s experience to determine
inventory levels and buffer stock. This results in ad hocism and nonoptimal
inventory planning.
2. Inadequate warehouse capacity due to a single warehouse catering to
47 customers. This is resulting in higher cost of transportation and longer lead
times. In order to resolve this, the management of the company has decided to
build three warehouses to be located at A, B, and C, but these will be operational
only by the year end. These three warehouses will be supplied by a central
warehouse which receives the paper products directly from the factory.

Rajeev, the director (materials management) of the company, knew that if the
company has to get back to its market leadership, it must optimize its inventory
management and do so in an integrated manner rather than treating each storage
11.10 Case Study 209

point in an isolated manner. He appointed Ashutosh, a materials management

consultant, to streamline the inventory management function in a coordinated
manner. Ashutosh had studied in his Master’s Program Advanced Materials Man-
agement Course and had exposure to multi-echelon inventory control. He decided
to address the problem from that perspective.
Ashutosh analyzed the present inventory control procedure and observed the
following steps being currently followed:

1. Get demand data of each product from marketing service section in the previous
period.
2. Approximately estimate the next month’s demand using his experience and the
previous month’s demand data.
3. Determine next month’s inventory level and safety stock by comparing them
with the last month’s inventory report.
4. Review inventory level every week.
5. Fill the product’s stock up to the inventory level planned.

The multi-echelon inventory system has the following structure:

Manufacturer Echelon - 0

Central Distribution
Warehouse Echelon - 1

Regional Regional Regional

warehouse warehouse warehouse Echelon - 2
A B C

24 Customers 6 Customers 17 Customers

SKIC Ltd. produces and sells 8 grades of paper which is further differentiated on
the basis of weight (BW) and size. Total product variety extends to 350 varieties of
paper. Ashutosh carried out a Pareto analysis of the past annual sales values and
found that 21 % of the product variety accounted for 75 % of the total annual sales
turnover. He identified top 65 product varieties and decided to focus on these to
evolve a more cost-effective inventory management system.
SKIC Ltd. required three major raw materials to produce these kraft papers:
imported long fiber pulp, bagasse pulp from its sister company, and waste kraft
paper blended in mix of imported and local waste paper. Ashutosh has been
210 11 Multi-echelon Inventory Models

assigned the following terms of reference to streamline the inventory management

system:

1. Examine if the central warehouse which is located in the same city as the
manufacturing plant is a right location to reduce lead times, pipeline inventory,
and total inventory in the system.
2. Compare the inventory and transportation costs in the present system of directly
supplying to 47 customers from the central distribution center with the proposed
multi-echelon system structure which will become effective next year.
3. Compare “pull” vs. “push” inventory strategies in the multi-echelon system
structure. Develop certain decision rules to advise on the inventory at each
location, under the push system.
4. Develop a coordinated replenishment policy with transshipment and safety
stocks in each of the warehouses for effective control of inventory.
5. Determine suitable review period for inventory control.

In the process of finding responses to these terms of reference, Ashutosh must

identify the data requirements and select an appropriate inventory model.
If you were Ashutosh, what report will you submit to Rajeev to improve the
performance of inventory management that will become effective when the three
regional warehouses become operational?

References
Hollier RH, Vrat P (1976) A review of multi-echelon inventory control research and applications,
Technical report. Department of Engineering Production, University of Birmingham,
Birmingham, pp 1–62
Muckstadt JA (1973) MOD-METRIC: a multi-item multi-echelon multi-indenture inventory
system. Manage Sci 20(4):472–481
Sherbrooke CC (1966) METRIC: a multi-echelon technique for recoverable items control. Oper
Res 16(1):122–141
Subash Babu A (1980) Optimal policies for spares in multi-echelon repair-inventory systems.
Unpublished Ph.D. Thesis, Mechanical Engineering Department, IIT Delhi