Manganese catalyzed asymmetric transfer hydrogenation of ketones

Article abstract of DOI:10.1016/j.cclet.2020.10.023

The asymmetric transfer hydrogenation (ATH) of a wide range of ketones catalyzed by manganese complex as well as chiral P_xN_y-type ligand under mild conditions was investigated. Using 2-propanol as hydrogen source, various ketones could be enantioselectively hydrogenated by combining cheap, readily available [MnBr(CO)₅] with chiral, 22-membered macrocyclic ligand (R,R,R',R')-CyP₂N₄ (L5) with 2 mol% of catalyst loading, affording highly valuable chiral alcohols with up to 95% ee.

Full text of DOI:10.1016/j.cclet.2020.10.023

Scientia Iranica E (2011) 18 (3), 731–741
Sharif University of Technology
Scientia Iranica
Transactions E: Industrial Engineering
www.sciencedirect.com
Cost and inventory benefits of cooperation in multi-period and
multi-product supply
M. Sepehri
Graduate School of Management and Economics, Sharif University of Technology, Tehran, P.O. Box 18534, Iran
Received 7 March 2010; revised 25 October 2010; accepted 5 February 2011
KEYWORDS
Abstract Cooperation among supply chain members, both horizontally and vertically, has become the
norm in practice. Unlike traditional supply chains with members competing to reduce their individual
costs, the overall cost of the entire supply chain is minimized in a cooperative supply chain. The savings
from cooperation may be shared among the members, while a lower average cost and a lower cost
variation is materialized for individual members. The problem is formulated as an integrated flow
network and expanded to multi-period and multi-product, with the possibility of holding inventories in
a multi-stage, multi-member cooperative supply chain. Simulation results indicate an approximately 26%
reduction in total costs of the supply chain, utilizing this formulation over competitive setups. In a multi-
period chain, members may hold an inventory or use an inventory policy. As the holding costs increase, the
problem decomposes into a single period (just-in-time) again. The disturbing bullwhip effect disappears
in cooperative supply chains.
Multi-period supply;
Inventory reduction;
Flow network;
Cooperative supply;
Supply chain.
©
2011 Sharif University of Technology. Production and hosting by Elsevier B.V.
Open access under CC BY license.
1
. Introduction
The coordination and integration of key business activities
undertaken by an enterprise, from the procurement of raw
materials to the distribution of end products to the customers,
are done in the supply chain planning process [3]. E-business
simplifies communication between suppliers and customers.
But many suppliers still find it challenging to provide a
timely delivery of goods and services to their customers due
to resource limitations and geographical distances [4]. Most
supply chain members act locally, as they only have local
visibility and incentive. Most real-time supplier management
systems lack optimization engines or dynamic capabilities for
re-assigning supply allocations [5].
‘‘A supply chain is a system of organizations, people, technol-
ogy, activities, information and resources involved in moving
a product or service from supplier to customer’’, according to
Wikipedia [1]. The Council of Supply Chain Management Profes-
sionals [2] defines ‘‘Supply Chain Management encompassing
the planning and management of all activities involved in sourc-
ing and procurement, conversion, and all logistics management
activities’’. Importantly, it also includes coordination and col-
laboration with channel partners, which can be suppliers, in-
termediaries, third-party service providers and customers. Thus
supply chain management integrates supply and demand man-
agement within and across companies, and may share informa-
tion, inventories and cost savings as well.
Supply chain literature has developed in the past two
decades. Little is currently known about ways to achieve
control and cooperation in supply chain networks. Much
academic literature focuses on control and cooperation in
simple supply chains, with conclusions frequently based on
results gathered from considering one upstream and one
downstream company [6]. This research presents an integrated
optimization model to include all aspects of cost and capacity
for multi-period, multi-stage and multi-products, and also
include customer priority or product inventory and shortage.
The overall optimization problem is not yet addressed in the
literature for a cooperative or corporate supply chain [7]. Such
optimization models have not been implemented in real cases,
or used as an integrated real-time mechanism with advances in
electronic procurement.
E-mail address: sepehri@sharif.edu.
1
026-3098 © 2011 Sharif University of Technology. Production and hosting by
Elsevier B.V. Open access under CC BY license.
Peer review under responsibility of Sharif University of Technology.
doi:10.1016/j.scient.2011.05.020
The main idea of the proposed mechanism in this paper is
to formulate the cooperative supply chain as a flow network,

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M. Sepehri / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 731–741
and then solve an integrated linear programming model for
the corresponding flow network. This model considers the
general case of multi-member, multi-stage, multi-product and
multi-period with the possibility of holding an inventory.
A Cooperative Supply Optimizer System can actually be
an electronic hub which gathers and processes necessary
information on capacities and operation costs from supply
chain members. It guides chain members in ordering decisions
and providing a minimum overall cost for the entire supply
chain. Without such a concept and mechanism, members
make decisions on their order quantities based on their
local and accessible information, resulting in the non-optimal
performance of the entire supply chain and higher cost
variances for individual members.
Information about member behaviour may be used to
punish selfish members (i.e. members that tend to act based
on their locally-optimum preference rather than the solution
provided) with a reduction of their order fulfilment priority
factor for future periods. The paper extends previous studies
with limited scope to multiple-period, multiple-stage and
multiple-product cooperative supply chains. Obviously, most
real-world scenarios involve more intricate and complicated
characteristics, such as the stochastic nature of demand
or different inventory management systems. The proposed
preliminary mechanism may be broadened and studied with
the potential for more complex situations.
Zipkin [17] compared the competitive and cooperative inven-
tory policies in a two-stage supply chain [18] to show that com-
petition reduces overall efficiency.
Outsourcing has become a hot topic for many companies
recently. Although each supplier is a distinct business, the
clients persist in complete or high control over the timing
and mix of their required supply. Many suppliers enter into
partnership or alliance agreements, so that they can share the
benefits of serving customers better in a particular market [19].
Such cooperation can result in lower overall costs shared by
all business units [20]. Cooperation among members at various
stages or, in other words among a network of buyers and sellers,
is a major challenge in cooperative supply chains [21]. As the
number of businesses related to the supply, manufacturing and
distribution of products increases in practice, the cooperation
issue becomes immensely complicated [6]. In real-world
situations, most firms pay attention to optimizing separately
their production and distribution planning decisions. But these
local decisions limit possible improvement in overall decision
effectiveness and efficiency.
Supply networks are known and widely publicized phenom-
ena, especially in high-tech sectors, such as Microsoft or Genen-
tech, which pursue their network strategies through strategic
alliances or research and development joint ventures [22].
Multinational companies in steel, paper and automotive in-
dustries interact tightly with their suppliers, sub-suppliers,
distributors and customers to develop new technologies or
increase efficiency [23]. There are many examples of large firms
from several sectors that rely strongly on networks for their
rapid growth, such as Apple Computers, Benetton, Toyota, Corn-
ing and McDonald’s [24]. Effective supplier management is re-
garded in Brazil, for example, as crucial to differentiate oneself
from competitors in the long run [25].
Supply chain management includes contract management,
information and revenue sharing, quantity-discounts, coopera-
tive advertising, promotional rebate and franchising, quantity-
price-discounts, and buy-back contracts [6,26–28]. Li and
Wang [21] provided a survey of traditional cooperation mech-
anisms for supply networks taking an inventory control ap-
proach. Cachon [29] provided a study of coordination contracts
to show the increase in the number of members in supply net-
works; transforming traditional contracts into inefficient co-
operation mechanisms. Lee and Whang [30] described sales,
inventory, demand forecast, order status and production sched-
ules as different types of information sharing. They, as well
as Cachon and Fisher [31], clearly show the significance of in-
formation sharing in a two-level supply chain. However, lack
of information sharing aggravates the incurred costs in a sup-
ply chain with multiple members at several stages [32–34].
Managing and sharing business information includes Customer
Relationship Management (CRM), Supplier Relationship Man-
agement (SRM), e-marketplaces and e-chains [4,35–38].
Dudek and Stadtler [39] studied a two-member supply
chain. By defining members’ mathematical operational model,
they proposed a negotiation mechanism to reduce total costs.
Chen et al. [40] proposed a flexible, negotiation-based, multi-
agent system where new members can join in the supply chain
or its current members may leave. Fox et al. [41] developed
a high-level framework for supply chain functions, with the
idea of encapsulating these functions in corresponding software
agents. Consequently, Fox et al. [42] presented a general
approach to supply chain management operations covering
the planning and execution of actions with different types of
software agent.
Organization of the paper is as follows. The next two sections
review the literature on cooperative supply chains, limited to
publications relevant to this research. Section four is devoted
to the problem definition, including flow networks and the
assumptions associated with the problem definition. The next
section covers evaluation of the model, including assessment
of its performance, bullwhip and just-in-time effects. The last
section is the conclusion and an extensive reference section.
Appendices provide formulation models. A simplified case
example with numerical analysis is provided.
2. Cooperative supply chains
Two opposite models of supplier chains, cooperative and
non-cooperative, have emerged from both practice and aca-
demic research [8]. The traditional, ‘‘more common arm’s
length’’, approach to supplier management is characterized by
the buying firm’s efforts to avoid dependence on the suppliers
and to maximize bargaining power’’ [9]. The metaphor of the
firm as an ‘‘island in a sea of market relationships’’ [10] cap-
tures fully the distinctive feature of this standpoint. In contrast
to the competitive/non-cooperative approach, many firms work
closely with their suppliers as partners, developing and inte-
grating them for the long-term. Various studies showed that
such a strategy leads to better information sharing and, as a re-
sult, constantly improving quality, a product development cycle
and a highly efficient governance mechanism that minimizes
transaction costs [5,8,11].
With the spread of a cooperative perspective, the business
world’s view changed thoroughly, giving rise to a strategic
network of interdependence firms pursuing convergent inter-
ests and deriving mutual benefits [12]. This alternative per-
spective, as a reaction to the competitive approach, partly
spread out initially from Japanese JIT purchasing [13]. It empha-
sizes the empowerment of a collaborative network. Economic
interest, keeping with current relationships rather than en-
tering new ones, creates reputational concerns [14]. It keeps
partners aligned to the norms of trustworthy behavior [15,16].

M. Sepehri / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 731–741
733
A significant question is that; if supply chain members
do not trust each other completely, why should they accept
sharing their own strategically important information? Sahin
and Robinson [43] used a literature review in product flow and
information sharing in supply chains, showing an advantage
based on the degree of information sharing. Li [44] investigated
the incentives for members in a two-level supply chain, with
one manufacturer and several retailers sharing information
horizontally. He concluded that voluntary information sharing
is not rationally preferable, and examined conditions under
which information can be traded, restricting unplanned shared
information as much as possible.
Zarandi et al. [45] attempted to provide an agent-based
architecture based on fuzzy logic to create a responsive and
cooperative supply chain. Ding and Chen [46] considered using
negotiations in the return policy to coordinate a three-stage
supply chain, with a single member at each stage. Fink [47]
proposed using a mediator software agent to conduct a bilateral
negotiation process until both firms accept a contract. Lee
et al. [32,33] developed a stochastic, periodic, order-up-to
inventory model to manage a procedure for process localization
in the supply chain. They proposed an approach to operation
and delivery processes target market structures. Cachon and
Lariviere [6] considered a two-stage supply chain, including a
supplier and a retailer in which time is divided into an infinite
number of discrete periods. Consumer demand at the retailer
is stochastic, independent across periods, and stationary. The
system’s optimal solution minimizes the total average cost per
period.
Cohen and Lee [48] developed an aggregate model integrat-
ing material control, production and distribution sub-models
for establishing a requirement policy for materials in every fac-
tory in the supply chain production system. Barbarsoglu and
Ozgur [49] developed a mixed-integer mathematical model
with a centralized planning to address production and two-
echelon distribution decisions simultaneously. A Lagrangean
relaxation approach was used to decouple imbedded distri-
bution and production sub-problems in solving the resultant
large-scale problem.
Lee and Kim [50] extended the concept of Byrne and
Bakir [51] to propose a hybrid approach combining analyti-
cal and simulation models to solve manufacturing-distribution
planning problems involving multi-products and multi-periods
in supply chains. Ozdamar and Yazgac [52] developed an inte-
grated production–distribution model for operation of a multi-
national company in a central factory where products are
distributed to geographically distant warehouses. A hierarchi-
cal planning approach was adopted to make use of medium
range aggregate information with an optimal fleet size.
Gunnarsson and Rönnqvist [53] considered the integrated
planning of production and distribution for a pulp company.
Their solution is based on heuristics, with a one year planning
period and several time periods. The work presented by
Almansoori and Shah [54] was an attempt to design and
operate a deterministic, steady-state hydrogen supply chain
network, using a mathematical modelling approach. The model
was developed to consider the availability of energy sources
and their logistics and the variation of hydrogen demand
over a long planning horizon leading to phased infrastructure
development. The proposed model was formulated as mixed-
integer linear programming.
extensively [17,55–60]. Designing distribution networks [61–
63], facility location allocation [64–66], the facility capacity al-
location problem [67] and aggregate planning [4,68] may also
use Linear Programming. Mixed Integer programming provides
a more accurate description of different supply chain problems.
But reaching fast and exact solutions to the problem might be a
challenge [69].
3. Problem definition
A multiple period, multiple product, cooperative supply
chain is considered, with multiple members, at four stages
which are suppliers, manufacturers, distributors and retailers.
Each product is manufactured from a number of basic compo-
nents or raw materials ordered from the suppliers. A supplier
has a limited capacity for providing each basic component. Each
manufacturer may produce any product limited by its produc-
tion and delivery capacity or decided by its strategy for each
product. The distributors, within their capacities too, may pro-
vide products from the manufacturers to the retailers who rep-
resent a number of end customers. Forecast demand is available
for the next several periods, depending on accessibility of infor-
mation from the retailers for the next T periods.
The above definition removes three simplifying assumptions
in the current supply chain literature, i.e. the limited number
of members in supply chain stages, the limited number of
planning periods and a single-product. The model assumes the
prices for the components, and the products are constantly
independent of the chain performance. They are derived from
the overall competitive supply and demand and are not
controlled significantly by individual members. The problem
is thus concerned with minimizing total costs of providing
products to customers, including any lost sales or excess
capacity costs. The proposed formulation therefore aims to
minimize total operational costs for the entire supply chain,
including production, transportation, lost sales, inventory
holding and excess capacity components. Such a supply chain is
thus more competitive, by considering the overall cost to end-
customers.
It is further assumed that the supplies received by the
manufacturers are entirely used to produce the final products,
without any waste. Initially, the retailers are provided with
demand information for various product types at different
periods. Members conversely decide on the quantities and
sources of their orders. In practice, the distributors examine
how to provide products from the manufacturers to the
retailers to place orders. Therefore, distributors are considered
as unpreventable intermediate nodes, and no excess inventory
may remain with distributors at the end of planning periods.
Contrary to distributors, holding of inventory by retailers and
manufacturers is commonplace.
3
.1. Flow networks
The fundamental concept used in the proposed mechanism
is the flow network. A flow network is a directed graph in which
each node can produce, consume or pass a flow. Each directed
arc is a one-way conduit for the flow with a defined capacity.
Nodes are conjunction points of flow paths and can only pass
the flow (not store or consume it), except for two special types
of node. A source node has outgoing arc(s) to produce the
flow, and a sink node has only incoming arc(s) to consume the
flow. Furthermore, a flow network may have several sources
and sinks, rather than just one of each. Several studies [70,71]
provide comprehensive surveys of algorithms for solving flow
network problems.
Using linear programming techniques to formulate and ana-
lyze the various supply chain management problems has a long
record in the literature. Inventory management and produc-
tion–distribution planning problems use linear programming

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M. Sepehri / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 731–741
Table 1: Optimal flows of products.
(u, v)
f1(u, v)
f2(u, v)
f3(u, v)
(4, 6)
(4, 7)
(5, 6)
(5, 7)
(6, 8)
(6, 9)
(6, 10)
(6, 11)
(7, 8)
(7, 9)
(7, 11)
3
4
1
0
2
0
0
2
1
2
1
0
3
0
3
0
0
0
0
1
5
0
2
3
5
1
1
0
4
2
1
3
0
Table 2: Optimal flows of basic components.
Figure 1: Example of a supply chain with 3-commodities.
(u, v)
f1(u, v)
f2(u, v)
f3(u, v)
f4(u, v)
f5(u, v)
(
(
(
(
1, 4)
1, 5)
2, 4)
3, 4)
2
0
2
6
5
1
3
2
0
2
3
1
1
8
0
9
4
4
6
12
6
5
Flow network, G = (V, E), is a directed graph in which each
arc, (u, v) ∈ E, has a nonnegative capacity, i.e. c(u, v) ≥ 0.
If (u, v) ̸∈ E, and it is assumed that c(u, v) = 0. Two nodes
are distinguished in a typical flow network: source node, s, and
sink node, t. Every arc lies on some path from the source to
the sink. f (u, v), which can be positive, zero or negative is the
flow from node, u, to node, v. A flow is a real-valued function,
f : V × V → R, that satisfies the following properties:
5
15
19
(3, 5)
d18 = 3,
d19 = 2,
d110 = 0,
d111 = 3,
d28 = 1,
d29 = 5,
d210 = 0,
d211 = 0,
d38 = 2,
d39 = 3,
(
(
(
a) Capacity constraint: for all u, v ∈ V, require f (u, v) ≤
d
= 4,
310
c(u, v);
d311 = 2.
b) Skew symmetry: for all u, v ∈ V, require f (u, v) = −f
d311 demand for Product 3 at Retailer 11. A unit of lost sales, due
to shortage of inventory, is assumed to impose 25 units of cost
on the supply chain.
(
v, u);
∑
c) Flow conservation: for all u ∈ V − {s, t}, require
v∈V
f (u, v) = 0.
Using the proposed coordination mechanism, Network I
consisting of 66 decision variables and 87 constraints, and
Network II with 25 decision variables and 40 constraints
are formed. Note that these are relatively small Linear
Programming models. Optimal values of decision variables are
shown in Tables 1 and 2. The total cost of the model, with
member cooperation, is obtained at 659. This is compared to
a cooperative case where each retailer tries to obtain the least
costly shipment at 782, which yields 27.2% reduction in overall
supply chain cost for this small example.
For multiple source or sink nodes, the source node or sink
node may be replaced with a set of source nodes or a set of sink
nodes in the definition [71]. Associated with each commodity is
a demand, shipped through the network. The multi-commodity
flow problem covers the distribution of different commodities
from their respective sources to their sinks through a common
network, so that total flow going through each edge does not
exceed its capacity. The mechanism searches for a feasible
multi-commodity flow solution, i.e. a way of shipping the
commodities that satisfies the demands within the capacity
constraints. This problem is solved using either existing exact
algorithms or approximation heuristics [72,73].
3
.3. General formulation
The cooperative, multi-period, multi-product, supply chain
3
.2. A simple illustration
problem is formulated with four stages, as a flow network
with a linear program format (a detailed formulation is shown
in Appendix A). The model is described by Expressions (A.1)–
(A.13). Appendix A shows the objective function, showing the
total operation costs of the supply chain. It consists of eight
terms logically separated by parentheses. The first and second
terms indicate flow costs (i.e. purchasing and transportation
costs) in Network I and Network II, respectively. The 3rd term
represents the cost of lost sales. The 4th and 5th parentheses
represent the holding cost for the remaining inventory from
the previous period. Costs incurred in the supply chain from
the excess capacity in Network I and Network II are shown by
the two subsequent terms. Finally, the 8th term stands for the
production costs.
A numerical example for a simple single period case is
provided below to illustrate the proposed mechanism. Consider
a supply chain consisting of 3 suppliers, 2 manufacturers, 2
distributors and 4 retailers as shown in Figure 1. The supply
chain provides 3 types of product to the customers. It is
assumed that Distributor 7, for example, does not supply to
Retailer 10. The products are made of 5 basic components. The
bills of materials for the products are:
A1 = {1, 0, 1, 0, 2} ,
A2 = {0, 1, 0, 0, 1} ,
A3 = {3, 1, 0, 2, 0} .
In Figure 1, capacities and costs are shown on the arcs. Numbers
before/on the arcs are capacities. Numbers after/are costs
for different types of product or basic components. Demand
information for Retailers 8, 9, 10 and 11 is, as follows:
There are 12 constraint sets denoted by numbers (2) to
(13) in the model. First, three constraint sets (2, 3, 4) are
equivalent to the capacity constraint, skew symmetry and
flow conservation properties of flow networks (for Network
I), respectively. Constraint 5 guarantees satisfying demand

M. Sepehri / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 731–741
735
for the retailers. Constraint 6 is equivalent to the capacity
constraint of flow networks (for Network II). Constraint 7
guarantees satisfying demand from the manufacturers for
basic components to produce sufficient products. Constraint 8
assures sufficient production by the manufacturers. Constraint
9
1
assures the non-negativity of lost sales. Finally, Constraints
0, 11, 12 and 13 are non-negativity constraints on the values
of outflow and quantities of product.
Specific elements used in the model are described as follows:
Inventory is allowed to be carried from one period to the next,
incurring a holding cost for each particular item, depending on
the combination of demands, capacities and costs. In a later
section, analyzing the bullwhip effects of inventory at various
stages, an inventory policy is set to include carrying the current
month’s consumption to the next period. The rationale for
such a policy may be to deal with possible changes in future
demand. The holding cost may include the usual interest and
opportunity costs, storage and insurance expenses, in addition
to any possible damage or obsolescence cost, which are product
and location specific.
As this model formulates the cost function, assuming that
income and price are constant and given, any incremental
costs resulting from deviations from maximum fixed values
should be considered and added to the model. Excess capacity
costs are therefore considered, as expenses are incurred to
insure maximum capacity, regardless of its actual usage. The
cost of the capacity used is built into production costs, while
excess capacity counts for expenses incurred anyway from the
unutilized capacity. Lost sales costs similarly count for any
unmet demand due to capacity or cost limitations. Again, lost
sales costs are product and stage dependent. They may cover
the value of expected opportunity or net profit.
Another coefficient is introduced in the model as the ‘‘order
fulfilment priority’’ assigned to the rth retailer and the ith type
of product in period t (0 < PRir ≤ 1). This is defined as the
portion of a retailer’s demand to be met for a product type. It
is set proportional to the level of cooperation by the retailer.
Originally, it is set to 1.0 for all retailers, unless using total
capacities would not produce a feasible solution to meet total
demands. If that is the case, the order fulfilment priorities are
reduced proportionally or by some priority rules, and the model
is solved again. In the general model, this urges the retailers
to avoid selfish behaviour in pursuing their local individual
solutions and abide by the global supply chain. This allows the
manufacturers to forgo profit temporarily to urge cooperation
in the long term.
If supply chain members choose order quantities according
to the timed solution of the model, they will not have any
excess inventory. However, they may opt for holding inventory
because of their own forecast of future demands, or keep
safety stock due to cost or capacity considerations. Therefore,
Inv Iirt and Inv Iimt are not necessarily zero at the beginning
of the planning periods. Please note that for the sake of
presentation simplicity, the order and production lead-times
are not considered or set to zero. However, with small changes
in the general formulation, a positive but deterministic lead-
time may be considered at each stage for each basic component
or product type.
Figure 2: Performance ratio as a function of variety.
programming model, although its number of variables and
constraints may be large. Existing polynomial-time algorithms,
such as Karmarkar’s algorithm [74], can be used to solve it
efficiently. Upon solving the model and informing the supply
chain members of their respective flow values, they are able to
place orders accordingly for an optimal situation for the entire
supply chain.
4
. Evaluation
A simulation program is developed and used where results
show how the proposed solution would perform and be useful
in different situations. To evaluate the performance of the
solution, locally optimum behavior by individual members
is considered, as a benchmark comparison, to determine the
usefulness of the proposed mechanism (Appendix A). Consider
performance ratio I as an indicator for this purpose:
total cost without CSO
performance ratio I =
.
(1)
total cost with CSO
It is also determined how the performance ratio is dependent
on the variety of flows in the supply chain. k + p is a
metric to represent the variety of flows in the supply chain.
A sample simulated supply chain contains 70 suppliers, 10
manufacturers, 20 distributors and 50 retailers. Values for k and
p are set randomly, such that k < p and their summation equals
the intended value. A planning period of one year, or twelve
monthly periods, is considered during the simulation. Figure 2
depicts simulation results from the ILOG CPLEX 11.0 standard
mathematical programming solver.
The average value for the performance ratio is 1.354, or
6.14% reduction in total costs. Its performance ratio is always
higher than 1.332, and its increase is the variety in supply chain
increases. Therefore, the proposed model performs better and
is more valuable in cases of high variety supply chains.
2
In order to determine the effectiveness of the mechanism in
different sizes of the supply chain, the problem is simulated,
considering a supply chain providing 20 different products from
50 various components. Network size can be expressed as the
total number of supply chain members.
1
Network Size = S + M + D + R.
(2)
Additional constraints may specify the inventory policy,
which are not all included in the paper but are used in
the analysis. The assumption for the deterministic nature of
demand may seem a limitation in real cases. However, the
solution may be used as a base, and some safety inventory may
make up for the variation in demand. The model is a linear
During the simulation, random values for the number of
members are set, such that D ≥ M, R ≥ D and S ≥ M. Figure 3
illustrates how performance ratio varies with network size.
Considering the average value for performance ratio is 1.358,
it can be concluded that network size does not affect the
performance ratio.

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M. Sepehri / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 731–741
Figure 5: Impact of number of planning periods.
Figure 3: Performance ratio as a function of network size.
philosophy, due to the large sum of all holding costs. Under
such a system, only current requirements are produced and no
inventory is held. At this point, it would be insightful to evaluate
the significance of the number of planning periods used in
finding the supply chain solution. Obviously, a global multi-
period optimization is better in total costs than the sum of sub-
optimum single-period solutions. For an example here, a small
sample with three periods is used. Hence, consider performance
ratio II, based on the following definition:
total cost with CSO when T = 1
performance ratio II =
.
(3)
total cost with CSO T = 3
In this example, the same parameters and supply chain setup
as above are used in the simulation. As expected and also
depicted by the graph in Figure 5, a three-month planning
horizon is more cost effective in comparison to a single-month.
It varies again as the variety in the supply chain increases. In this
example, the average value of the performance ratio is 1.138, or
Figure 4: Performance ratio as a function of percentage misbehaving members.
1
2.13% reduction in total costs.
As the number of periods in the planning horizon increases,
Further, we investigate how the ratio (percentage) of
misbehaving members (those that do not behave in a locally
optimum style) affects the performance ratio. Consider a supply
chain with 70 suppliers, 10 manufacturers, 20 distributors and
the performance ratio also increases. However, the rate
of increase diminishes rapidly. For the above example, if
the number of periods increases from 3 to 6, the average
performance ratio in the simulation increases from 1.138 to
5
0 retailers in which 20 different products from 150 various
components flow.
1.174. Therefore, periods beyond the first few are insignificant,
Note that the number of misbehaving members at each stage
of the supply chain is appropriate to the relative number of
stage members, compared with the whole number of supply
chain members. Figure 4 depicts the effect of the percentage
of misbehaving members, i.e. PMisbehaving, on the performance
ratio.
even though the inventory is to be held.
The Just-In-Time (JIT) approach implies a lack of necessity
to hold inventory. It however requires accurate planning and
supply mechanisms [13]. In the proposed model, supply chain
members may hold inventory as available information about
future costs of the supply chain may indicate buying and
holding some items, which is more cost effective than buying
the items at a future period when they are needed. However,
a higher holding cost may cancel out the preference to hold
inventory.
According to simulation results, the performance ratio
deteriorates when the percentage of misbehaving members
increases. With PMisbehaving = 10%, the performance ratio is
equal to 1.23. When PMisbehaving = 30%, the performance ratio
falls to 1.07. A stable performance ratio of about 1.03 is
observed when PMisbehaving ≥ 40%. Thus a higher percentage of
misbehaving members leads to the lower effectiveness of the
proposed solution.
To determine the impact of holding costs, the supply chain
is simulated at different levels of total inventory costs, while all
other parameters of the model are fixed. To demonstrate the
JIT concept, the holding cost parameters of the supply chain are
set, so that no inventory is held. In other words, supply chain
members exclusively purchase components/products that they
need in the current period. It can be concluded from simulation
results illustrated in Figure 6 that increasing holding costs
results in a lower performance ratio II due to the impact of
higher inventory costs, as supply chain members would opt
to purchase their current needs and hold fewer inventories. In
fact, the point of no inventory (JIT) is reached quickly, when the
multiple components of holding costs commonly add up.
4
.1. Just-in-time supply chain
The concept of just-in-time purchasing, originally publicized
by the success of the Toyota Corporation in Japan, and
later accepted by corporations universally, requires that
requirements are ordered and delivered each period to match
the exact utilization of materials and products [13]. In fact,
inventory is considered evil and wasteful in the just-in-time

M. Sepehri / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 731–741
737
Table 3: Fluctuations of production levels along supply chain for small changes in demand [75].
Period Supplier Manufacturer Distributor
Stock Stock Stock
Retailer
Demand
Flow
100
Flow
100
Flow
100
Flow
100
Stock
1
00
00
100
100
100
100
100
100
1
100
95
95
95
95
95
1
1
00
100
80
100
90
100
95
2
3
4
5
6
20
180
60
60
120
90
80
100
95
90
95
95
95
95
6
0
6
0
80
100
90
95
95
95
1
20
20
1
100
95
95
95
95
95
9
0
9
9
0
5
95
95
95
95
95
95
100
95
95
95
9
9
5
5
95
95
95
95
95
95
95
95
supply chain components, which are difficult to deal with using
managerial intuition.
In a supply chain, although consumer sales do not seem
to vary much, there is pronounced variability in the retailer
orders to the wholesaler. Furthermore, the wholesaler order
quantities to the manufacturer, as well as the manufacturer
orders to the supplier, vary even more in time [76]. This
effect is a problem of cooperation, consisting of an amplifi-
cation of demand variability in the supply chain. Thus sup-
pliers receive more variable and unpredictable orders than
retailers [78]. The semiconductor equipment industry is, for ex-
ample, more volatile than the personal computer industry [79].
Multi-echelon supply chains do have an ‘‘uncoupling’’ effect on
the operations they connect, with some advantages for each in-
dividual operation’s efficiency. Unfortunately, they introduce
some ‘‘elasticity’’ into the chain as well, which often dramati-
cally limits the effectiveness of the chain as a whole [75].
To demonstrate the bullwhip effect, a simple supply chain
example with one product in four stages is used in Table 3.
Demand for the final product starts at 100, but reduces by
a small amount in period 2. All prior stages in the supply
chain work on the principle of keeping in stock one period’s
demand. The column ‘‘stock’’ shows the starting inventory
and the ending inventory for each period. A change of 5 in
retailer demand has produced a change of 10 in distributor
demand. Carrying the logic to the supplier’s column, the flow
has fluctuated by at least four times, as did the inventory levels.
The bullwhip effect may have a number of negative effects
in a supply chain, causing significant inefficiencies. The bull-
whip effect typically leads to excessive inventory investments
throughout the supply chain, as the parties involved need to
protect themselves against demand variations [80]. This prob-
lem leads to unnecessary inventory and decreased customer
service levels due to backorders or to inventory shortages/lost
sales [32,33]. By eliminating or controlling the bullwhip effect,
it is possible to increase supply chain profitability [81]. Tech-
niques to reduce the bullwhip effect, based on considering the
supply chain as a dynamic system and the application of control
techniques, have been summarized by Sarimveis et al. [82].
To quantify the bullwhip effect in a supply chain, a
simple measure is used as the standard deviation of flow
across multiple periods for a product at each stage. For the
simple example in Table 1, the standard deviation for retailer
demand in 6 periods comes to 2.04. The standard deviation for
supplier flow in 6 periods is amplified to 53.08. The bullwhip
Figure 6: Performance ratio II as a function of increase in the inventory costs.
However, from examining the detailed results, further
increase in holding costs will actually change the problem back
into independent single period problems, as members opt to
secure only what they need for the current period. It will in fact
occur when the cost of holding inventory exceeds the difference
of purchasing another cooperative member at that same stage.
This is another indication that lengthy forecasts are not needed
in cooperative supply chains, and the just-in-time system will
prevail.
4
.2. Bullwhip effect
Supply chains are often referred to as a pipeline of products,
which is somewhat misleading. Pipelines are supposed to
carry liquid at a reasonably ordered and constant rate, while
supply chains have their own dynamic behaviour patterns that
tend to distort the smooth flow of information up the chain
and the product moving down the chain [75]. The flow at
lower levels of the supply chain may be turbulent, even when
demand at the end of the chain is relatively stable. Small
changes in one part of the chain can cause seemingly erratic
behaviour in other parts. A phenomenon that is now well
known as ‘‘supply chain amplification’’ or ‘‘the bullwhip effect’’
suggests that the variability of orders increases as they move up
the supply chain from retailer to wholesaler to manufacturer
to supplier [32,33,76]. The first academic description of the
bullwhip phenomenon is usually ascribed to Forrester [77]
who explained it as a lack of information looping between the

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M. Sepehri / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 731–741
effect has grown more than 26 times. Simulation results
for non-cooperative supply chains, using the formulation in
Appendix B, also shows that the average standard deviation for
the supplier is more than 20 times that of the retailer for 6
periods.
In evaluating the deviations from the members of the
optimum allocation, it was shown earlier that the deviation
in competitive behaviour actually disappears in cooperative
supply chains. A more critical criterion for evaluating the
solution here is the effect of bullwhip phenomenon. For the
integrated production–distribution solution, with cooperative
information sharing among supply chain members, simulation
results verified that the average standard deviation of retailer
demand is closely reflected in supplier demand with only 4%
error, using the formulation in Appendix A. It may, therefore, be
argued that there is no bullwhip effect in the cooperative supply
chains.
relationship (i.e. organization u). The notation used in the model
is described below:
i:
j:
index indicating type of product, where
i = 1, 2, . . . , k;
index indicating type of component (or raw
material), where j = 1, 2, . . . , p;
t:
p:
index indicating time period, where t = 1, 2, . . . , T;
index for number of different types of
components/materials;
k:
index for number of different of types of products;
aij: quantity of component/raw material type j
necessary to produce a unit of product type i.
Ai = {ai1, ai2, . . . , aip}: set of components/raw materials to
compose one unit of a product type i (for example A4
=
{0, 2, 1} shows a unit of 4th type of products contains 2
units of component type 2 and 1 unit of component type 3.
Component type 1 is not needed for this product).
Sset = {sps, ∀s = 1, 2, . . . , S}: set of suppliers;
5. Conclusion
Mset = {manum, ∀m = 1, 2, . . . , M}: set of manufacturers;
Dset = {distd, ∀d = 1, 2, . . . , D}: set of distributors;
Rset = {retr , ∀r = 1, 2, . . . , R}: set of retailers.
Traditionally, the members in a supply chain compete
selfishly to minimize their own local costs. But the trend
has changed towards cooperative supply chains where the
members collaborate to minimize the overall cost for the entire
supply chain. This paper studies cooperative supply chains
versus competitive ones, to show that members gain a lower
cost average and a lower cost and inventory variance over time.
This is to assume that customer demand is known and the price
is fixed for all suppliers in a general case of multi-member,
multi-stage, multi-product and multi-period. Lost sales and
inventory are allowed for manufacturers or retailers to lower
the overall multi-period cost.
The original directed graph, G, representing the supply chain,
may be logically decomposed into two parts: Network I
which includes manufacturers, distributors and retailers, and
Network II which covers suppliers and manufacturers. In
Network I, products flow, where are considered as sources and
sinks of flow, while in Network II, components/raw materials
flow where suppliers and manufacturers are to take these
roles. However, a single integrated mathematical model which
involves both the Network I and Network II is solved.
A flow network is developed and solved for an integrated
supply chain framework, by using a set of linear programming
models. Considering operation capacities and costs for all
members in the supply chain, each type of product is produced
from a set of basic components and sent to the distributors who
in turn, ship to retailers to satisfy customer demands. Using
the solution from this model, the members are able to make
decisions that result in overall minimum cost for the entire
supply chain. From simulation results, the proposed solution
responds efficiently. It is also shown that only a small number
of periods are practically effective in the multi-period solution.
The problem becomes a single period (JIT), if inventory holding
costs increase. The bullwhip effect of competitive supply chains,
it is argued and exhibited, disappears, as members act in an
integrated competitive fashion.
Network I:
a flow network with nodes consisting of
Mset, Dset, Rset and arcs, which connect
these;
a flow network with nodes consisting of
Sset, Mset and arcs, which connect these;
set of vertices of Network I
Network II:
V1:
V2:
(
V1 = Mset ∪ Dset ∪ Rset);
set of vertices of Network II
(
V2 = Sset ∪ Mset);
V:
dirt :
set of vertices of directed graph G;
quantity of customer demand for product
type i from retailer r in period
t (r = 1, 2, . . . , R);
cit (u, v):
oit (u, v):
fit (u, v):
cjt (u, v):
capacity of arc (u, v) for flow of product i in
period t (in Network I);
cost of flow of each unit of product i through
arc (u, v) in period t (in Network I);
value of flow of product type i in arc (u, v)
in period t (in Network I);
capacity of arc (u, v) for flow of
component/material type j in period t (in
Network II);
cost of flow of component/material type j
via arc (u, v) in period t (in Network II);
amount of flow of component/material type
j via arc (u, v) in period t (in Network II);
quantity of production of ith type of
products in mth manufacturer in period t;
inventory level for ith type of product at rth
retailer at the beginning of the planning
period t;
Appendix A. Problem formulation
Consider a directed network graph, G = (V, E) where each
node represents a member of the supply chain and each
directed arc represents a potential relationship between two
members. Every directed arc (u, v) shows the possibility of
providing basic components/raw materials or finished products
from member u to member v. Arc capacities are given as
capacities for supply, production, distribution or transportation
from an organization to another for each period, depending
on the nature of a relationship. A cost factor is then assigned
to each arc, representing the costs of supply, production,
distribution and transportation, for each unit of a product or a
component. These costs are assigned to the first member in a
ojt (u, v):
fjt (u, v):
QPimt :
Inv Iirt :

M. Sepehri / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 731–741
739


T
k
−
− −
Inv Iimt :
Hirt :
inventory level for ith type of product at mth
manufacturer at beginning of planning
period t;
holding cost for rth retailer for a unit of ith
type of product inventory at end of planning
period t;
holding cost for mth manufacturer for a unit
of ith product inventory at end of planning
period t;
lost sale cost for rth retailer and every unit
of ith type of products in period t;
excess capacity cost corresponding to arc
+
−
+
−
+
(cit (u, v)
u,v∈V1 t=1
i=1

fit (u, v))ECCit (u, v)


Himt :
− −
T
−
p
(cjt (u, v)
u,v∈V2 t=1
j=1
LSirt :

fjt (u, v))ECCjt (u, v)
ECCit (u, v):
ECCjt (u, v):
UCimt :
(
u, v) in period t(u, v ∈ V1);


excess capacity cost corresponding to arc
(
T
M
k
−
− −
u, v) in period t(u, v ∈ V2);
QPimt UCimt
,
(A.1)
production cost for each unit of ith type of
product by mth manufacturer in period t;
order fulfilment priority assigned to rth
retailer and ith type of product in period
t(0 < PRir ≤ 1);
t=1 m=1 i=1
subject to:
PRirt :
fit (u, v) ≤ cit (u, v), ∀i = 1, 2, . . . , k,
∀u, v ∈ V1, ∀t = 1, 2, . . . , T;
(A.2)
(A.3)
z:
objective function representing the total
cost incurred by the supply chain.
fit (u, v) = −fit (v, u), ∀i = 1, 2, . . . , k,
∀
u, v ∈ V1, ∀t = 1, 2, . . . , T;
−
fit (u, v) = 0, ∀i = 1, 2, . . . , k,
Parameters cit (u, v), cjt (u, v), oit (u, v) and ojt (u, v), are given
as input data for the planning horizon. cit (u, v) is inter-
preted as the maximum feasible capacity of organization
u (i.e. distributing and transporting) for providing product
i and delivering it to organization v with cost oit (u, v);
oit (u, v) is the distribution/transportation cost. cjt (u, v) and
ojt (u, v) have similar interpretations, replacing products with
basic components/materials. dirt is an input parameter to the
model. LSirt , Hirt , Inv Iirt , Inv Iimt , ECCit (u, v), ECCjt (u, v) and
UCimt are also predefined parameters as inputs to the model.
These parameters may be available from previous period
data.
Parameters PRirt are initially assigned value one. If there is no
feasible solution for the model, it is reduced for some retailers
with less cooperative backgrounds and it solves the model
again. Application of PRirt and other parameters are clarified
further in the next section. Finally, fit (u, v), fjt (u, v) and QPimt
are decision variables. The proposed model for the whole supply
chain is as follows:
v∈V1
∀u ∈ Dset, ∀t = 1, 2, . . . , T;
(A.4)
−
fit (u, retr ) ≥ (dirt − Inv Iirt )PRirt
,
∀i = 1, 2, . . . , k,
u∈V1
∀
r = 1, 2, . . . , R, ∀t = 1, 2, . . . , T;
(A.5)
(A.6)
f (u, v) ≤ c (u, v), ∀j = 1, 2, . . . , p,
jt
jt
∀
u, v ∈ V2, ∀t = 1, 2, . . . , T;


k
−
−
−
fjt (u, manum) ≥
aij
fit (manum, v) ,
u∈V2
i=1
v∈V1
∀
j = 1, 2, . . . , p, ∀m = 1, 2, . . . , M,
∀t = 1, 2, . . . , T;
(A.7)
(A.8)
−
QPimt + Inv Iimt
≥
fit (manum, v),
v∈V1
∀
j = 1, 2, . . . , p, ∀m = 1, 2, . . . , M,


∀t = 1, 2, . . . , T;
k
T


−
− −
D
−
min z =
oit (u, v)fit (u, v)
dirt − Inv Iirt
−
fit (distd, retr
)
≥ 0,
u,v∈V1 i=1 t=1
d=1


p
T
−
− −
∀hi = 1, 2, . . . , k, ∀r = 1, 2, . . . , R,
+
ojt (u, v)fjt (u, v)
∀
t = 1, 2, . . . , T;
(A.9)
(A.10)
(A.11)
u,v∈V2 j=1 t=1
fjt (sps, manum) ≥ 0, ∀s = 1, 2, . . . , S,


R
k
T
−
− −
∀
∀
m = 1, 2, . . . , M, ∀ j = 1, 2, . . . , p,
t = 1, 2, . . . , T;
+
−
+
+
dirt − Inv Iirt
r=1 i=1 t=1





f (manu , dist ) ≥ 0, ∀m = 1, 2, . . . , M,
it
m
d
−
fit (u, retr
)
LSirt
∀d = 1, 2, . . . , D, ∀i = 1, 2, . . . , k,
u∈V1
∀
t = 1, 2, . . . , T;


R
k
T
fit (distd, retr ) ≥ 0, ∀d = 1, 2, . . . , D,
−
− −
(Inv Iirt Hirt
)
∀
∀
r = 1, 2, . . . , R, ∀i = 1, 2, k,
t = 1, 2, . . . , T;
r=1 i=1 t=1
(A.12)
(A.13)

M
k
T
−
− −
QPimt ≥ 0, m = 1, 2, . . . , M,
(Inv Iimt Himt
)
∀
i = 1, 2, . . . , k, ∀t = 1, 2, . . . , T.
m=1 i=1 t=1

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M. Sepehri / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 731–741
Appendix B. Description of locally optimum behavior
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member, v:
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UnfulfilledDemand = Demand
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a
Sort array S ascendingly based on o(t, v)
(
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[
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{
f (t, v) = min(UnfulfilledDemand, c(t, v))
[
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UnfulfilledDemand = UnfulfilledDemand − f (t, v)
t = t + 1 (i.e. going to the next, potential sources
with the lowest cost)
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}
.
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[
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first R1 do its sourcing, followed by R2, and finally R3 tries to
find its sources based on what is available. Finally, the cost of
the supply chain will be sum of the costs of all members of the
supply chain.
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Mehran Sepehri is Associate Professor at the Graduate School of Management
of Sharif University of Technology where he earned a B.S. degree in Industrial
Engineering. He completed his Ph.D. in Industrial Engineering and Engineering
Management at Stanford University.
Dr. Sepehri is an Editor of the Journal of Service Sciences. His teaching and
research areas include Operations Management, Supply Chain Management,
Project Management and Business Process Reengineering. His recent research
has been appeared in the journal of ‘Scientia Iranica’, and the ‘South African
Journal of Business Management’.
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