European Journal of Operational Research 183 (2007) 148–161 www.elsevier.com/locate/ejor
Production, Manufacturing and Logistics
Development of an Air Force Warehouse Logistics Index to continuously improve logistics capabilities So Young Sohn *, Hong Kyu Han, Hye Jin Jeon Department of Information and Industrial Engineering, Yonsei University, Seoul, Republic of Korea Received 21 September 2005; accepted 21 September 2006 Available online 8 December 2006
Abstract For the effective operation of air power in the modern war, the logistics systems of Air Force warehouses need to be well-maintained. The best logistics system can be established through continuous improvements in logistics capabilities. Although there have been some studies on key performance indicators for logistics capability, they have neither considered the structural relationship among various influential factors, nor the feedback mechanisms in warehouse logistics capabilities. In this study, we propose a structural equations model (SEM) to develop an Air Force Warehouse Logistics Index (WLI). The concept of a Customer Satisfaction Index is used to assess the WLI for strategic improvement plans for various warehouse groups. It is expected that our model can be used to evaluate the logistics support capability of ROKAF (Republic of Korea Air Force) warehouses and contribute to warehouse modernization plans. 2006 Elsevier B.V. All rights reserved. Keywords: Air Force warehouse; Warehouse Logistics Index; Structural equations model
1. Introduction Logistics systems in Air Force warehouses play an important role in the effective operation of air power in the modern war. Logistics systems can and often do prove as deadly as any weapon on the battlefield (Cardinali, 2001). According to Rutenberg and Allen (1991), an adequate logistics system for the stocks of various materials is an essential condition to be able to withstand successfully the strain of battle. Currently, there is a popular SCOR (Supply Chain Operations Reference) which is often considered a current ‘‘standard’’ model for civilian sector logistics (Stephens, 2001). Geisler and Murrie (1981) mentioned the needs for a new class of models that can deal with large capital development programs at an early stage of military aircraft logistics planning. The best logistics system can be established through continuous improvement of the logistics capabilities. There have been various studies on the factors which affect the capability of warehouse logistics: material
*
Corresponding author. Tel.: +82 2 2123 4014; fax: +82 2 364 7807. E-mail addresses:
[email protected] (S.Y. Sohn),
[email protected] (H.K. Han).
0377-2217/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2006.09.073
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Fig. 1. Logistics flows in Air Force warehouses.
management (Nam, 2002; Wills and Wills, 1998; Tummala et al., 2006; Ayers, 2000), support for operations (Hatch and Badinelli, 1999; Napolitano, 2001), facility management (Wills and Wills, 1998; Brooks and Wallace, 1989; Fleischmann et al., 1997), manpower management (Graham et al., 1994; Ellinger, 2003; Thornhill and Saunders, 1998), quality management (Holcomb, 1994; Mentzer, 1993; Sohail et al., 2004; Anderson et al., 1998), logistics information systems (Brooks and Wallace, 1989; McClure, 1997; Lau et al., 2004). However, previous studies have neither considered the structural relationships among these factors nor paid attention to the feedback mechanisms in warehouse logistics capabilities. Note that there have been some studies on key performance indicators for JIT (Just-In-Time) (Fullerton and McWatters, 2001), Information Technology (Gunasekaran and Nath, 1997), ILS (Integrated Logistics Support) (Geier and Vilsmeier, 1988; Strain and Preece, 1999) and BPR (Business Process Reengineering) (Gunasekaran and Nath, 1997; Teng et al., 1996). But they were not developed in the manner of identifying structural relationships among various influential factors. In this study, we propose an SEM (structural equations model) that produces WLI (Warehouse Logistics Index) for both internal customers (warehouse workers) and external customers (end users) of ROKAF’s warehouses as described in Fig. 1. The Concept of Customer Satisfaction Index (CSI) is applied to assess the WLI of various warehouse groups according to units, locations, construction years, management items, the ways of transporting materials and storage facilities. It is expected that our model can be used to evaluate various logistics support capabilities of ROKAF (Republic of Korea Air Force) warehouses and contribute to warehouse modernization plans. This paper is organized as follows. Section 2 introduces the proposed SEM along with our research hypotheses. In Section 3, we fit the model and analyze the results. Then, we compare the WLI according to the warehouse groups in Section 4. Finally, Section 5 summarizes the results of our study and suggests the areas for further research. 2. Proposed model The SEM has become one of the most widely used multivariate statistical tools in various areas, such as psychology, education and behavioral sciences (Joreskog and Sorbom, 1989; Christopher et al., 2004). SEM is basically formulated by two types of equations: measurement equations and construct equations. While the measurement equations can be used to study the relationship between observed (measurement) variables and unobserved (latent) factors, the construct equations can be used to assess the hypothesized relationships among latent factors. The main interest here is in latent factors where the WLI represents the capability of warehouse logistics. We briefly review the existing studies on the factors potentially affecting the WLI. The following literature has investigated various factors which can improve the capability of warehouse logistics. Wills and Wills (1998) showed that the five key elements for logistics efficacy are facilities, communications, inventory, transportation and unitization. Nam (2002) showed that material management, logistics quality
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management, warehouse management, storage management, logistics information management, logistics organization and human resources management must be developed for military logistics systems. Li et al. (2006) designed the SCM practice framework using five dimensions of SCM practice: strategic supplier partnership, customer relationship, level of information sharing, quality of information sharing, and postponement. Many practitioners of SCM have recognized that effectively managing the flow of materials across the supply chain is one of the important strategic success factors (Tummala et al., 2006). A popularly cited example is Wal-Mart, whose points-of-sale data is transmitted back through its system and sent to suppliers; which reduces the dependence on forecasts (Ayers, 2000). According to Hatch and Badinelli (1999), in order to achieve the overall logistics objectives, product designs must incorporate the impact on operations, transportation and supply. Products are often expected to perform their intended functions over a period of several years and, as a result, they require an extensive support structure consisting of personnel, equipment and spare assets. Also, warehouse management systems often contain information on operational efficiencies and crossdocking requirements, whereby a product is received in a facility, occasionally grouped with other products going to the same destination, then shipped at the earliest opportunity without going into long-term storage (Napolitano, 2001). Meanwhile Fleischmann et al. (1997) indicated that the management of facilities and human resources are two important areas of resource management decisions. Brooks and Wallace (1989) suggested that manpower and personnel, support equipment, computer resources support, and training and support facilities are the important factors when planning for a logistics support system. Graham et al. (1994) and Ellinger (2003) considered that coaching had a positive impact on individual and team performance. Thornhill and Saunders (1998) showed that employee commitment is improved when line managers are actively involved in developing a high-quality workforce through coaching, team building, and employee involvement. Also, the importance of quality management practices in the achievement of operational results and customer satisfaction in logistics has been mentioned by a number of scholars in logistics academic journals (Holcomb, 1994; Mentzer, 1993; Sohail et al., 2004). Sohail et al. (2004) pointed out that along with the increase in the implementation of quality management practices in recent decades, the attention paid to the information and material flow processes of the supply chain or logistics has increased as well. According to Anderson et al. (1998), quality management influences logistics performance. In addition, firms need to invest the necessary resources and time in training programs, information systems, and benchmarking to improve the efficiency and effectiveness of their logistics operations. Finally, McClure (1997) indicated that information technology capabilities significantly influence the overall competence of logistics systems. Recently, Lau et al. (2004) investigated the impact of different levels of sharing information on inventory replenishment of enterprises in three-stage distribution supply chains by using a multi-agent-based simulation model. Against this background we set up a set of latent variables (material management, support for operations, facility management, manpower management, quality management, and logistics information system) that would influence the WLI. The WLI in turn would influence improvements in logistics support capability and warehouse modernization. So we include a contribution factor representing these aspects. Consequently, it can lead to a warehouse modernization in the military (Chief of Staff ROKAF, 1995, 1999, 2002, 2003, 2004). Details regarding the measurement variables selected for the latent factors introduced are given in Table 1. These measurement variables are selected based on interviews with managers who are in charge of warehouse and the reviewed literature above. Based on the military references (Chief of Staff ROKAF, 1995, 1999, 2002, 2003, 2004) and many experts’ opinions, we set up the following research hypotheses related to the structural relationships among latent variables. H1: Material management, support for operations and facility management would have direct influences on the WLI (Nam, 2002; Wills and Wills, 1998; Hatch and Badinelli, 1999; Brooks and Wallace, 1989; Fleischmann et al., 1997). Of these factors, improving facility management would have the highest direct effect on the WLI (Brooks and Wallace, 1989; Fleischmann et al., 1997).
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Table 1 Confirmatory Factor Analysis Latent variable (factor)
Measurement variables
Factor loadings
Cronbach alpha test
R2 of endogenous variable
Material management
Rate of stock inspection Rate of exhaustion of excess stocks Extent to which management procedures are observed Proportion of stocks classified Proportion of first-in first-out of stock Level of material support
0.795 0.704 0.698
0.87
0.731
Degree of possession of operational support items Sufficiency of storage space for operational support items Level of warehouse protection Level of readiness of material support against emergency Suitability of warehouse location
0.714 0.638
0.84
0.546
Facility management
Level of warehouse deterioration Suitability of protection facility against fire Degree of inefficiency of warehouse space Suitability of Warehouse design Level of cooperation with facility-related department
0.507 0.636 0.599 0.656 0.636
0.85
0.377
Manpower management
Suitability of staff’s deployment by items Proportion of managed items with suitable quantity? Level of technical education for staff Proportion of supplementary staff Level of observance of leave, stopping out and vacation Level of management of obsolescing items Extent to which defects on hand are treated Extent to which defects to be requested are treated Suitability of temperature and humidity in warehouse Accuracy of logistics information system Extent to which logistics operations system operates properly Level of acquisition of various information Level of supply of computers
0.648 0.538
0.80
Warehouse Logistics Index
Logistics Logistics Logistics Logistics Logistics Logistics
Contribution
Contribution for improvement of logistics support capability Contribution for Warehouse modernization
Operation support
Quality management and logistics information system
capacity capacity capacity capacity capacity capacity
of of of of of of
material management support for operations facility management manpower management quality management logistics information system
0.676 0.622 0.708
0.657 0.611 0.568
.
0.677 0.652 0.660 0.742 0.720 0.754 0.671
0.85
0.529
0.81
0.478
0.717 0.747 0.748 0.720 0.745 0.811
0.91
0.758
0.742
0.75
0.130
0.738 0.658 0.634 0.635
0.616
H2: Manpower management, quality management and logistics information system would have indirect effects on WLI (Thornhill and Saunders, 1998; Sohail et al., 2004; McClure, 1997). Among them, the manpower management would have the highest indirect effect on the WLI (Graham et al., 1994; Ellinger, 2003). H3: WLI would contribute to the improvement of logistics support capability and warehouse modernization plans (Nam, 1998; Nam, 2002).
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Fig. 2. The proposed structural equations model (SEM).
H4: Air Force WLI would vary according to warehouse group characteristics such as units, locations, construction years, management items, the methods of transporting materials, and storage facilities. In order to test these hypotheses, we construct an SEM as illustrated in Fig. 2. 3. Data analysis In order to conduct confirmatory factor analysis and to test the proposed hypotheses, we conducted a survey of the related personnel in the Air Force warehouses in Korea. There are 30 ROKAF warehouses where about a total of 558 officers, noncommissioned officers, private soldiers, and civilian employees are employed. The survey inquired about not only the measurement variables in Table 1 but also personal characteristics of the respondents, and information about the warehouse where they are involved. Each respondent was asked to score the measurement variables on a five-point Likert scale. Out of 558 questionnaires dispatched, 251 forms were returned and 237 were valid. Among them, about 51.9% were from air bases, 25.7% were from central warehouses, and 22.4% were from headquarters class warehouses. Also, the respondents consist of officers (8.5%), noncommissioned officers (33.8%), private soldiers (50%), and civilian employees (7.6%). These proportions show that our samples represent the population. Confirmatory factor analysis was performed before fitting SEM. The reliability of the research instrument is often tested by using Chronbach’s Alpha (a) statistic (Hair et al., 1998). Our results show that a for every factor is higher than 0.70, which confirms the consistency among the measurement variables within each latent variable as shown in Table 1. MLE (Maximum Likelihood Estimation) and PLS (Partial Least Squares) are common tools to estimate SEM. Although MLE is widely used, it still has limitations since the MLE needs not only distributional assumptions but also a large number of samples. PLS, however, is free from such limitations and has been widely used for index estimation. Accordingly, we use the PLS method to estimate the proposed SEM and verify relationships among the factors. In addition, we calculate the WLI of various warehouse groups based on the Customer Satisfaction Index (Sohn and Moon, 2003; Fornell and Bookstein, 1982; Fornell, 1992). Generally, with PLS one cannot evaluate the goodness of fit of fitted models. For this limitation, Hulland (1999) insisted that R2 values for the dependent (endogenous) constructs be clarified to judge the fitness. According to the literature which dealt with R2 values for the endogenous constructs, they range from a low of 12% (Birkinshaw et al., 1995) to a high of 64% (Cool et al., 1989). We calculated R2 values for endogenous constructs of our model: the results range from a low of 13% to a high of 75.8% for the Warehouse Logistics
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Index, which is satisfactory. Note that ‘Manpower Management’ variable is an exogenous latent factor. Therefore, there is no R2 value unlike other endogenous factors. 3.1. Analysis of structural equations model The path coefficients of the proposed SEM estimated by PLS are displayed in Fig. 2. In addition the significance of the path coefficient is verified by the 95% bootstrap confidence interval (Sohn, 1996; Sohn and Moon, 2003) as given in Table 2. Note that there is a path that turns out to be insignificant at the 5% level. However when the 90% bootstrap confidence interval was assessed, this path appears significant. Therefore, one can say that the general path relationships set in hypotheses 1, 2, and 3 are supported. Next, we assess both direct and indirect effects on WLI in order to identify the most influential factors. 3.2. Analysis of direct and indirect effects Direct effects are associations of one variable with another specified in the model. Indirect effects are associations of one variable with another mediated in the model through other variables. Total effect is represented
Table 2 Confidence intervals for the path coefficients of SEM Latent variable
Path coefficient
Upper
Support for operations Warehouse Logistics Index Warehouse Logistics Index
Lower 0.167 0.081 0.005
0.310* 0.201* 0.038*
0.464 0.294 0.140
!
Material management Quality management Warehouse Logistics Index
0.030 0.194 0.121
0.138* 0.349* 0.303*
0.226 0.466 0.373
Manpower management
!
Material management Support for operations Facility management Quality management Logistics information system Warehouse Logistics Index
0.129 0.287 0.535 0.344 0.611 0.014
0.251* 0.397* 0.614* 0.458* 0.691* 0.104*
0.372 0.561 0.694 0.587 0.781 0.226
Quality management
!
Material management Support for operations Warehouse Logistics Index
0.144 0.079 0.121
0.278* 0.099** 0.254*
0.453 0.256 0.373
Logistics information system
!
Warehouse Logistics Index
!
Material management Warehouse Logistics Index Contribution
0.193 0.014 0.003
0.321* 0.119* 0.141*
0.425 0.190 0.305
Material management
!
Support for operations
!
Facility management
* **
Significant parameters at 5% bootstrap confidence interval. Significant parameters at 10% bootstrap confidence interval.
Table 3 Relation between the Warehouse Logistics Index and other factors Latent variable
!
Latent variable
Direct effect
Indirect effect
Total effect
Material management Support for operations Facility management Manpower management Quality management Logistics information system
!
Warehouse Logistics Index
0.201 0.038 0.303 0.104 0.254 0.119
0.012 . 0.051 0.411 0.063 0.068
0.213 0.038 0.354 0.515 0.317 0.187
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by the sum of direct and indirect effects (Kim and Kang, 2001). Table 3 displays the relationships between the factors. As shown in Table 3, the facility management factor has the highest direct effect on WLI (hypothesis 1). This implies that the deterioration of Air Force warehouses and difficulties in storage management are likely to cause many problems. Therefore, systematic reinforcement of the facilities management in ROKAF is essential to effectively increase the WLI in the short-term. The manpower management factor turns out to have the highest indirect effect on WLI (hypothesis 2). This explains that proper deployment and reinforcement of staff and technical education for staff have the potential to improve WLI in the long term. We assume that it takes more time for indirect effects to materialize than direct effects because indirect effects are realized via some other factors. Due to its huge indirect effect, the manpower management factor has the highest total effect on WLI. This finding implies the importance of the manpower management factor in ROKAF. Therefore, in order to improve WLI, the importance of proper recruitment, suitable deployment of staff by items and technical education for staff cannot be overemphasized. The facility management factor is the second highest total effect holder on WLI. Along with manpower management, proper maintenance and repair for the deterioration of warehouse facilities, cooperation with facilities-related departments, new construction of modern warehouses, and full equipment for protecting facilities against fire are also required to obtain higher WLI. In summary, ROKAF needs to pay attention to the systematic facilities management in the short-term and manpower management on a long-term basis to attain higher WLI. This is worth noting in view of the fact that military society values manpower’s morale above everything else. 4. Analysis of the logistics index In order to test hypothesis 4, we estimate WLI for each group: units, locations, construction years, management items, the method of transporting materials and storage facilities. This index is calculated by following the ACSI concept (Fornell, 1992). The overall logistics index is related to the six measurement variables as shown in Fig. 3. The relationship between the overall logistics index and six observed variables for respondent i is as follows: gi ¼ s1 y i1 þ s2 y i2 þ s3 y i3 þ s4 y i4 þ s5 y i5 þ s6 y i6 ;
ð1Þ
where sj is the score between measurement variable (yij) and latent factor (gi). Details regarding the analytical framework are described in Appendix. In order to find a scaled Warehouse Logistics Index varying from 0 to 100 for a group, the following formula can be used:
Fig. 3. Relationship between the logistics index and measurement variables.
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P6
P6 j¼1 sj WLI ¼ 100; P ðr 1Þ 6j¼1 sj yj j¼1 sj
ð2Þ
where y j is the average of measured variable j for a group and r is the range of Likert scale used. In our case, r is 5. Table 4 displays the calculated WLIs by groups. As shown in Table 4, one can see firstly that WLI varies according to units. The WLI of air base warehouses is the lowest, which implies that institutional policies to support air base warehouses are required. Fig. 4 shows spider maps of the latent variables by units. As shown in Fig. 4, the spider maps have a similar shape by units. While central warehouses have relatively high values in every aspect, air base and headquarters class warehouses have low values. The material management index is higher against other indices. This implies that all warehouses carry out stock inspections and observe storage management procedures in a satisfactory manner. Air base and headquarters class warehouses appear to have poor conditions in most aspects. Especially the facility management index is lower than other indices. This may be mainly due to the fact that air base and headquarters class warehouses were constructed before 1980 and their storage facilities are old and have deteriorated. In facility management, systematic reinforcement is required to improve the logistics index in the shortterm. Between air base and headquarters class warehouse types, the support for air base warehouses must precede headquarters class warehouses since air base warehouses are directly related to air operations. Secondly, it shows the difference of WLI by locations in Table 4. The WLI of airbase warehouses located far from the aircraft is higher than the others. Thus it is necessary to find a way to improve WLI in the warehouse located near aircraft or those outside the airbase. Table 4 Types of Warehouse Logistics Index Types of Warehouse Logistics Index
Items
Frequency
Warehouse Logistics Index
By units
Overall Air base warehouses Central warehouses Headquarters class warehouses
237 123 61 53
52.4 49.2 53.8 53.5
By locations
Overall Warehouses located near aircraft Warehouses located far from aircraft Etc(Warehouse located far away from the airbases)
237 18 187 32
52.4 48.6 54.1 47.5
By construction years
Overall 1960s 1970s 1980s 1990s 2000s
237 24 73 47 52 41
52.4 35.7 49.2 49.6 50.9 52.3
By management items
Overall Spare part Equipment General material Oils, etc
237 75 30 88 44
52.4 48.6 54.2 46.9 52.3
By the ways of transporting materials
Overall Manpower Auto car
237 175 62
52.4 49 54.8
By storage facilities
Overall Angle structure Mix(Angle+Rack) Rack structure
237 148 58 32
52.4 51.3 56.4 61.9
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Fig. 4. Spider maps of latent variables by units.
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Thirdly, it shows the difference in WLI by construction year. The more recent the construction year, the higher the WLI. Therefore, we can see that WLI increases reflect warehouse modernization. It also shows the difference in WLI by management items. The WLI of warehouses that store equipment. This shows that it is easier to manage equipment than spare parts and general material since equipment is easier to handle than the others and the value for equipment is in general smaller than that of the others. Also, it shows the Table 5 Checklist for improvement by units Latent variable
Measurement variable
Material management
Rate of stock inspection Rate of exhaustion of excess stocks Extent to which management procedures are observed Proportion of stocks classified Proportion of first-in first-out of stock Level of material support
Operation support
Degree of possession of operational support items Sufficiency of storage space for operational support items Level of warehouse protection Level of readiness of material support against emergency Suitability of warehouse location
Facility management
Level of warehouse deterioration Suitability of protection facility against fire Degree of inefficiency of warehouse space Suitability of Warehouse design Level of cooperation with facility-related department
Manpower management
Suitability of staff’s deployment by items Proportion of managed items with suitable quantity? Level of technical education for staff Proportion of supplementary staff Level of observance of leave, stopping out and vacation
Quality management
Logistics information system
Warehouse Logistics Index
Level of management of obsolescing items Extent to which defects on hand are treated Extent to which defects to be requested are treated Suitability of temperature and humidity in warehouse Accuracy of logistics information system Extent to which logistics operations system operates properly Level of acquisition of various information Level of supply of computers Logistics Logistics Logistics Logistics Logistics Logistics system
capacity capacity capacity capacity capacity capacity
of of of of of of
material management support for operations facility management manpower management quality management logistics information
Air base warehouse p p p
Central warehouse
p
Headquarter class warehouse p p
p p p
p
p p
p
p
p p
p p p p p p
p p p p p
p
p p
p p
p p p
p p
p p p
p
p
p p
p p
p
p p
p p p p p p
p p p p p p
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difference in WLI by the methods of transporting materials. A higher WLI for auto cars shows that the automation of materials transportation would contribute to improvement of the warehouse logistics capacity. Finally, it shows the difference in WLI by storage facilities. The WLI of warehouses with rack structures is the highest. The rack is a kind of automated storage/retrieval systems to make good use of a limited workplace (Kim et al., 1998). This again supports the importance of the modernization and expansion of storage facilities. On the basis of the fitted SEM, we showed the causal relationships, impacts and WLI by groups. However, it may not be good enough to provide the warehouse unit of ROKAF with the feedback information necessary for the improvement. Accordingly, we made a check-list based on the measurement variables. Ticked units have a lower value than the overall average of the three types of units for each category of the measurement variable. Table 5 shows the measurement variables which need to be improved for each warehouse unit. According to this result, most aspects were required to be improved for air base and headquarter class warehouses. This reflects the low WLI of the air base and headquarters class warehouses. Headquarters class warehouses, improvement on support for operations and manpower management is needed. There are many others and it is only an example of guidelines which can be derived from the checklist analysis. Likewise, the feedback information for the improvement can be inferred by locations, construction years, management items, the ways of transporting materials, and storage facilities. 5. Conclusion In order to effectively operate air power in the modern war, the logistics systems of Air Force warehouses needs to be well-maintained. The best logistics system can be established by improving logistical capabilities continuously. However, none of the previous research looked at the measurement tools and feedback mechanisms in warehouse logistics capabilities. In this paper, we applied a Structural Equations Model (SEM) to develop the Warehouse Logistics Index (WLI) by considering the relationships among various factors. The results of our study showed that the facility management factor has the highest direct effect on the WLI. The importance of the facility management factor for different groups can be observed from the WLI analysis as well. For instance, the WLI of central warehouses is higher than that of air base and headquarters class warehouses. It is because most of the central warehouses are fitted with modernized facilities while other warehouses have deteriorated and lack automated warehouse facilities for material management. Therefore, intensive investment in facility improvement is needed. Considering the limit of the defense budget, the support for air base warehouses directly connected with air operations must precede headquarters class warehouses. Warehouse logistics capacity cannot be improved by controlling a single facility factor only. Consideration of the structural relationship among many factors, for instance, indicates that manpower management which has the highest indirect effect on WLI should be developed in the long-term as well. We not only compared warehouse logistics indices by units, locations, construction years, management items, the methods of transporting materials, and storage facilities, but also made a checklist based on the measurement variables in order to provide practical feedback information for the improvement. The results of our study are expected to be used to evaluate logistics support capability and contribute to warehouse modernization plans for ROKAF. In order to maximize the utilization of our proposed WLI and obtain real improvement, the ongoing interest of government and the continuous efforts of the Ministry of National Defense are required on a long-term basis. Our proposed model has the potential to be extended to other military services (Army, Navy) as well as many other areas (e.g. the satisfaction of a military life for soldiers, and so on). This kind of extension is left for a further study.
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Appendix. SEM and partial least squares The formal expression of the SEM model depicted in Fig. 2 may be spelled out as a series of equations that the systematic part of the predictor relationship is the conditional expectations in which the dependent variables for given values of predictors (Fornell et al., 1996). The general equation is thus specified as stochastic: E½gjg; n ¼ Bg þ Cn where g 0 = (g1, g2, . . . , gm) and n 0 = (n1, n2, . . . , nn) are vectors of unobserved (latent) endogenous and exogenous variables, respectively. B(m · n) is a matrix of coefficient parameters for g, and C(m · n) is a matrix of coefficient parameters for n . This implies that E[gf 0 ] = E[nf 0 ] = E[f] = 0, where f = g E[gjg, n]. The general equations relating the latent variables to the measurement variables are y ¼ Ky g þ e; x ¼ Kx n þ d; where y 0 = (y1, y2, . . . , yp) and x 0 = (x1, x 2, . . . , xq) are the measured endogenous and exogenous variables, respectively. Ky(p · m) and Kx(q · n) are the corresponding factor loading matrices. By implication from PLS estimation (Fornell and Bookstein, 1982), we have E[e] = E[d] = E[ge 0 ] = E[nd 0 ] = 0. The SEM is estimated by PLS (Partial Least Squares) estimation to search for relationships between unobserved P P (latent) P variables and observed (measurement) variables. The PLS are used to minimize residuals ( d2, e2 and f2) in the structural relationship (Rodgers, 1999). For example, consider the specification of the structural relation between n and g1 of the SEM model in Fig. 5. In PLS, the unobserved variables are estimated as exact linear combinations of their empirical indicators g ¼ sg y; n ¼ sn x; g ¼ cn þ f; where sg(p · m) and sn(q · n) are regression matrices (Fornell and Bookstein, 1982). We estimate Fig. 5 by giving arbitrary starting values to the weights sg1, sg2 and sg3, normalizing g to unit variance and regressing it on x1, x2 and x3 . Let ^ n be the predicted value of g in this regression. ^g is estimated by a corresponding procedure as the predicted value of n. That is, sn1, sn2 and sn3 are given arbitrary starting values and n is normalized to unit variance and regression on y1, y2 and y3. g and n are replaced by ^g and ^n, each normalized to unit variance, and the procedure is repeated k times until ^gk equals ^gk1 and ^nk equals ^nk1 . At this point, the estimated ^ gk is regressed on the estimated ^nk to obtain the structural relationship (c) between the two. The WLI (Warehouse Logistics Index) is as follows: P6 P6 y j j¼1 sj j¼1 sj WLI ¼ 100; P6 ðr 1Þ j¼1 sj where y j is the average of measured variable j for a group and r is the range of Likert scale used. In our case, r is 5.
Fig. 5. PLS model.
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