Utility Approach and Analytical Hierarchy Process for Juzis Decision Analysis - Case Study Example

Utility Approach and Analytical Hierarchy Process (AHP) for Juzi’s Decision Analysis [Name] [Professor Name] [Course] [Date] Utility Approach and AHP Evaluation Methods for Juzi’s Profitability And Visibility Expansion Plan Abstract: This paper describes a decision analysis Juzi’s implementation decisions under uncertainty. It uses a utility approach (the lottery approach) to construct a utility function for two persons for each criterion and secondly, it uses Analytical Hierarchy Process (AHP) to find the appropriate weights for each criterion. 1. Utility Approach Introduction A business case analysis was carried out in the previous assignment to determine the alternatives to fill a capability gap for Juzi Accessories (Juzi Online n.d.). From the business case analysis, the company’s options to make a decision regarding increasing its visibility and profitability were evaluated based on four parts of its corporate strategy that included dominating the jewelry market, expanding globally, global recognition and customer satisfaction as well as branching out into new sectors (Wen-feim 2004). From the evaluations of its strategic option, it was determined that Juzi should implement the best available options. The three options include: a. Sales and marketing power: Investing in marketing and public relations to achieve the much-needed global acceptance, which would consequently make inroads for future expansion plans. b. Production: Dealing in a range of product lines to ensure it appeals to the wider and more demanding global market c. Frontier expansion Analysis of capability of the options with reference to performance, risk analysis and economic analysis concluded that implementing a ‘dynamic marketing strategy’ was the most preferable option. The option integrates vibrant sales and marketing power and investing in marketing and public relations. It was viewed as the best possible option that are most likely to ensure more profitability and visibility of the company as it satisfied majority of the assessed criteria (Assel 1985). The utility approach model will be applied in this paper to create a utility function for two people for the above options to satisfy the company’s visibility and profitability objectives (Linkov and Steeven n.d). In assignment 3, an experimental test plan was carried out to assess the applicability, suitability and efficiency visibility and profitability requirement. This utility approach will consider the suitability of the three options in ensuring that the visibility and profitability objective is attained at any particular time as a criterion against which the model will be applied. Several effectiveness, suitability and performance parameters were examined to determine the company’s visibility and profitability options (Bordley and LiCalzi 2000). The capability of the options to maintain the company’s visibility and profitability across various socio-political, economic, environmental, technological environments included the criteria selected against which the utility approach is applied (Fraser and Hite 1988). Utility approach process The criteria of effectiveness selected involve the ability of the options to maintain the company’s visibility and profitability despite any socio-political, economic, environmental, technological and environmental factors (Labiosa et al nd). The utility approach will be carried out for two employees of Juzi Accessories. The two employees include: Nancy Randal – who is the founder and CEO of Juzi Accessories; Ruth Randal – who is the marketing manager of Juzi Accessories. Nancy and Ruth both ranked the three options of Juzi’s visibility and profitability basing on the most to the least preferred. The table below shows their order of ranking. Preference Option 1 A 2 C 3 D Table 1 – Preference of options From table 1, it is not that both Ruth and Nancy preferred: The utility of A as the most preferred, defined as 1, depicted as U(A)=1 Utility of option C as the least preferred, defined as 0, depicted as U(C)=0 Basing on the above inference, the lottery approach will be used to determine the utility of option B. To establish the utility of option B, both Ruth and Nancy were asked on their preference to option B’s capability to be effective in any socio-political, economic, ecological and technological environment or engaging in a lottery through probability (p) of returning option A or D, the question was repeated using based on the three options until Ruth and Nancy were undecided on whether to select option B or engage in lottery. Analysis Table 2 and table 3 below shows the results of Ruth and Nancy’s preferences to determine the utility for option B. Option B or: Iteration 1 Iteration 2 Iteration 3 Iteration 4 Probability of returning option C (p) 0.6 0.7 0.5 0.6 Probability of returning option A (1-p) 0.4 0.3 0.5 0.4 Decision Option B Lottery Option B Indifferent Table 2 – Nancy, utility of option C Option B or: Iteration 1 Iteration 2 Iteration 3 Iteration 4 Probability of returning option C (p) 0.8 0.3 0.5 0.4 Probability of returning option A (1-p) 0.2 0.7 0.5 0.6 Decision Option B Option B Indifferent Lottery Table 3 – Ruth, utility of option B From the analysis of the lottery questioning, option B’s utility can be determined using equation 1 as shown below. Equation 1 – Determining Utility U(C) = pU(D) + (1-p)U(A) Substituting U(A) for 0 and U(C) for 1 gives, Utility for option B via Nancy is: U(B) = 0.6 x 1 = 0.6 Utility for option B via Ruth is: U(B) = 0.5 x 1 = 0.5 The results for the utility for option B for both Ruth and Nancy were displayed in a graph as shown in figure 1 below. Option A, B and C are represented in the order of the preference, which is Option A, Option A and lastly Option B. Figure 1: Utility function for Juzi’s Options Conclusion From the graph, it is evident that the decisions made by both Ruth and Nancy were risk taking in nature. However, Nancy’s decision was slightly more risk avoiding in nature. 2. Analytical Hierarchy Process (AHP) The Analytical Hierarchy Process (AHP) will be applied to find the weight for the measure of effectiveness (MOE), measures of performance (MOP) and measure of suitability (MOS, as determined in the experimental test plan in assignment 3 to validate whether Option A is the most applicable solution for the company’s visibility and profitability objective. Option A involves integrating a dynamic sales and marketing strategy in order to improve Juzi’s competitiveness and operational efficiency (Triantaphyllou and Mann 1995). The comparisons are applied to determine the weights of significance of the decision criteria and the relative performance measures of the alternative attributes considered by the decision. If the comparison is not perfectly consistent, then it shows the need to improve consistency. The figure below details the decision hierarchy for the parameters of assignment 3. Figure 2 – AHP Hierarchy Decision tree The information detailed in the AHP hierarchy tree is then combined, compared and analysed to establish the relative rankings of each attribute using Pairwise Comparison Pairwise comparison will be conducted of the characteristics of each level of the decision hierarchy. By using the criteria, the relative importance one attribute against the other is expressed. First, the comparison is conducted between the highest level of performance, effectiveness and suitability. A matrix is then created where each characteristic is ranked against the other using a scale of 1 to 9. In this case, 1 represents equality in weight, while 9 represents the most extreme or most preferred attribute. The table below represents the matrix.   Effectiveness Performance Suitability Effectiveness 1/1 1/2 3/1 Performance 2/1 1/1 4/1 Suitability 1/3 1/4 1/1 Table 4: Pairwise comparison matrix The values transformed to decimals. Effectiveness Performance Suitability Effectiveness 1.0 0.5 3.0 Performance 2.0 1.0 4.0 Suitability 0.33 0.25 1.0 TOTAL 3.33 1.75 8.0 Table 5: Pairwise comparison matrix Each of the values obtained from the matrix is divided by the totals in their respective columns to get the normalized matrix. Concerning the normalized matrix, the rows are totalled up and their average obtained to find the priority vector, which represents the value of weighting each attribute of Option A. The table below shows the results.   Effectiveness Performance Suitability Priority Vector Effectiveness 0.30 0.29 0.38 0.32 Performance 0.60 0.57 0.50 0.56 Suitability 0.10 0.14 0.13 0.12 TOTAL 1 1 1 1 Table 6: Normalised Pairwise comparison matrix and Priority Vector After determining the weighting of each attribute, their consistency checks are then conducted. This involves multiplying the priority vector and the matrix values acquired from the Pairwise comparison process to find the weighted sum vector. To determine the consistency vector, the weighted sum is divided by the priority of the corresponding attribute. The table below represents the results.   Weighted Sum Vector Consistency Vector Effectiveness 0.96 3.0 Performance 1.68 3.0 Suitability 0.36 3.0 Average 3.0 Table 8 – Weighted Sum and Consistency Vector After determining the average of consistency, it is substituted in equation 2, as shown below, to find the consistency index of the comparison as well as the consistency ratio established by equation 3 (as shown below). Equation 2: Consistency Index (CI) = (Average (Consistency Vector) – n) / (n-1) where n is the number of attributes CI = (3.0 – 3) / (3-2) = 0 Equation 3: Consistency Ratio (CR) = CI / Once the above equation is substituted by values, the result CR = 0 Since the CR value is 0, which is less than 0.1, the Pairwise comparison is considered as perfectly consistent, which means that the weighting that was determined in Table 4 is satisfactory. Conversely, if the CR value was higher than 0.1, then it would mean there was no consistency in the comparison of the attributes, thus the whole process decision making process would have to be repeated. Conclusion AHP applied to establish the weights of significance of each of the measures of suitability, performance and effectiveness uniquely indicates the consistency of the decision criteria, through validation of consistent comparison between the attributes provided that the consistent ratio is less than 0.1. References Assel, Henry. 1985. Marketing Management Strategy and Action. Boston: Kent Publishing Company. Bordley, R. & LiCalzi, M. 2000. "Decision analysis using targets instead of utility functions." Journal of Economic Literature Classification, DEF 23, 53 – 74 Fraser, C. & Hite, R. 1988. “An Adaptive Utility Approach for Improved Use of Marketing Models.” Journal of Marketing. Vol. 52, No. 4 , pp. 96-103 Juzi Online, n.d. Juzi [Online] Retrieved from [http://www.juzionline.com/about-us-pg-1?osCsid=7dkvs8k6mkcr3jekol8cb97dk7] 31 May 2013 Labiosa, W, Leckie1, J, Mumley, T., Rytuba,J and Bernknopf, R. A Decision Analysis Approach To Tmdl Implementation Decisions: Mercury Tmdls In The San Francisco Bay Area. (Onlone) Retrieved from: [http://eil.stanford.edu/publications/bill_labiosa/TMDL03_final_draft_0903.pdf] Linkov, I. & Steeven, J. n.d. Chapter 35 Appendix A: Multi-Criteria Decision Analysis. (Online) retrieved from: [http://www.epa.gov/cyano_habs_symposium/monograph/Ch35_AppA.pdf] Triantaphyllou, E. & Mann, S. 1995. “Using The Analytic Hierarchy Process For Decision Making In Engineering Applications: Some Challenges.” International Journal Of Industrial Engineering. Vol. 2, No. 1, pp. 35-44, Wen-feim, Uva. April 2004. Managing Marketing Risks. [Online] Retrieved from [http://hortmgt.dyson.cornell.edu/pdf/smart_marketing/uva4-04.pdf pg 1,2] Accessed 30 May 2013 Read More