application of analytical hierarchy process in operations management

Application of Analytical Hierarchy

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Application of Analytical Hierarchy Process in

Operations Management Fariborz Y. Partovi, Jonathan Burton and Avijit Banerjee

Drexel University, Philadelphia, USA

Introduction The use of qualitative judgements in multi-factor decision models is receiving increasing attention and a variety of approaches have been developed which cover a wide range of techniques. One method which has received increasing attention in the literature is the relatively recently developed Analytical Hierarchy Processf[1]. This method has been widely documented in a variety of problem areas[2]. With the exception of a few cases, this qualitative decision-making model has not been used extensively in operations management. This article briefly reviews the Analytical Hierarchy Process (AHP), cites published work in a number of production and operations management areas, and suggests further potential applications. We outline in general terms the problems addressed, and provide a description of the resulting hierarchy.

Practitioners generally believe that many problems in production and operations management are so complicated that it is necessary to think in a complex way in order to solve these problems. Traditional operational research models, using techniques such as cost minimisation, are mathematically elegant and often helpful in providing clues to the right decision. However, in most cases, relatively few such approaches are complete and can be directly employed in practice[3]. Traditionally, alternatives or complements to these operational research techniques have been managers' ad hoc decisions which are based on their experience or feelings. These ad hoc decisions, although sometimes very effective, are not always logical and may not consider all of the factors and alternatives that may be relevant. One major contribution of AHP is its focus on overcoming these drawbacks. The AHP models presented here are qualitative techniques which rely on the judgement and experience of managers to prioritise information for better decisions.

The Analytical Hierarchy Process: A Review The Analytical Hierarchy Process is a decision-aided method which decomposes a complex multi-factor problem into a hierarchy, in which each level is composed of specific elements. The overall objective of the decision lies at the top of the hierarchy, and the criteria, subcriteria and decision alternatives are on each descending level of this hierarchy. The hierarchy does not need to be complete, i.e., an element in a given level does not have to function as a criterion for all the elements in the level below. Thus, a hierarchy can be divided into subhierarchies sharing only a common topmost element.

Received February 1989 Revised July 1989

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Once the hierarchical model has been structured for the problem, the participating decision makers provide pair-wise comparisons for each level of the hierarchy in order to obtain that level's weight factor with respect to one element in the next higher level. This weight factor provides a measure of the relative importance of this element for the decision maker. To compute the priorities of the element in each matrix, we solve the eigen-vector value problem for each matrix. This new vector is then weighted with the weight factors of the higher level element which was used as the criterion in making the pair-wise comparison. The procedure is repeated by moving downwards along the hierarchy, computing the weights of each element at every level, and using these to determine composite weights for lower levels [1]. The optimal solution will be the alternative with the greatest cumulative weight. The procedure is illustrated below.

Example An engineer must decide among three alternative engine fuel control systems as part of a special aircraft engine design. The three alternative control systems are mechanical (MEC), electromechanical (ELECMEC), and electronic (ELECTRON). The criteria considered are direct cost, flow time, reliability, and performance. The first step in AHP is to develop a graphical representation of the problem in terms of the overall goals, criteria and the decision alternatives.

Figure 1 shows the hierarchy for the fuel control system selection problem. The top level of the hierarchy is the overall goal; determination of the best fuel control system. The second level shows the four criteria stated above that contribute to the achievement of the overall goal. The three decision alternatives, mechanical, electromechanical, and electronic fuel control systems are shown at the third level.


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In using AHP, the decision maker must specify his judgements of the relative importance of each criterion's contribution towards achieving the overall goal.

The evaluations would then be solicited using questions such as "What is the importance of cost reduction relative to an increase in reliability in accomplishing our overall goal?". Similar pair-wise comparisons for other criteria can be done to generate Saaty's pair-wise comparison matrix[4]. From this evaluation we develop a preference matrix, a corresponding set of weights (the eigen-vector, W, determined by a computer program), and a consistency ratio (CR) for the first level of the model, as shown below. The consistency ratio is the ratio of the decision maker's inconsistencies and inconsistencies resulting from randomly generated preferences.

Cost Reliability Performance Flow time

Cost Rel. Perf. Flow time

CR = 0.078 W=

The decision maker believes, for example, that reliability is four times as important as cost. Consequently, cost is 1/4 as important as reliability, as shown above. The next step is to make pair-wise comparisons of each fuel system alternative, with respect to each of the criteria. We will illustrate this with respect to the second attribute, reliability.

MEC ELECMEC ELECTRON

MEC ELECMEC ELECTRON

CR = 0.016 W=

Here, the decision maker believes, for example, that the electronic system is three times as reliable as the mechanical system. Similarly, pair-wise comparisons must be made with respect to each of the other three attributes. The overall consistency results for each of the alternatives with respect to each criterion are presented in the following matrix.


MEC 0.544 0.210 0.075 0.458

Fuel System ELECMEC 0.278 0.240 0.183 0.416

ELECTRON 0.178 0.550 0.742 0.216

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Finally, the best fuel system alternative is found by determining the product of the criteria priorities and the alternative weights as shown below.


MEC ELECMEC = ELECTRON

The composite score indicates that the electronic fuel system is the best alternative. The evaluation proposed here is not intended to be an "answer" to the fuel system design decision but serves to illustrate the steps entailed when using AHP.

Axioms of AHP Saaty[4] and Harker and Vargas [5] give a formal statement of the axioms of AHP. We provide here a short, simplified version of these axioms:

(1) Reciprocal condition axiom: This axiom derives from the intuitive idea that, if alternative or criterion A is n times preferred to B, then B is \ln times as preferred as A.

(2) Homogeneity: This axiom states that comparisons are meaningful if the elements are comparable. In other words, we cannot compare automobiles with apples.

(3) Dependence. This axiom allows comparisons among a set of elements with respect to another element at a higher level. In other words, comparisons at the lower level depend on the element at the higher level.

(4) Expectations: This axiom simply states that any change in the structure of the hierarchy will require new evaluations of preferences for the new hierarchy.

Narasimhan[6] outlines the following benefits of using AHP: (a) it formalises and renders systematic what is largely a subjective decision process and thereby facilitates "accurate" judgements; (b) as a by-product of the method, management receives information about the implicit weights that are placed on the evaluation criteria; and (c) the use of computers makes it possible to conduct sensitivity analysis on the results. Another advantage of using AHP is that it results in better communication, leading to clearer understanding and consensus among the members of decision-making groups so that they are likely to become more committed to the alternative chosen[5].

AHP differs from other multi-criteria methods in its ability to identify and take into consideration the decision maker's personal inconsistencies. Decision makers are rarely consistent in their judgements with respect to qualitative issues. The AHP technique incorporates such inconsistencies into the model and provides the decision maker with a measure of these inconsistencies. A consistency ratio is derived from the ratio of the consistency of the results being tested to the consistency of the same problem evaluated with random numbers.


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This ratio provides the user with a value that can be used to judge the relative quality of the results. If a consistency ratio of less than 0.10 is obtained, the results are sufficiently accurate, and further evaluation is not required. Conversely, if the consistency ratio is greater than 0.10, the results may be unpredictable and the priorities should be re-evaluated.

In the remainder of this article, various published and potential applications of AHP in the area of operations management will be discussed. It should be noted that in each of the following cases the user can tailor the hierarchy to meet the needs of a specific environment. Thus it is possible to eliminate or add new criteria when necessary.

Existing AHP Models for Operations Management Supplier Selection Decision Most techniques for finalising the supplier selection decision utilise a candidate-ranking process based on a number of relevant criteria. The task is to identify the "key factors" involved in the selection and assign weights to the factors based on their importance. The candidate suppliers are then "scored" for each factor[7]. Figure 2, which is adapted from Narasimhan[6], shows the hierarchy for supplier selection in an AHP framework.

In this figure, the goal is to select the best supplier; their price structure, delivery, quality and service make up the elements in the second level of the hierarchy. The next level of the hierarchy further subdivides each of the above criteria into measurable subcriteria. For example, the delivery criterion is subdivided into timeliness and costs. The last level of the hierarchy shows the alternative vendors, A, B and C.

Facility Location Decision Facility location decisions provide another potential application for AHP. There are many operations research based models available to assist decision makers in solving facility location problems. These models rely almost exclusively on the use of fixed costs and variable transportation costs. However, there are certain qualitative issues regarding plant locations that are not easily quantifiable. Wu and Wu[8] identified nine issues related to plant location, some of which are qualitative. They are manufacturing costs at present value (MFG-C), freight costs based on last year's volume (FRT-C), community attitude towards industry (COM-A), water availability (W-A), availability of labour (A-L), probability of a union within ten years (PR-U), cultural attributes (CUL-A), schools (SCH), and airline service (AIR-S). Figure 3 represents the model suggested by Wu and Wu[8]. As shown by this hierarchy, the integration of qualitative and quantitative aspects of a decision in a rational and consistent manner represents a major strength of AHP.

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Time Series Forecasting Adjustments Time series forecasting is another area where AHP techniques can be applied. Traditionally this method of forecasting applies various models and formulae to extrapolate into the future, using a series of observed data. Commonly used time series forecasting techniques in operations management include trend analysis, exponential smoothing, and moving average methods. Although a great deal of effort has gone into the study of such methods, no statistical or mathematical technique can model the sensitivity and quality of human judgements.


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Most time series forecasting models must be tempered by managerial experience and knowledge. These forecasting adjustments are necessary owing to the external and internal factors that impact on the system at any given time. The influence of new product designs, marketing promotions, price changes or service upgrades must be estimated and converted into quantitative adjustments. In addition, external factors such as changes in the economy, new government regulations, anticipation of competitors' actions, and other environmental activities must be evaluated to assess their influence on forecasted values. Wolfe[9] has suggested a hierarchy for finding adjustment ratios in an accounting context. We outline the same framework but substitute factors suggested by Krajewski and Ritzman[10] which are perhaps more appropriate criteria for evaluating adjustment ratios in operations management. Figure 4 illustrates the hierarchy used to define the forecast adjustment ratio for each period.

The goal of the process is to find the right adjustment ratio. In the second level we separate the major factors affecting the forecast into internal and external factors. The internal factors can be further subdivided into: product design (PD),

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price and advertising promotions (PA), packaging design (PKD), salesperson quotas or incentives (SQ), expansion or contraction of geographically targeted market (EC), product mix (PM), and backlog policy (BP). The external factors consist of the state of the economy (SE), consumers' taste (CI), service image (SI), competitors' actions (CA), governments' actions (GA), and the availability of complementary products (CP). These criteria and subcriteria will not be defined here; the interested reader should refer to Krajewski and Ritzman[10].

The lowest level in the hierarchy contains, as alternatives, the range of percentages which can be used to adjust a forecast. AHP can be used in this case to combine human judgements with time series forecasting methods to enhance the quality of the forecast. In Figure 4 the alternatives represent the various percentage ranges that can be used to adjust the forecast. In this case, each of the final alternatives was selected to have an arbitrary width of ten per cent. Different percentage ranges are selected for specific situations, which are selected so that the ranges are narrow enough to make fine adjustments to a forecast, yet wide enough to make comparisons feasible. The questioning is straightforward in this hierarchy; decision makers participating in the forecasting process are asked to rank the relative importance of each criterion affecting the forecast adjustments over a specific period. For example, the decision maker would be asked to rank the importance of internal versus external factors with respect to the overall goal. Finally, questioning would focus on ranking the range of percentages with respect to each of the factors affecting the forecast.

Choice of Technology Capital-budgeting models, such as payback, net present value and internal rate of return, are commonly used models when choosing new technology in manufacturing[11,12]. These models have been used extensively in industry


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owing to their ease of use, their tactical financial assumptions, and their treatment of the time value of money. Although these models may provide a good technique for the evaluation of tactical issues in project selection, they fail to consider long-term, strategical, non-monetary factors in technological decision making. Kleindorfer and Partovi[13] have suggested an AHP relating manufacturing strategy to the choice of technology (see Figure 5).

This hierarchical model begins with competitive strategy based on the internal and external analysis of the firm. Below competitive strategy, there are three general groups of elements. The first group, manufacturing strategy elements, consists of competitive forces such as cost, quality, dependability, and flexibility. The second group is an intermediate group linking the forces driving competition. This group is identified with specific activities in the value chain, including inbound logistics, design, process, outbound logistics, sales, and customer service. The final group is related to the technology projects themselves, as they influence specific value chain activities and are evaluated with respect to the specific manufacturing strategy.

Some New AHP Models for Operations Management In the remainder of the article we will propose four new hierarchy models for operations management.

Product Design Decision Product design requires that crucial decisions be made regarding manu-facturability, cost, performance, reliability, conformance, durability, serviceability, safety, aesthetics, flexibility, and through-put time[14]. An effective product design requires an understanding of these factors, and the ability to resolve trade-offs among them to meet different customer needs. AHP can be a useful tool for analysis of trade-offs and interpretation of product characteristics rather than product formulation. In other words, once the conceptual design has been established, AHP can be employed to select the particular characteristics of design from among several alternatives. Figure 6 shows our suggested hierarchy.

At the highest level of the hierarchy, the designer seeks to select the best design possible for a particular product. At the second level, the key factors or criteria affecting the decision and trade-offs are identified. We will use Garvin's framework[14], as well as others, to define some of these criteria.

Product cost consists of direct and indirect costs. Direct cost relates to the production of the product, and includes material and direct labour. Indirect costs are non-volume sensitive, such as fixed overhead costs. Performance refers to the primary operating characteristics of the product. In most cases performance characteristics are measurable and, as a result, different designs can be compared objectively with respect to performance. Product features are the secondary characteristics that supplement the product function. Features, like product performance, are objective criteria. Reliability is the probability of a product failing within a specified period of time. Durability is a characteristic very closely linked to reliability. Durability is the amount of use one gets from

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a product before it physically deteriorates. Conformance is the degree to which a product and its operating characteristics meet pre-established standards. Aesthetics refers to the product's look, feel, sound, taste, or smell. Manufacturability is another important design consideration. In the past, designers have dealt with this issue near the final stage in the product development cycle when designs have been completed. The new team approach involves people from manufacturing, marketing, and purchasing early in the product design process[15].

Design for manufacturability consists of two parts: (a) design in producibility consists of designing products to fit existing machinery and processes in fabrication, and (b) design for assembly which considers the ease of product assembly. The serviceability aspect of product design pertains to how quickly and easily the product can be repaired, as well as considering possibilities for future add-ons to the design. Some aspects of service can be measured objectively. Flexibility in design allows products to have a variety of applications without the need to design several different products. Through-put time is another major design concern because often products fail, not because of their cost, performance, or aesthetics, but because they are not available when the customer needs them[15].

In general, to obtain meaningful responses to criteria comparisons, these factors have to be explicitly bench-marked. Such bench-marks typically follow from a strategic goal with respect to design. A strategic goal, for example, might be stated as the reduction of a product's price or cost by 10 per cent compared with a decrease in through-put time of 20 per cent or an increase in reliability of 15 per cent. The lowest level of the design hierarchy (Figure 6) consists of different design alternatives.

Plant Layout Design Another potential application for AHP is in designing a plant layout. A satisfactory layout provides a sound basis for maintaining effective use of employees, machines, space and providing safety. This layout, in turn, contributes to the


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firm's efforts to maintain low material-handling costs, low inventory costs, and a better factory environment.

Traditionally, layout design problems can be divided into two basic categories[16]. The first category is characterised by its use of material-handling distances, loads or costs. The second category is characterised by its qualitative approach to the relative positions of departments. An effective technique for developing a process layout under such conditions is known as SLP (systematic layout planning) [17]. Analytical Hierarchical Process can integrate the load-distance-cost method and the relationship method into one hierarchy. Figure 7 illustrates how a simple AHP was developed to generate and evaluate various layout configurations. Specifically, Figure 7 illustrates an AHP hierarchy for generating and evaluating spatial relations between pairs of facilities. This information, together with the characteristics of the facilities in general, can then be developed into a floor plan.

The hierarchy focuses on the ideal layout configuration. At the second level the various factors affecting a decision maker's judgements are presented. These factors are safety (SAF), flexibility of layout to incorporate future design changes (FLEX), noise (NOISE ), aesthetics (AES ), floor space utilisation (FS-U), through-put time (TP-T), manpower utilisation (MP-U), in-process inventory (IP-I), and load-distance score (LD-S )[18]. As in the previous cases, the criteria must be quantified as in the following: 2,000 units per plant operation hour (through-put time); $50,000 per product model changeover (flexibility); 85 per cent utilisation of available space (floor space utilisation); 70 per cent utilisation of each worker (manpower utilisation); and two minor injuries per 1,000 man-hours worked (safety). Once these criteria are defined it is possible to compare the relative importance of each in determining the ideal plant design. When evaluating the alternatives in the lowest level of the hierarchy, the proximity

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of a pair of facilities will be compared with another pair with respect to the above criteria. It should be noted that, once an alternative has been chosen as the ideal layout, that alternative should be removed from the hierarchy. Consequently, the remaining alternatives of the modified hierarchy require new evaluations with respect to all criteria (fourth AHP axiom).

Preventive Maintenance Frequence Determination The proper maintenance of equipment is essential for the smooth running of operations. In most organisations, maintenance activities involve repairs and preventive maintenance. The timing of preventive maintenance is important for operations to function efficiently. The decision to schedule certain preventive maintenance activities, quarterly, monthly, weekly or daily, depends on a number of different criteria.

We will use Dhavale and Otterson's[19] framework for defining appropriate criteria and subcriteria for evaluating preventive maintenance frequency. An AHP-based hierarchy for preventive maintenance strategy is illustrated in Figure 8.

In this Figure the criteria are divided into two groups: maintenance planning and productivity. The subcriteria under maintenance planning are related to everyday decisions of the maintenance department and include age of the equipment (AE ), ease of repair (ER ), maintenance history (MH), likelihood of breakdown (LB ), danger of machine failure (MF), tolerance (TOL ), machine deterioration (MD ), and availability of spare parts (SP). Productivity relates to the overall objectives of the production system and consists of the following: the number of available machines (AM), normal in-process inventory (IPI), investments in machines (MI), average length of repair (LR ), average projected machine load (ML ), and operator idle time (IT). The bottom of the hierarchy consists of the various maintenance frequencies. With the hierarchy thus constructed, we generate the appropriate pair-wise comparison matrices and as a result we will identify the appropriate maintenance frequency.

Choice of Logistic Carrier The logistics of delivering finished goods or picking up raw materials involves choosing a carrier. The performance of various carrier services can be evaluated based on several criteria. Many authors[20,21,22,23] conceptualised a number of variables that are important in the carrier selection process. Recently, Bagchi, Raghunathan and Bardi[24] statistically validated these variables and grouped them into four categories using factor analysis. These criteria are rate related factors; customer service, claims handling, equipment availability, and service flexibility. Each of these categories can be subdivided into finer criteria distinctions: door-to-door transportation rates or cost (A ); willingness of the carrier to negotiate rate changes (B ); transit time reliability or consistency (C ); total door-to-door transit time (D ); claims processing (E ); freight loss and damage (F); shipment tracing (G); pick-up and delivery service (H); shipment expediting (I); equipment availability (J); special equipment (K); quality of operating personnel (L ); line-haul service (M); and schedule flexibility (N)[24].


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Figure 9 illustrates the hierarchy of logistic carrier selection. As before, the criteria at each level in the hierarchy are shown. In a similar manner, the alternatives in this case include three carriers, and the optimal solution involves choosing the carrier alternative with the greatest cumulative weight.

Conclusions This article has presented the use of AHP in eight decision areas of operations management. Decision hierarchies have been suggested for: (1) product design decisions, (2) plant layout design decisions, (3) preventive maintenance frequency selection, and (4) choice of logistic carrier. Furthermore, published AHP application hierarchies in (5) facility location planning, (6) supplier selection decision, (7) choice of technology, and (8) time series forecasting adjustments have been reviewed. The eight hierarchies presented in this article illustrate the wide range of multi-factor operational decisions to which AHP can be applied. AHP offers a unique and valuable method for integrating judgements with the traditional quantitative methods used in operations management. This integration will facilitate the application of operations management techniques in manufacturing and service organisations' practices. Several interesting questions remain to be explored in future research. First, the evaluation of these hierarchical models using field studies is desirable. Secondly, the extent to which the suggested AHP models would offer a better procedure than ad hoc or other existing approaches is an empirical question that needs field or laboratory testing. What we have attempted to provide here is an introductory framework to serve as a foundation for further refinements and additions.

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11. Noble, J.L., "Techniques for Cost Justifying CIM", Journal of Business Strategy, Vol. 10 No. 1, 1989, pp. 44-9.

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application of analytical hierarchy process in operations management

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