1. Warehouse operator selection by combining AHP and DEA methodologies

2. Abstract
In this paper we propose an approach for selecting the warehouse operator network by combining the analytic hierarchy process (AHP) and the data envelopment analysis (DEA).
With the AHP, the alternative warehouse operators can be evaluated by using multiple, both qualitative and quantitative criteria.
The outcome of the AHP analysis is a preference priority for each alternative operator describing the expected performance level.

3. Abstract
The DEA method can then be used to solve this multi-criterion problem by developing a DEA model for measuring warehouse operators’ efficiency by using the information of the AHP analysis and combining that with data concerning the process inputs.
The utilization of the proposed approach is demonstrated with an illustrative example.

4. Introduction
The distribution centre or warehouse location problem is a strategic level network design problem (Powers, 1989). The decision is long-term and the influence on the profitability of the company will remain for years.
Because outstanding service when distributing products has become one of the most important element in competition (Perkins,2004) and also because of increased computing capacity, it has been possible to introduce more qualitative aspects, e.g. customer service requirements or deliverer's own strategic views into the decision-making process in the warehouse location problem..
The validity of the input data has increased which helps to rely more on the outcome of the models.

5. The warehouse location problem
The most traditional quantitative framework for distribution network design problem is the cost minimization approach.
The focus of a more advanced warehouse location problem framework is on profit maximization.
In several papers, for example Meshkat and Ballou (1996) and Canel and Khumawala (1996), customer service elements have been included in the distribution design problem, in addition to cost and profit information.
Typically the service sensitive framework, includes elements like product availability, delivery time requirements and delivery frequencies.

6. Proposed approach Objective
Warehousing activities have been outsourced.
Preceded by an analysis to define the best potential location for the warehouse, to determine the feasible alternative warehouse operators and to gather extensive information on them.
Objective
Decide which warehouse operators of the feasible alternatives will be included in the distribution network of a company.

7. Preliminary analysis
Stating the objectives for the warehouse network design problem
Determining the best potential locations for the warehouses
Defining the alternative warehouse operators on the locations
Gathering and analyzing information concerning all aspects of their operations.

8. Defining the final evaluation problem
This phase involves defining the alternative warehouse operators among which the final selection will be made.
The most feasible alternative warehouse operators are defined based on the information gathered in the previous phase
the warehouse operators that do not satisfy the basic requirements set on, e.g. customer service and cost level are eliminated from the final evaluation.

9. The AHP analysis
the criteria used for analysing the alternative warehouse operators are defined, and the basic requirements concerning each criterion are defined.
the criteria are structured into an AHP-hierarchy.
priorities are derived for the criteria and the corresponding requirements.
The focus on AHP-model is on service-related criteria.

10. The DEA-analysis
The DEA-analysis uses the preference priorities derived in the previous phase as input.
These priorities are combined with cost information in order to define the most service/cost-effective warehouse operators.
The DEA-analysis is based on linear optimization and the analyses are performed separately to each warehouse.

11. Implementation and follow-up
After implementing the decided warehouse network in practice, the AHP-models can be used for supporting periodical reviews of the actual performance of the warehouse network.
The DEA-based analysis can also be used on a regular basis for analysing the actual service/cost-effectiveness of the selected warehouse operators.
New alternative warehouses can also be included very easily in the analysis.

12. Defining the problem Production Plant Customers/ Market Areas
Market Area Warehouse

13. AHP-based Analysis(1/4)
Identify two main service aspects of warehouse performance to be included in the analysis: reliability and flexibility.
Reliability : the ability to deliver products to the customers according to the target schedule, in right quantities, and without damage.
Flexibility : the ability of a warehouse to arrange urgent deliveries when needed, to the flexibility of the frequency of deliveries, to the ability to conform to any special requests set by the customer, and the ability to respond to changes in warehousing capacity needs of a customer.

14. TO PRIORITISE THE WAREHOUSE OPERATORS BASED ON SERVICE CAPABILITIES
The AHP hierarchy
TO PRIORITISE THE WAREHOUSE OPERATORS
BASED ON SERVICE CAPABILITIES
RELIABILITY
FLEXIBILITY
DELIVERY TIME
URGENT DELIVERIES
FREQUENCY
QUALITY
SPECIAL REQUESTS
QUANTITY
CAPACITY

15. AHP-based Analysis(2/4)
The priorities are set by comparing each set of elements with respect to each of the elements in a higher level.
A verbal or a corresponding 9-point numerical scale can be used for the comparisons,

16. AHP-based Analysis(3/4)
Use ratings instead of the actual decision alternatives at the lowest level of the hierarchy.
By deriving priorities for the ratings using pairwise comparisons, the customers can define what the real utility of each performance level is for them.
EX: Delivery time
Using the 1-9 scale to compare the options “within 2 h” and “within 4 h”, decide which of the two options is more preferable and define how much more preferable it is.

17. AHP-based Analysis(4/4)
Rating
Delivery time: The products are usually delivered within 2, 4, 6 or 8 h of the target delivery time.
Quality and quantity of deliveries: The accuracy of the deliveries with regard to the quality and quantity of products is usually over 99%, 95–99%, 90–95%, or below 90%.
Urgent deliveries: Urgent deliveries can usually be arranged within 1, 2–3, 4–5 days, or over 5 days of placing the order.
Frequency: The frequency of deliveries can be 3, 2 times a week, once a week, or once in 2 weeks.
Special requests: The performance is at the preferred, acceptable or unacceptable level.
Capacity: The ability of a warehouse to conform to capacity changes is outstanding, above average, average, below average, or unsatisfactory.

18. The priorities of the subcriteria

19. The DEA analysis
Uses the preference priorities derived in the previous phase as input.
These priorities are combined with cost information in order to define the most service/cost-effective warehouse operators.

20. The analysis of the alternative warehouse
Reliability
Fexibility
Time(h)
0.2829
Quality(%)
0.1782
Quantity(%)
0.1123
Urgdel(day)
0.2112
Frequency
0.0761
Specreq
0.0980
Capacity
0.0412
WH1 2
90-95
95-99 1
1/W
Acceptable
Above average
WH2 6
>99
2-3
2/W
Preferred
Below average
WH3 4
<90
1/2W
Unacceptable
Average
WH4
3/W
WH5

21. The DEA analysis - input and output
Alternative
Directcosts
Indriect
costs
Reliability
Flexibility
Time
0.2829
Quality
0.1782
Quantity
0.1123
Urgdel
0.2112
Frequency
0.0761
Specreq
0.0980
Capacity
0.0412
WH1
500
200
0.139
0.026
0.028
0.112
0.011
0.044
0.012
WH2
700
250
0.032
0.057
0.066
0.072
0.03
0.046
0.003
WH3
550
170
0.1
0.006
0.015
0.008
WH4
600
140
0.033
WH5
650
220
0.004

22. Efficiency of the warehouse
Alternative
Efficiency
WH1
1.000
WH2
WH3
0.824
WH4
WH5
0.950
The warehouses one, two and four got the maximum value in the optimization.
According to the DEA-philosophy
the efficiency of the selected warehouses does not mean that those warehouses are absolutely efficient but those are efficient among the other warehouses.

23. Conclusions
The proposed approach provides a systematic and flexible framework for selecting a warehouse network that maximizes the service/cost-effectiveness.
The proposed approach is strongly customer-driven as the customers are provided with the possibility of presenting their preferences for the alternative warehouses in an analytic manner.