This paper presents a supplier selection and order allocation (SSOA) model to solve the problem of a multiperiod supplier selection and then order allocation in the environment of short product life cycle and frequent material purchasing, for example, fast fashion environment in apparel industry. At the first stage, with consideration of multiple decision criteria and the fuzziness of the data involved in deciding the preferences of multiple decision variables in supplier selection, the fuzzy extent analytic hierarchy process (FEAHP) is adopted. In the second stage, supplier ranks are inputted into an order allocation model that aims at minimizing the risk of material purchasing and minimizing the total material purchasing costs using a dynamic programming approach, subject to constraints on deterministic customer demand and deterministic supplier capacity. Numerical examples are presented, and computational results are reported.
Most manufacturers nowadays face cutthroat competition in the everchanging market, which leads to establishment of network organizations. Supply chain management offers an integrated decisionmaking framework to administer such organizations. One of the key functions of supply chain management is the purchasing strategy. For a general producer, purchased items (e.g., raw materials) can account for 60% of total sales; purchasing shares normally account for 50% to 90% of total turnover in an industrial company [
Suitable suppliers can give a company a competitive edge and are instrumental to cost reduction and improvement in product quality. Various techniques have been presented to effectively evaluate and select suppliers. For order allocation problem, material purchasing managers firstly determine the optimal materials quantities purchased from each supplier during the purchasing period. An integrated mathematical programming model has then been established to solve supplier selection and order allocation problems based on various assumptions adapting to realworld production.
To deal with supplier selection, many methodologies have been proposed, including categorical methods, casebased reasoning systems [
For material purchasing process, after choosing suitable suppliers, order allocation is the next important stage to determine the optimal materials quantities purchased from each supplier, especially in a multiplesupplier environment. Various techniques have been developed to solve the optimal order allocation problem, including linear programming [
Based on the aforementioned discussion, few studies [
The main purpose of this paper is to develop a supplier selection and order allocation (SSOA) model, which is an effective multicriteria decisionmaking model, to handle material purchasing. Various features in fast fashion environment will be considered, including imprecise supplier evaluation measure, multiple order allocation objectives, varying purchasing prices, supplier capacities, and customer demands in different periods. The SSOA model will combine FEAHP with multiobjective dynamic linear programming technique to generate effective material purchasing solutions.
The rest of this paper is organized as follows. Section
To meet customers’ demands and make a healthy profit, a manufacturer must make an effective sourcing plan based on customers’ orders. In the textile industry, manufacturers always need to source common materials (e.g., white fabric) from suppliers over a planning horizon of different periods in order to encourage competition among suppliers and ensure access to a wide variety of goods or services. Therefore, selection of suitable suppliers and an optimal order allocation plan become crucial. This study proposes a model to handle optimal order allocation based on supplier ranking.
The assumptions of this study are as follows.
Each supplier can provide materials for manufacturers, and suppliers have different production capacities.
Manufacturers can get information on each supplier in terms of production capacity and price at the beginning of each planning horizon.
There is no inventory of materials, and manufacturers need to purchase all materials for production.
Let
Formula (
This paper proposes an effective supplier selection (ranking) and order allocation (SSOA) model based on the FEAHP and dynamic programming (DP). This model comprises an FEAHPbased supplier/criteria ranking process and a DPbased order allocation process (Figure
The processes of SSOA.
The details of the SSOA model are described as follows.
The AHP has been widely used to address multicriteria decisionmaking problems. It only requires a discrete scale from one to nine. However, human judgement is uncertain of criteria’s preferences. The linguistic assessment of human feelings and judgement is vague and cannot be represented reasonably in precise numbers. Hence, triangular fuzzy numbers are used to decide the priority of decision variables. Synthetic extent analysis is used to decide the final priority weights based on triangular fuzzy numbers.
A fuzzy set [
TFNs
The membership functions of triangular fuzzy numbers.
The FEAHP was originally introduced by Chang (1996). Some calculation steps are essential and explained as follows.
Let
Constructing a hierarchical structure with decision elements, decisionmakers are required to make pairwise comparisons between decision alternatives and criteria using a ninepoint scale (Table
Triangular fuzzy numbers.
Linguistic variables  Positive triangular fuzzy number  Positive reciprocal triangular fuzzy number 

Extremely strong 


Intermediate 


Very strong 


Intermediate 


Strong 


Intermediate 


Moderately strong 


Intermediate 


Equally strong 


The fuzzy synthetic extent value with respect to the
To obtain
To obtain
And the inverse of the previous vector is computed as
As
Equation (
The intersection between
The degree of possibility that the convex fuzzy number is greater than
Assume that
Via normalization, the normalized weight vectors are
The upward composition of these weights (from the lowest to the top level) generates the ranking scores (weights) of elements at the lowest level (i.e., suppliers) in fulfilling the topmost objective (i.e., suppliers ranking).
As discussed in the introduction, supplier ranking gives decisionmakers an effective technique to choose suitable suppliers. In this research, supplier ranking is implemented by the FEAHP method. The procedure is detailed as follows.
To define effective criteria for supplier selection, this research collects promising candidate criteria based on existing research results (Dickson 1966; Chan and Kumar [
On the basis of the candidate criteria selected, structured interviews are used to evaluate these criteria by three senior specialists, including a senior designer and two purchasing managers denoted by (
To evaluate suppliers more precisely, each selected criterion in Step
In this step, the FEAHP hierarchy model is built, and the weight of each supplier selection model is calculated. The developed FEAHP model, based on the identified criteria, subcriteria and subcriteria’s subcriteria, has five levels: goals, criteria, subcriteria, subcriteria’s subcriteria, and candidates. Figure
General hierarchy for supplier selection.
The FEAHP model (Figure
In order to obtain the priority weight of each criterion on each level, a second structure is done in a similar manner as Step
The fuzzy evaluation of criteria of the overall objective.





Weights  




































After obtaining the priority weight of each criterion and subcriterion, the third structured interview is designed and modified. This interview collects the weights of alternatives to identify the best suppliers.
The priority weight is determined for alternatives in this step. The competitive rivals that are supposed to be suppliers for manufacturers are compared by each subcriteria standard. After finding the local weight of each alternative in subcriteria, the global weight of each alternative in each criterion can be calculated. The evaluation of the global weight of each alternative can be obtained by multiplying the global weights of subcriteria and the local weight of each alternative. Based on the global priority, the weight of each alternative can be evaluated and summarized. An example of FEAHPbased supplier ranking is described in Section
As purchasing price is timevarying in the model, the cost objective is judiciously captured by the following dynamic value function:
To account for both objectives, a distancetoideal framework is employed to integrate the risk and cost objective functions, using the optimal values of individual objectives obtained earlier.
To incorporate the ideal values of risk and cost, the sum (weights) of deviations from such ideal values is minimized. Hence, a dynamic value function is derived as follows:
To validate the effectiveness of the proposed SSOA model, a series of experiments are conducted to obtain industrial data from an apparel manufacturer. The manufacturer needs to purchase a specified amount of raw fabric from 3 appropriate material suppliers for the production of its customers’ orders. The 3 suppliers have been selected from its
The FEAHP starts from the pairwise comparison matrices of five criteria (Table
The fuzzy evaluation of the attributes of criterion




Weights  

























The fuzzy evaluation of the attributes of criterion



Weights  
















The fuzzy evaluation of the attributes of criterion




Weights  

























The fuzzy evaluation of the attributes of criterion



Weights  
















The fuzzy evaluation of the attributes of criterion


Weights  









This paper presents the results of 6 experiments.
The criteria for selection of global suppliers are as follows:
overall cost of products
product quality
risk factors
supplier’s profile
service performance of suppliers
These criteria can be found in the hierarchical structure shown in Figure
Hierarchy for supplier selection.
The example of the pairwise comparison matrices shows that the fifth row and column attach importance to the row’s criterion relative to the column’s criterion (Table
Due to a good cost performance, the criterion for the first row is slightly preferred to the one on product quality, risk factors, and service performance of suppliers (the fuzzy values of
Calculate various decision alternatives of fuzzy numbers based on Section
After normalization of the values, priority weights of the main goal are calculated as
Different attributes are compared by each criterion separately with the same procedure as discussed above. The fuzzy evaluation matrices of attributes and the weight vectors of subcriteria are shown in Tables
Similarly, the fuzzy evaluation matrices of decision alternatives and the corresponding weight vector of each alternative with respect to the corresponding attributes are determined. The priority weights of suppliers with respect to each criterion are given by adding each supplier’s weight to each corresponding attribute’s weight. The results are shown in Tables
The fuzzy evaluation of the subcriteria of criterion




Alternative priority  

Weight  0.49  0.31  0.09  0.11  weight 
Alternatives  

0.51  0.51  0.69  0.87  0.57 

0.23  0.23  0.08  0.01  0.19 

0.26  0.26  0.23  0.12  0.24 
The fuzzy evaluation of the subcriteria of criterion



Alternative priority  

Weight  0.55  0.19  0.26  weight 
Alternatives  

0.42  0.49  0.53  0.46 

0.28  0.23  0.15  0.24 

0.30  0.28  0.32  0.30 
The fuzzy evaluation of the subcriteria of criterion




Alternative priority  

Weight  0.59  0.39  0.01  0.01  weight 
Alternatives  

0.51  0.53  0.69  0.68  0.52 

0.21  0.23  0.08  0.11  0.22 

0.28  0.24  0.23  0.21  0.26 
The fuzzy evaluation of the subcriteria of criterion



Alternative priority  

Weight  0.51  0.18  0.31  weight 
Alternatives  

0.39  0.49  0.51  0.45 

0.28  0.21  0.17  0.23 

0.33  0.30  0.32  0.32 
The fuzzy evaluation of the subcriteria of criterion


Alternative priority  

Weight  0.52  0.48  weight 
Alternatives  

0.39  0.35  0.37 

0.33  0.41  0.37 

0.28  0.24  0.26 
Finally, the priority weight of each supplier can be calculated by multiplying the weight of each corresponding criterion. The results are shown in Table
Demand information.
Period  1  2  3 

Demand  6  6  6 
The suppliers based on the criteria.
Final priority weights of the suppliers.
A real apparel manufacturer purchasing environment usually has the following four scenarios. (1) A manufacturer’s demand for common material is the same in all planning periods; in order to obtain orders steadily, suppliers reserve a certain capacity and offer a reasonable price. (2) Demands for common material are steady, but suppliers do not reserve a certain capacity; so, price and capacity fluctuate in different planning periods. (3) Suppliers’ prices are different throughout the planning period. (4) Suppliers’ capacities and prices are different throughout the planning periods.
After getting the weight score of each supplier and criterion in the first stage,
If the manufacturer entirely just focuses on minimizing cost alone, the risk will increase substantially by 215% than entirely focusing on minimizing risk. On the opposite extreme, if the manufacturer just entirely focuses on minimizing risk, this would raise its cost by 20% than just entirely focuses on minimizing cost only.
By applying the biobjective dynamic function, the tradeoff solution incurs at 13.9% and 94% higher than the objective of minimizing cost and minimizing risk respectively. These experimental results show that the proposed dynamic programming approach can generate a better tradeoff solution than entirely focusing on minimizing cost and minimizing risk alone. (Tables
Price and capacity information.
Supplier  Ordering price (per unit)  Capacity  

Period 1  Period 2  Period 3  

12  12  12  6 

10  10  10  6 

11  11  11  6 
Optimal order quantities with respect to minimum risk.
Period  1  2  3  Total risk  Total cost 


6  6  6  30  216 



Optimal order quantities with respect to minimum cost.
Period  1  2  3  Total risk  Total cost 


94.7  180  

6  6  6  

Optimal order quantity with respect to minimum cost and risk.
Period  1  2  3  Total risk  Total cost 


4  3  2  58  205 

1  1  

1  3  3 
After getting the weight score of each supplier and criterion in the first stage,
If the manufacturer entirely just focuses on minimizing cost alone, the risk will increase substantially by 141% than entirely focusing on minimizing risk. On the opposite extreme, if the manufacturer just entirely focuses on minimizing risk, this would raise its cost by 20.7% than just entirely focuses on minimizing cost only.
By applying the biobjective dynamic function, the tradeoff solution incurs at 9.2% and 77% higher than the objective of minimizing cost and minimizing risk respectively. These experimental results show that the proposed dynamic programming approach can generate a better tradeoff solution than entirely focusing on minimizing cost and minimizing risk alone. (Tables
Demand information.
Period  1  2  3 

Demand  6  6  6 
Price and capacity information.
Supplier  Ordering price (per unit)  Capacity  

Period 1  Period 2  Period 3  

12  11  14  5 

11  12  10  6 

9  11  10  4 
Optimal order quantities with respect to minimum risk.
Period  1  2  3  Total risk  Total cost 


6  6  6  30  222 



Optimal order quantities with respect to minimum cost.
Period  1  2  3  Total risk  Total cost 


5  72.24  184  

2  2  

4  1  4 
Optimal order quantity with respect to minimum cost and risk.
Period  1  2  3  Total risk  Total cost 


3  5  3  53.1  201 

3  

3  1 
If the manufacturer entirely just focuses on minimizing cost alone, the risk will increase substantially by 61.1% than entirely focusing on minimizing risk. On the opposite extreme, if the manufacturer just entirely focuses on minimizing risk, this would raise its cost by 12.2% than just entirely focuses on minimizing cost only.
By applying the biobjective dynamic function, the tradeoff solution incurs at 4.1% and 17.8% higher than the objective of minimizing cost and minimizing risk respectively. These experimental results show that the proposed dynamic programming approach can generate a better tradeoff solution than entirely focusing on minimizing cost and minimizing risk alone. (Tables
Demand information.
Period  1  2  3  4 

Demand  6  6  6  6 
Price and capacity information.
Supplier  Ordering price (per unit) 
Capacity 


period  1  2  3  4  

12  11  14  10  5 

11  12  10  11  6 

9  11  10  11  4 
Optimal order quantities with respect to minimum risk.
Period  1  2  3  4  Total risk  Total cost 


5  5  5  5  54.76  276 



1  1  1  1 
Optimal order quantities with respect to minimum cost.
Period  1  2  3  4  Total risk  Total cost 


5  88.21  246  

6  6  

6  1 
Optimal order quantity with respect to minimum cost and risk.
Period  1  2  3  4  Total risk  Total cost 


5  5  5  64.48  256  

2  

1  1  4  1 
After getting the weight score of each supplier and criterion in the first stage,
If the manufacturer entirely just focuses on minimizing cost alone, the risk will increase substantially by 28% than entirely focusing on minimizing risk. On the opposite extreme, if the manufacturer just entirely focuses on minimizing risk, this would raise its cost by 4% than just entirely focuses on minimizing cost only.
By applying the biobjective dynamic function, the tradeoff solution incurs at 1% and 16% higher than the objective of minimizing cost and minimizing risk respectively. These experimental results show that the proposed dynamic programming approach can generate a better tradeoff solution than entirely focusing on minimizing cost and minimizing risk alone. (Tables
Demand information.
Period  1  2  3 

Demand  11  9  10 
Price and capacity information.
Supplier  Ordering price (per unit)  Capacity  

Period 1  Period 2  Period 3  

95  95  99  4 

87  87  89  4 

93  91  91  6 
Optimal order quantities with respect to minimum risk.
Period  1  2  3  Total risk  Total cost 


4  4  4  90.69  2802 

1  

6  5  6 
Optimal order quantities with respect to minimum cost.
Period  1  2  3  Total risk  Total cost 


1  116.8  2706  

4  4  4  

6  5  6 
Optimal order quantity with respect to minimum cost and risk.
Period  1  2  3  Total risk  Total cost 


4  4  0  105.21  2728 

4  4  4  

3  1  6 
If the manufacturer entirely just focuses on minimizing cost alone, the risk will increase substantially by 32% than entirely focusing on minimizing risk. On the opposite extreme, if the manufacturer just entirely focuses on minimizing risk, this would raise its cost by 4% than just entirely focuses on minimizing cost only.
By applying the biobjective dynamic function, the tradeoff solution incurs at 1% and 15.7% higher than the objective of minimizing cost and minimizing risk respectively. These experimental results show that the proposed dynamic programming approach can generate a better tradeoff solution than entirely focusing on minimizing cost and minimizing risk alone. (Tables
Demand information.
Period  1  2  3  4 

Demand  11  9  10  12 
Price and capacity information.
Supplier  Ordering price (per unit)  Capacity  

period  1  2  3  4  

95  95  99  96  5 

87  87  89  90  4 

93  91  91  93  6 
Optimal order quantities with respect to minimum risk.
Period  1  2  3  4  Total risk  Total cost 


5  5  5  5  121.38  3950 

1  

6  4  5  6 
Optimal order quantities with respect to minimum cost.
Period  1  2  3  4  Total risk  Total cost 


1  2  160.29  3816  

4  4  4  4  

6  5  6  6 
Optimal order quantity with respect to minimum cost and risk.
Period  1  2  3  4  Total risk  Total cost 


5  5  5  140.43  3853  

4  4  4  4  

2  6  3 
After getting the weight score of each supplier and criterion in the first stage,
If the manufacturer entirely just focuses on minimizing cost alone, the risk will increase substantially by 20% than entirely focusing on minimizing risk. On the opposite extreme, if the manufacturer just entirely focuses on minimizing risk, this would raise its cost by 5% than just entirely focuses on minimizing cost only.
By applying the biobjective dynamic function, the tradeoff solution incurs at 1% and 9% higher than the objective of minimizing cost and minimizing risk respectively. These experimental results show that the proposed dynamic programming approach can generate a better tradeoff solution than entirely focusing on minimizing cost and minimizing risk alone. (Tables
Demand information.
Period  1  2  3 

Demand  11  9  10 
Price and capacity information.
Supplier  Ordering price (per unit)  Capacity  

period  1  2  3  1  2  3 

95  95  99  4  6  5 

87  87  89  4  7  7 

93  91  91  6  5  6 
Optimal order quantities with respect to minimum risk.
Period  1  2  3  Total risk  Total cost 


4  6  5  85.7  2818 

1  

6  3  5 
Optimal order quantities with respect to minimum cost.
Period  1  2  3  Total risk  Total cost 


1  103.5  2688  

4  7  7  

6  2  3 
Optimal order quantity with respect to minimum cost and risk.
Period  1  2  3  Total risk  Total cost 


4  2  93.2  2708  

4  7  4  

3  6 
This paper investigates the topic of multiobjective order allocation based on supplier selection in the purchasing stage with single material and multiple suppliers taken into consideration. A mathematical model for investigation is established, which considers minimizing the total cost and risk in all purchasing processes. These objectives are particularly useful for manufacturing companies to survive in a maketoorder environment and improve the performance of supply chain management.
The SSOA model comprises two processes, namely, an FEAHPbased supplier/criteria ranking process and a DPbased order allocation process. In the FEAHP process, the weight of each criterion and supplier is obtained. Based on their weights, the optimal order allocation solution is obtained using the DP technique.
The effectiveness of the proposed optimization model is validated by using real data from a manufacturing company. The experimental results show that the proposed model can handle order allocation effectively.
The proposed optimization model can handle order allocation based on supplier selection. Further research will consider the effects of various uncertainties on supply chain management, such as uncertain customers’ orders and possible material shortages.
The authors would like to acknowledge the financial support of The Hong Kong Polytechnic University under the RPUG project.