Supplier selection and multi-period demand allocation

Supplier Selection and Demand
Amol Singh
IIM Rohtak
Presentation Plan
Humanitarian Supply chain
Literature Review
Research Issues and objectives of the study
Hybrid Fuzzy, TOPSIS and MILP Methodology
Case Study
Results and discussion
Conclusion and future research directions
Humanitarian Supply chain
• The process of planning
• Implementing and
• Controlling the efficient and cost effective flow of
goods of humanitarian SCM network
• Includes procurement of goods
• Storage of goods and
• distribution of goods
in such a way that
• it alleviates the suffering of the vulnerable peoples
as efficiently as possible.
Commercial versus Humanitarian Supply Chains
• Characteristics of Commercial versus Humanitarian Supply Chains
Commercial Supply Chain
Humanitarian Supply Chain
Demand Pattern
Relatively stable, predictable. Demands.
occur at fixed locations in set quantities.
Demand is generated from random events that are unpredictable in
terms of timing, type, and size. Demands are estimated after they
are needed, based on an assessment of disaster characteristics
Inventory Control
Uses well-defined methods for determining
inventory levels based on lead time, demand
and target customer service levels
Inventory control is challenging due to high variations in lead times,
demands, and demand locations.
Lead Time
Lead time determined by the SupplierManufacturer-DC-Retailer-chain
Zero time between the occurrence of the demand and the need for
There exist methods for supply chain
network design.
Challenging due to the nature of unknowns (locations, type and size
of events, politics, culture) and “last mile” considerations.
Typically, well-defined, making use of
advanced technology
Information is often unreliable, incomplete or non-existent.
Historically, focused on resource
performance measures, such as maximizing
profit or minimizing costs.
Primary focus on output performance measures, such as the time
required to respond to a disaster or ability to meet the needs of the
disaster victims.
Strategic Goals
Usually, to produce high quality products at
low cost in order to maximize profitability
and achieve customer satisfaction
Minimize the loss of life and alleviate suffering.
Background of the Research work
• Purchasing is an important function of humanitarian supply
chain management.
• The demand is generated from random events that are
unpredictable in terms of timing, type and size.
• The literature focused on choosing the right suppliers and
allocating the appropriate demand.
• The opportunities in this research area include determining
the number of suppliers, managing supplier buyer supplier
relationship, sourcing strategies and outsourcing decisions.
• The main objective of the present research work is to address
the problem of optimal allocation of demand among
candidate suppliers in order to maximize the purchase value
of items.
Literature review
• Literature review shows that supplier selection is a multi-criteria
decision making process involving cost, quality, lead time reliability
• These criteria can be defined variously as buyers take into account
numerous conflicting factors.
• Dickson identified 23 criteria in his study of various supplier
selection problems.
• Butta (2003) presented a review of 154 articles and showed a
variety of methodology and approaches used for supplier selection.
• Traditionally, linear weighing models, total cost approach multiple
attribute theory, and total cost ownership used for supplier
• In last one decade researchers focused on optimization techniques,
multi-objective programming, AHP, DEA, AI, and hybrid approaches.
• Each approach has its own limitation.
Research Issues and Objective of the study
A critical review of literature brings to the fore some crucial issues for
• A humanitarian supply chain deals with the pool of supplies rather than a
single supplier.
• Supplier selection is a multi-criteria decision making problem
encompassing risk and uncertainties.
• Existing studies have not devoted much attention to this aspect of supplier
selection environment.
• Supplier selection models based on fuzzy set theory adopt the practice of
data defuzzified into a crisp one in the initial stage.
• This approach undermines the advantage of collecting the fuzzy data
(opinion of all decision makers).
• In literature multi-period demand aspect of the supplier evaluation
process have not received much attention.
Research Issues and Objective of the study
Taking cues from the critical research issues identified in the literature
review, the present study aims at addressing the following tasks.
• A complex problem of multi-period customer demand
allocation is considered and the rating of the suppliers is
integrated with the MILP process in order to maximize
the value of procurement.
• Qualitative and quantitative criteria applies in the
computation of the supplier rating.
• A hybrid Fuzzy TOPSIS algorithm tackles the risk of
supplier selection environment. It defuzzifies the fuzzy
data in the final step of the ranking process.
• The hybrid Fuzzy TOPSIS algorithm is integrated with the
MILP process for optimal multi-period demand allocation
among suppliers.
Hybrid Fuzzy, TOPSIS and MILP Methodology
The steps of methodology is explained below:
1. A group of k decision makers is identified and this group defines a set of relevant
criteria for supplier evaluation. The scores of the suppliers with respect to the criteria
and weight of each criteria is considered as linguistic variables.
Table : Linguistic variables for the rating of the suppliers
Very Poor (VP)
Poor (P)
Moderately Poor (MP)
Fair (F)
Moderately Good (MG)
Good (G)
Very Good (VG)
[(0, 0); 0; (1, 1.5)]
[(0, 0.5); 1; (2.5, 3.5)]
[(0, 1.5); 3; (4.5, 5.5)]
[(2.5, 3.5); 5; (6.5, 7.5)]
[(4.5, 5.5); 7; (8, 9.5)]
[(5.5, 7.5); 9; (9.5, 10)]
[(8.5, 9.5); 10; (10, 10)]
Table : Linguistic variables for the importance of the criterion
Very Low (VL)
Low (L)
Medium Low (ML)
Medium (M)
Medium High (MH)
High (H)
Very High (VH)
[(0, 0); 0; (.1, .15)]
[(0, 0.05); 0.1; (0.25, 0.35)]
[(0, 0.15); 0.3; (0.45, 0.55)]
[(0.25, 0.35); 0.5; (0.65, 0.75)]
[(0.45, 0.55); 0.7; (0.8, 0.95)]
[(0.55, 0.75); 0.9; (0.95, 1)]
[(0.85, 0.95); 1; (1, 1)]
2. Each decision maker assigns fuzzy score to the supplier against a criterion and similarly
assigns the fuzzy score to each criterion. These fuzzy scores are expressed in the fuzzy
matrix format.
Hybrid Fuzzy, TOPSIS and MILP Methodology
3. Compute average score of each supplier with respect to a criterion and
average weight of each criterion. The average scores of each supplier with
respect to a criterion and importance of each criterion are computed by using
the following relations:
4. The fuzzy scores computed in step 3 are in different units hence, these
scores are normalized by converting them into non-dimensional ratio for
comparison. Fuzzy scores xij = [(aij, aij’); bij; (cij cij’)] computed in step 3 are
converted into non-dimensional ratio by using the following equations:
, i = 1, 2, ………m, j ϵ Ωb
, i = 1, 2, ……….m, j ϵ Ωc
Hybrid Fuzzy, TOPSIS and MILP Methodology
5. Convert the normalized fuzzy decision matrix computed in step 4 into
weightage normalized fuzzy decision matrix (v = [vij]n×m , where vij = rij × wj) by
using the following relation:
vij = [(r1ij × w1j , r1ij × w1j’); r2j × w2j; (r3ij × w3j’ , r3ij × w3j)
= [(gij, gij’); hij; (lij, lij’)].
6. Determine positive ideal (A+) and negative ideal (A-) solutions by using the
following equations:
A+ = [(1, 1); 1; (1, 1)] for j ϵ Ωb
A- = [(0, 0); 0; (0, 0)] for j ϵ Ωc
7. Compute the separation measures (Euclidean distances) of each supplier
from the positive ideal (A+) and negative ideal (A-) solutions by using the
following relations:
Hybrid Fuzzy, TOPSIS and MILP Methodology
Where, D- (N, M) and D+ (N, M) are the primary and secondary separation
measures hence, the separation measure of each supplier (D+i1, D+i2) from the
positive ideal solution is computed by using the following equations:
Similarly, the separation measure of each supplier (Di1-, Di2-) from the negative
ideal solution is computed by using the following relations:
Hybrid Fuzzy, TOPSIS and MILP Methodology
8. Compute the fuzzy relative closeness of each supplier by using the each
pair of separation measure as computed in step 7. The fuzzy relative
closeness of supplier Ai is computed by using the following equations:
9. Compute crisp value of fuzzy relative closeness as computed in step 8 of
each supplier by using the following relation:
Hybrid Fuzzy, TOPSIS and MILP Methodology
10. Finally, the output of fuzzy TOPSIS model as computed in step 9 is
integrated with MILP. The multi-period optimal demand allocation model is
formulated by using the following equations:
for i = 1 to nth supplier and j = 1 to 4th quarter
Subject to:
• Budget Constraint
• Demand Constraint
• Delivery lead time constraint
• Supplier Capacity constraint
Case study
• 4 Potential suppliers were considered S1, S2, S3, and S4.
• These 4 suppliers were evaluated by four decision makers M1, M2, M3, and
M4 based on four criteria, namely quality (C1), price (C2), on time delivery
(C3) and consistency (C4).
• The expected demand, available capacity of suppliers, their lead times and
cost for the next 4 quarters are as follow; company wants to purchase at
least 5000 but less than 5500 units of an item in each quarter. The unit
material cost for supplier S1, S2, S3 and S4 are $9, $8, $10, $12 respectively
and the quarterly capacity of candidate suppliers are 3000, 3500, 2500,
and 3200 units respectively. The annual budget for purchasing the items is
$200000. The quarterly delivery times of suppliers are 2, 4, 6, 3 days
respectively. According to company’s policy, average delivery time should
not be more than 4 days.
Results and discussions
Table: Interval value of relative closeness and the final relative closeness of each supplier
Interval of relative closeness
Final score of suppliers
(0.51, 0.59)
(0.53, 0.60)
(0.55, 0.63)
(0.52, 0.60)
• The demand allocation to the suppliers and their optimum values calculated
by the Lindo software are Q11 = 2667, Q12 = 2898, Q13 = 0, Q14 = 2435, Q21 =
333, Q22 = 530, Q23 = 3000, Q24 = 2137, Q31 = 2500, Q32 = 2072, Q33 = 2500,
Q34 = 928, Q41 = 0, Q42 = 0, Q43 = 0, Q44 = 0. The value of the binary variables
are X11 = 1, X12 = 1, X13 = 0, X14 = 1, X21 = 1, X22 = 1, X23 = 1, X24 = 1, X31 = 1,
X32 = 1, X33 = 0, X34 = 1, X41 = 0, X42 = 0, X43 = 0, X44 = 0. Total purchase value
Z = 12528.
Results and discussions
• According to the relative closeness computed by single approach (i. e.
TOPSIS), supplier S3 is the best supplier. However, a total of 8000, 6000,
8000, and 0 units are assigned to suppliers S1, S2, S3, and S4 by using the
hybrid algorithm, which maximize the total value of the procurement.
• The maximum units are assigned to supplier S1 and S3, 8000 to each.
• This allocation of the units maximizes the value of procurement.
• On the contrary, the individual approach (i. e. TOPSIS) assigns the lowest
rating to the Supplier S1.
• In this context, it may be concluded that the hybrid approach improves the
efficacy of the individual approaches.
• However, the wide applicability of individual approach in literature is due
to its simplicity, ease of use and great flexibility.
• These observations support the literature findings to develop more hybrid
approaches for the supplier selection problems.
The present research work aimed at providing a new scenario to the supplier selection
problem pertinent to the humanitarian supply chain management.
Rating of the suppliers was computed and the demand allocated optimally among the
This should be encouraging to the SCM managers interested in improving the reliability
of the suppliers as well as quality of the items, maximization their value of
procurement, and switch over to the demand from one supplier to another supplier
when the first supplier is not capable of supplying the items due to unavoidable
The present research work will be helpful for the Humanitarian SCM managers who are
interested to reconfigure their supply chain under the failure of any supply chain
partner or in a changing environment.
The suitability of the proposed hybrid model to the supplier selection problem derives
from four distinctive characteristics: (i) its ability to capture qualitative as well as
quantitative criteria consistent with the real supplier selection environment, (ii) its
ability not only assign the rating of the suppliers but also they can assess the status of
all possible suppliers, (iii) its ability to capture the subjective estimates of the decision
makers in terms of linguistic variables, and (iv) its ability to optimal demand allocation
among suppliers.
The proposed hybrid model provides more objective information for supplier
evaluation and demand allocation among suppliers in supply chain.
• If a supplier declines to supply the units in a particular quarter then the
proposed model is supportive for the managers as they can adjust the
value of variables in the model as per their choices and determine the
optimal quantity for allocation among rest of the suppliers.
• The model provides flexibility to the managers for evaluation of the
different available alternatives in order to take a decision of optimal
demand allocation among the suppliers.
• The supply chain network is witnessing a changing business environment
due to government policies aimed promoting new small manufacturing
enterprises (SMEs) for intermediate parts and components. Hence, the
managers have an option to select the new group of suppliers and allocate
the optimal multi-period demand among new group of suppliers in order
to maximize their purchase value. In this context, the proposed hybrid
model would be beneficial for the managers to operate their supply chain
effectively and efficiently.
Future research directions
The study on supplier evaluation and multi-period demand allocation among
suppliers presented in this research paper could be extended in various ways.
• Firstly, more case studies could underline the practical usefulness of the
hybrid methodology as derived from the experimental results.
• Secondly, future research could consider the transportation cost during
demand allocation among suppliers.
• Thirdly, uncertainty of multi-period demand instead of fixed multi-period
demand in supplier selection problem could be taken up.
• Finally, research can be extended by developing more hybrid approaches
for uncertain multi-period demand allocation among suppliers.
Thank You

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