A STOCHASTIC MULTI-CRITERIA DECISION-MAKING ANALYSIS FOR A WAREHOUSE LOCATION SELECTION PROBLEM: A CASE STUDY

The problem of a warehouse location selecting which has a significant impact on logistics costs is an important decision problem based on the best choice of alternatives under multiple conflicting criteria. Multiple-criteria decision-making (MCDM) methods are used as a solution approach for the decision problems including several criteria. In this study, a new stochastic multi-criteria decision-making approach has been developed to solve the warehouse location selection problem (WLSP) in the stochastic environment which contains uncertain situations. In the proposed approach, the SAHP (Stochastic Analytic Hierarchy Process) method was used to calculate the weight of criteria, and the alternatives were ranked and evaluated by fuzzy MOORA (Multi-Objective Optimization by Ratio Analysis). The proposed approach is applied to warehouse selection problem of a supermarket chain located in Turkey. The results of the research indicated that A2 is the best alternative. It can be said that the proposed method can be applied to the real life problems because it found a suitable solution to the problem.


Introduction
In the globalizing world, many institutions and organizations are able to flow products, services and information easily by reaching the customer network thanks to effective communication opportunities and especially with the developments in the field of informatics. The intense and mobile information environment that has continued with globalization has led to the rapid development of a whole new economic structure. Within this economic structure, companies focus on reducing costs and ensuring customer satisfaction has led to the increasing importance of logistics. Storage is seen as the most important function in logistics processes. Warehousing processes have an important place in logistics systems as a separate operating activity as they Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [134] require efficient product movement in their structures and cause maximum space loss. This is the reason why storage is a critical point in terms of providing quality service and profit in the activities of enterprises.
Multi-criteria decision making (MCDM) techniques are the techniques that help determine the most appropriate option or options by considering the criteria that can affect each other among many options.
In this context, in this study, a model was created using SAHP and Fuzzy MOORA (F-MOORA) method for distribution network design which provides connection between warehouses and customer which are the most important elements of logistics distribution problem. Two methods are that SAHP and Fuzzy MOORA (F-MOORA) to rank alternatives was hybridized in this study. This hybrid method has not been used in the literature before, to our knowledge.
Considering the literature of warehouse location selection problem, it is seen that different methods are used; the article studied a successful application of multi-criteria Choquet integral to a real warehouse location selection problem of a big Turkish logistic firm [1]. Tabu Search algorithm was used for warehouse layout problem [2]. Particle swarm optimization was used an automobile spare part warehouse location problem [3]. It was presented a model that looks for the optimal allocation of goods in order to maximize the storage space available within the restrictions of the warehouse. Computational tests performed on a set of randomly generated and real warehouse instances showed the effectiveness of the proposed methods [4]. Rath and Gutjahr developed a ''math-heuristic'' for a three-objective ware-house location-routing problem in disaster relief [5]. A continuous approximation model was proposed for warehouse location. This model was applied to the real case of a company [6].

Materials and Methods
In this study, SAHP and F-MOORA techniques which are MCDM were used for a warehouse location selection problem.
There are many studies in different fields related to multi-criteria decision making (MCDM). The some of these studies: smart wristband selection [7], ERP deployment strategy selection [8], healthcare waste treatment technology selection [9], selection of on-site energy generation technology [10],evaluation of framed building types [11], strategic alliance partner selection in third-party logistics [12], logistics center location selection [13], the medical company selection [14], cargo company selection [15], location selection for underground waste containers [16], warehouse location selection [17], industrial engineering sector choosing [18], personnel selection [19], location selection for a yarn factory [20], data center location selection [21].
The stages of the proposed method for the appropriate warehouse location selection are described in Figure 1. In the first stage, criteria and alternatives are determined by the decision makers. In the second stage, criteria weights are calculated by using the SAHP technique. In the third stage, the most suitable alternative is selected by using the F-MOORA. In this study, F-MOORA method was used for evaluating the alternatives. The steps of F-MOORA methods are described as follows.

Stage 1. Data Collection
Determination of decision makers, alternatives and criteria Stage 2. Determine the criteria weights using SAHP Stage 3. Selection of the best warehouse location selection by Fuzzy MOORA method Step 1. Compare elements using the pairwise comparison scale.
Step 2. Convert imprecise preferences of experts into stochastic pairwise comparisons Step 4. Convert beta distributed pairwise comparisons to crisp values.
The median of beta distribution, , ] ] (1) , , values in the FDM, represents small, medium and large value in triangular fuzzy numbers for i th alternative in terms of j th criteria, respectively. Decision-makers have benefited from the scale in table 2 in the creation of the fuzzy decision matrix. Step 2: vector normalization is performed and normalized FDM is calculated [22].
Step 4: ranking is calculated for all alternatives in terms of cost and benefit criteria For benefit criteria [22].
Step 5: Performance points for all the alternatives are calculated. For performance scores, benefits and costs of criteria values for alternatives are defuzzified by using the vertex method [22].
Step 6: Alternatives are ranked according to their performance scores. Alternative which has the highest performance scores is preferred [23].

Application
In the first stage of the application, decision-team is created which consists of 3 decision makers. 17 criteria and four alternative locations which are determined by this decision team are presented Figure 2. In the second stage, SAHP technique was used to determine criteria weights. The steps of SAHP were taken from the work of [17].

Results and Discussions
Decision makers evaluated the criteria by using scale in Table 1. These values were converted to beta distribution by applying equality 5-7 to stochastic PCM. Table 2 presents stochastic PCM of decision maker 1 following the conversion to the beta distribution. The values in Table 2 were converted to net value by using equality 9-10. Table 3 presents net values.  PCM of decision makers are combined with the geometric mean method. Table 4 and Table 5 present combined PCM and normalized PCM, respectively.   Weight values of each criterion were calculated by applying calculation in AHP method to normalized PCM. Calculated weight values of the criteria are shown Figure 3. This value is used in weight found by calculating the F-MOORA.

Conclusions and Recommendations
In today's conditions, firms must constantly question their costs and be more careful when making decisions in order to survive in a globalized world. Hence, effective methods should be used for decisions to be taken and decision-making process should be carried out carefully.
A common problem that faced by decision makers is bounded rationalness. This means that decision maker's choices are limited. This lead to crisp as well as imprecise pairwise comparisons. Therefore, we propose a beta distribution to model the varying stochastic choices of the decision maker. By doing this, wider choice options were provided for decision makers. It is suggested that a combination of SAHP and F-MOORA can be used for different types of problems in future studies. Also, a combination of other MCDM techniques