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The effect of deviations from optimal production schedules on batch-level cost drivers.

Gaining an understanding of manufacturing overhead drivers is fundamental to designing an accurate cost management system. The designer associates general ledger costs with activities, then attaches activity costs to products as a function of demand for activities. The purpose of this article is to extend the existing body of cost driver literature and test the hypothesis that batch-level cost drivers as developed by Cooper [1990] can be affected by exogenous factors unrelated to units following a batch-level activity. Examples of exogenous factors include deviations from theoretically optimal production schedules to accommodate special orders, or to reverse the effects of an inventory stockout or oversupply. This study statistically tests the association of changes in batch-level activities with deviations from a theoretically optimal production schedule using data gathered at two manufacturing firms in two different industries.

Cooper's hierarchy of overhead cost drivers outlines the primary theory underlying activity-based costing. The hierarchy consists of four overhead cost levels: unit-level, batch-level, product-sustaining, and facility-sustaining. Unit level activities tend to be primarily volume related (as are traditional cost allocation systems). Therefore, the unit level category does not add significantly to our understanding of activity-based costs. Additionally, facility-sustaining costs do not fit meaningfully into the other three levels; they represent residual costs. Facility-sustaining costs are allocated to cost objects in an arbitrary manner, if allocated at all. Thus, the major theoretical contribution of the overhead hierarchy lies in defining batch-level and product-sustaining categories. Evidence from this article suggests that further refinement of one of the primary activity-based categories, batch-level costs, is necessary.

The article is organized into four sections. The first section motivates the study by identifying linkages to prior research. The next section describes manufacturing processes of two industries from which data were gathered. Then statistical methodology and results are presented. The article closes with a summary and conclusions section.

Background and Motivation

Activity-based Costing/Management (ABC)/(ABM) has received much attention in recent years, and researchers have demonstrated the applicability of ABM for measuring product costs and improving manufacturing performance (Albright and Sparr, 1994; Cooper, 1990, 1988a, 1988b, 1989a, 1989b; Greenwood and Reeve, 1992; King, 1991; Kaplan, 1990; Roth and Borthick, 1991; Smith and Leksan, 1991; Turney, 1991, 1989; Turney and Anderson, 1989). Additionally, cost driver analysis has been empirically evaluated by Babad and Balachandran (1993), Banker and Johnston (1993), and Datar et al. (1993).

Swenson (1995) identified the use of ABC to support various decisions within manufacturing organizations. Key decision categories include strategic decisions, materials sourcing, pricing and product mix, customer profitability, operating decisions, process improvement, product design, and performance measurement. Thus, ABC is used by managers to support a wide variety of decision types. Anderson (1995) developed a framework for evaluating the evolutionary sequence of implementation stages.

Consistent with the hierarchy of overhead costs developed by Robin Cooper (1990) and the definitions of activity-based management developed by Raffish and Turney (1991), this study, attempts to understand the impact of deviations from a theoretically optimal production pattern. Cooper identifies four levels of overhead as follows: unit-level, batch-level, product-sustaining, and facility-sustaining. This article focuses on batch-level activities to understand associated manufacturing complexities and costs. Batch-level activities are important because they result in costs independent of the number of units produced within a batch. For example, a machine setup requiting two hours is independent of the number of units produced following the setup. Thus, economies of scale dictate that units produced in large batches receive less setup overhead cost per unit than those produced in small batches.(1)

Examples of batch-level costs have been well documented in the literature and include machine cost per setup hour, cost per machine setup (Cooper, 1988a), and waste resulting from grade changes in the production of paperboard (Albright and Reeve, 1992). In previous studies, a batch activity (order processing in Siemens Motor Works(2), and machine setup, production order, and materials handling in John Deere(3)) was assumed to be constant and invariant to changes in the level of production that followed an activity. Cooper concludes that "Batch-level bases . . . assume that inputs are consumed in direct proportion to the number of batches (italics added) of each type of product produced" (1990: 13). Additionally, Cooper (1996) indicates that an ABC system will report that batch-level costs are higher than previously thought. Cooper's assessment of the importance of batch-level costs is supported by Selto (1995) who examined four ABM projects and stressed insights gained from studying change-over costs for products. Small sizes produced in low volumes were found to have a higher cost per unit than larger products produced in higher volumes. Thus, batch-level costs are a significant cost category that may influence a wide variety of decisions across the firm.

The industrial engineering literature also explores the relationship of variables such as setup time, lot sizes, and sequence-dependent setup costs (Drexl and Haase, 1995; Hahm and Yano, 1995). This study extends prior studies that associate batch costs with activities and provides evidence that certain batch-related activities are significantly affected by events unrelated to the number of batches of each type of product. The cost management implications imply batch-level costs may have a direction of association other than downstream. Such batch costs are termed sequence-dependent. For example, events such as unplanned schedule changes may have a direct influence on the cost of subsequent setups. Thus, setup costs may be affected by events unrelated to products manufactured following a setup. Therefore, for internal purposes, some batch-level costs may be more accurately classified as sales expenses or other period expenses unrelated to a batch of product. For example, if a marketing Vice President commits to a delivery date inconsistent with existing production schedules, extra setup costs may be appropriately associated with marketing functions, rather than manufacturing.

This study was partially motivated by a recurring question raised by Executive MBAs after considering Activity-based Management principles within their companies. Managers noted in processing industries such as chemicals, steel, paperboard, or steel tube manufacturing, time required for machine setups can vary as a result of machine specifications existing at the time a setup begins. For example, paper machine tolerances are adjusted between batches to meet unique product specifications across a product mix. Changeovers in basis weight (thickness) of more than 1/1,000th of an inch can create instabilities in a process that materially affect quality (and costs) for several hours. Thus, the amount of batch-level cost resulting from paperboard grade changeovers may not be driven exclusively by the nature of a product following a changeover, but by absolute differences in the basis weight of current and prior product grades. As shown in Figure I, Panel A, a setup is associated with each production run; setup costs are attached to individual units within a production run. Figure I, Panel B illustrates the nature of the research problem identified in this article. Previous production runs may affect setup costs for subsequent production runs. In this situation, the direction of causality reverses. Units within production runs do not exclusively determine setup costs. These setup costs may be affected by other factors.

In this study, we consider scrap resulting from grade changeovers to be a setup cost. Statistical tests of differences in scrap rates between the first reel of paperboard produced following a grade change and all other reels in a production run (batch) has shown the first reel to contain significantly higher scrap rates (Albright and Reeve, 1992). Thus, for the purposes of this article, the scrap produced during the period of instability subsequent to a grade changeover is considered a setup cost. Production scheduling can generate scrap costs if multiple grades are skipped with respect to an optimal production sequence. Similarly, deviations from optimal production schedules while manufacturing steel tubing may necessitate changing specifications of three sections of the tube mill for a particular product that normally requires changing only one or two sections.

To increase research generalizability, the field studies were conducted in two diverse manufacturing industries, paperboard and steel tube manufacturing. Theoretically optimal production schedules have been prepared for each industry based on physical manufacturing characteristics of each firm's product line. The next section describes the manufacturing process for each industry and develops the logic supporting each theoretically optimal production schedule.

Manufacturing Processes

The manufacturing processes for industries evaluated in this article are very different in nature. The first example illustrates a continuous process, while the second example illustrates a discrete batch process. Though the products and processes are diverse, the same cost management principles apply to each industry.

Paperboard Manufacturing

A paperboard manufacturing process consists of eight sequenced operations as follows: (1) Head Box, (2) Wire Section, (3) Press Section, (4) Drying Section, (5) Size Press, (6) Calendar Stack, (7) Coater Section, and (8) Reel Section. As shown in Figure II, these eight operations occur simultaneously within a single paperboard machine. The stock flow (pulp) is mixed in the head box and applied to a porous wire mesh; formation of paperboard actually occurs within the wire section. In the press section, the pulp mixture is forced against the wire with pressure and suction to eliminate water within the mixture and to form the desired paperboard attributes. The material proceeds to the drying section along a fabric carrier, where it travels across numerous cylindrical dryers heated with steam. After drying, the paperboard advances to a size press where various coatings are applied. The calendar stack section presses the material to reduce variation across the width and length of a sheet, thereby improving the surface quality. The coater section applies a clay-based opaque material if required by engineering specifications. The reel section is the final process before shipping. Long sections of material in a continuous sheet, termed reels, are rolled up (rewound) immediately from the paper machine and cut into parent rolls (termed jumbo rolls or sets) to await shipment (Albright and Reeve, 1992).

Some dynamics and problems associated with continuous-process manufacturing have been addressed by Reeve (1991). To minimize shocks to a continuous process, such as paperboard manufacturing, different product grades are produced according to a schedule that typically follows a theoretically optimal, symmetrical pattern. Instabilities following grade changes are introduced as a result of changes in pulp mixture and other manufacturing variables. The product mix should be produced according to a pattern that begins with the thinnest product, followed by a slightly thicker product, until the thickest product in the mix has been produced. At such time, the basis weight (thickness) of the paperboard begins to decline in increments until the thinnest product once again is manufactured. Figure III illustrates a symmetrical, theoretically optimal production schedule for products manufactured by the paperboard mill observed in this study.

In actuality, exogenous factors can encourage the production engineer to violate the integrity of an optimal production schedule. For example, one or more grade thicknesses may be skipped in the current production cycle because of a special order (or stockout, or excessive inventory). Figure IV illustrates the actual production pattern for a sample of 49 batches of paperboard. A basic underlying symmetrical pattern exists, as suggested by the optimal pattern from Figure III; however, the pattern illustrated in Figure IV contains gaps representing deviations from an optimal schedule.

Steel Tube Manufacturing

Equipment used in the production of steel tubing consists of three machining stations, each with a distinct but related function, linked together to form a complete production system. As shown in Figure V, in the first section, termed breakdown section, the sides of a continuous flat strip of steel are gradually curved upward into a "U" shape. In the second, or finishing section, the upper edges of the "U" shape are forced together and welded to approximate a circular piece of tubing. In the third section, where final shaping occurs, the circular steel tube is shaped progressively between rollers until the desired external geometry (round, square, rectangular, etc.) is achieved. Some production runs require a complete breakdown and setup of all three stations because of characteristics, such as tube diameter, that radically differ from the tubing currently under production. Alternatively, some setups require changing only the last section or sections of the tube mill to accommodate square or rectangular specifications made from an identical tube from the finishing section. For example, changeovers from a 2[inches] x 3[inches] rectangle to a 2 1/2[inches] x 2 1/2[inches] square would require changing only the third, or final shaping section. The same round tube produced by the finishing section is used for both products. Alternatively, changeovers from a 2[inches] x 3[inches] rectangle to a 4[inches] x 6[inches] rectangle would require changing over all sections because of the large size differential.

Figure VI illustrates the asymmetrical pattern of a theoretically optimal tube mill setup schedule. The schedule is designed to permit changes of all three sections, followed by changes of only two sections, followed by changes of only one section. As illustrated in Figure VI, the schedule is optimized when only two three-section setups are performed within a production cycle. Figure VII illustrates a series of setups representing data obtained from the plant site. Deviations from the optimal schedule are evidenced by multiple unscheduled one-section and two-section changeovers. Such changeovers extend the production cycle, increase lead times, and further encourage deviations from the optimal cycle.

Unlike the paperboard basis weight plot that approximates a wave pattern, many setup patterns are possible within a tube mill subcycle. A setup pattern consisting of three sections, followed by two sections, followed by one section contains the same number of setups as a one-section setup, followed by a two-section setup, followed by a three-section setup. Both scenarios contain six setups. In a steel tube manufacturing environment, an optimal setup pattern is achieved by minimizing total setups while producing the required product mix in a two-month cycle. As shown in Figure VI, the optimal schedule attempts to minimize the "average" height of the bars representing setups over a production cycle. Short-term deviations from the schedule may appear to be favorable. For example, substituting a one-section changeover for a three-section changeover may appear to result in fewer section changes in the short run. However, the number of setups should be considered with respect to the entire production cycle. By introducing an unplanned setup, even if it appears to be less costly (as in the one-section venus three-section setup), the production cycle is extended. Extended production cycles often result in delayed shipments. Thus, maintaining the integrity of the production schedule (consistent with market demand) is extremely important.

To extend the hierarchy developed by Cooper (1990), the steel tube mill actually has "levels" of batch level costs. For example, as shown in Figure VII, a three-section change-over for Product 1 benefits all subsequent products until the next three-section setup occurs (Product 12). Subsequent setups require only two-section, or one-section changes; the first section remains unchanged.

Differences between Figure VI (theoretical) and Figure VII (actual) explain how deviations are determined. Figure VI illustrates a theoretical sub-cycle in which 15 different products are to be manufactured. As shown in Figure VII, Products 1 and 2 are produced according to an optimal plan; however, before producing Product 3, another product (X1) was inserted into the production schedule. Potential causes for the deviation include stockouts, or delivery promises made to important customers. After setting up two sections of the mill for the deviation, two sections of the mill must be reconfigured in a different manner to produce Product 3. Products 4 and 5 are made with a one-section setup as scheduled; however, X2 (a product requiring a two-section setup) is introduced prior to making Product 6. Product 6, normally a one-section changeover, must now become a two-section change because of introducing X2 into the schedule. The pattern continues until the end of the seven-month production cycle. Note that because of introducing deviations into the cycle, Products 9, 10, and 11 were not manufactured during the subcycle. In this cycle, actual sections setup totaled 32 versus an optimal 25.

Actual

2 x 3 = 6 11 x 2 = 22 4 x 1 = 4

32

Optimal

2 x 3 = 6 6 x 2 = 12 7 x 1 = 7

25

Options include omitting Products 9, 10, and 11 from the cycle (to maintain the timeliness of the cycle) or to make them and delay the beginning of Sub-cycle 2. Unfortunately, if the cycle is delayed, experience suggests that even more deviations occur in the next period as attempts occur to accommodate customers whose orders are delayed from the late start-up of Sub-cycle 2. The scenario is reminiscent of the "death spiral" described by Kaplan where future actions are caused by past inefficiencies. Thus, controls were put in place to ensure schedule integrity. Order scheduling is now based on minimizing the number of setups and adhering to a master schedule.

Hypotheses, Methodology, and Results

Hypotheses and Methodology

Two forms of research methodology are utilized to investigate independence of batch-level activities. Consistent with McGrath et al., a multi-method approach attempts to "gain substantive convergence by methods that compensate for one another's vulnerabilities" (1982: 80). Field study techniques consisting of direct observations and interviews of plant personnel were used to identify activities surrounding the change from one grade to another in two manufacturing environments, paperboard and steel tubing. Statistical analyses were conducted to determine whether statistically different levels of setup categories (for the steel tube facility) and scrap following a grade change (for the paperboard mill) exist between an optimal schedule and actual observations. Optimality was operationalized through the use of a predetermined production schedule representative of Figure III and Figure VI. The hypotheses may be expressed in null form as follows:

[Ho.sub.1]: No difference exists in the scrap rate of paperboard production for observations deviating from an optimal production pattern and those observations not deviating from an optimal production pattern. Optimality is defined as changes occurring within 1/1,000th of an inch when compared to the previous grade of paperboard.

[Ho.sub.2]: No difference exists between the actual number of observations from the steel tube mill falling into each of three classifications of machine setup and the theoretical number as defined by the optimal production schedule.

[Ho.sub.3]: No difference exists in the setup time for steel tube production between observations occurring in the absence of controls and those manufactured in the presence of controls, which encourage production consistent with an optimal schedule.

The data set from the paperboard mill contains 1,096 observations of reels of paperboard and the related scrap proportion taken over a six week cycle. The data suggest any instabilities resulting from grade changes will not continue beyond the first reel produced following the grade change. Thus, for each of 49 hatches manufactured during the production cycle, the first reel was selected, and the proportion of in-specification pounds relative to total pounds within the reel was recorded. Four observations (two each from the optimal and sub-optimal classifications) were removed from the sample because of extreme values approaching zero percentage of acceptable quality. A fifth observation (the first one in the data set) was deleted because the classification scheme (optimal vs sub-optimal) is based upon the amount of change from prior production.

A t-test for two independent samples was used to examine differences between the optimal and deviate groups across the paperboard product line. In addition, the nonparametric analogue to the parametric t-test, the Mann-Whitney U-test, was applied for sensitivity analysis purposes since little is known about the distributional features of the sample data.

Setup data from the steel tube mill include 181 setups within twelve production cycles, encompassing a twenty-two month period. The setup data from the steel tube mill were analyzed using two different statistical techniques. First, the Chi-square goodness-of-fit test was used to determine whether the actual number of A, B, and C setups (which correspond to three-section, two-section, and one-section setups, respectively) fit the optimal schedule for each of twelve production cycles. The number of setups in each classification is a good proxy for the order of setups because the classification (A, B, or C) is a function of the order. A key point of the analysis is that each setup is dependent upon the machine specifications of the preceding product. An A setup is an "end-to-end" reconfiguration that uses none of the existing machine specifications. Alternatively, a B setup retains the specifications of the first section and changes the second and third sections of the mill. Finally, a C setup changes only the third, or last section of the mill while retaining the specifications of the first two sections.
Table 1

Two Group T-test For Optimal Versus Suboptimal Grade Changes in
Paperboard Production: 1 - Scrap Percentage

 Std
Groups N Mean Dev T Statistic P-value

Optimal 19 .911 .10
 2.047 .046
Suboptimal 25 .795 .22


Further evidence of the effects of deviations from an optimal schedule is presented by comparing the standard setup times allowed for the actual number of setups under two different conditions. Production cycles 1-6 represent observations during a period when production scheduling was dictated by the timing of orders received, with little focus on an optimal schedule derived from setup characteristics of the tube mill. Alternatively, production cycles 7-12 were gathered during a period when controls were implemented to minimize production time lost to setups. Production schedules were based on characteristics of the tube mill relative to the engineering specifications of the products to be manufactured. Production was scheduled to minimize downtime and increase overall throughput. A t-test was conducted to determine whether statistically different standard setup times occurred between two samples that correspond to periods with and without manufacturing controls in place.

Results

Table 1 presents the results of a two-group t-test for differences in means between the optimal and suboptimal groups. The null hypothesis is rejected with a p-value of .046. Table 2 reports the results of the Mann-Whitney U-test for differences in medians between the two samples. The Z-score is -1.655 with an associated p-value of .097. The data suggest that deviations from a theoretically optimal production pattern are associated with lower quality production. Consistent with Albright and Reeve (1992), who identify scrap from grade changes as a significant batch-level cost driver, this research suggests that manufacturing dynamics can affect the batch-level driver, even across identical products at different time periods.

Hypotheses two and three relate to the data obtained from the steel tube mill. As reported in Table 3, evidence from the Chi-square tests suggests that the actual number of setups does not always fit the standard number of setups related to each cycle. This finding suggests in order to achieve the desired output quantity, some cycles required more setups of certain types than others because of deviations from the optimal schedule. In cycles where significant differences occur, deviations from the optimal schedule are associated with more complex, longer setups to produce a given mix of product. As with the paperboard analysis, the data suggest batch-level activities are not consistent across multiple times and grades.
Table 2

Mann-Whitney U-test for Optimal Versus Suboptimal Grade Changes in
Paperboard Production: 1-Scrap Percentage

 Average
Groups N Rank Z-Value P-Value

Optimal 19 26.05
 -1.655 .097
Suboptimal 25 19.80


Table 4 illustrates the impact of deviations from the optimal schedule in terms of lost hours of production. (Cycles 1-6 occurred during a period when few controls existed to encourage production consistent with an optimal schedule.) The number of setup hours is significantly higher for production cycles 1-6 than for production cycles 7-12. Thus, further evidence suggests that factors exogenous to the batch-level activity, machine setups, are affecting the amount and severity of the activity. Therefore, variations in batch-level activities do not appear to be associated with subsequent products.

Activity based Costing principles suggest that the number of setup hours should be used to attach machine preparation costs to a batch when setup times are not uniform across the product mix (Cooper 1989a). This procedure assumes that the number of setup hours is related exclusively to the characteristics of the batch that follows the setup and is independent of exogenous factors that precede the setup. Evidence from this analysis suggests that grade changes and machine setup hours are not independent of prior events.

Summary, Implications, and Conclusions

This study seeks to understand additional influences that may impact activities surrounding certain batch-level activities occurring in continuous-process manufacturing companies. Field-based research techniques were employed to gain a deeper understanding of manufacturing processes and to identify events that may impact setup activities.

Statistical analyses were performed to determine whether batch-level [TABULAR DATA FOR TABLE 3 OMITTED] costs differ between units manufactured according to a theoretically optimal production schedule and those deviating from a theoretically optimal schedule. Since a statistically significant difference was found in each of two industries considered, evidence suggests cost system designers must consider scheduling options that impact batch-level activities. For example, setup costs that normally are allocated to a batch of production following a setup may contain costs attributable to events totally unrelated to a specific production run. This study attempts to understand these relationships and the potential magnitude of the misallocation. The implications for cost system design may include a recognition that batch-level costs can have an association with activities and units of production other than those occurring downstream from the batch-level activity.

The study both enhances the theory supporting activity-based cost system design and underscores opportunities for process improvements in manufacturing organizations. In addition, gaining a better understanding of the nature of batch-level driven may assist marketing managers when making special pricing decisions. For example, the steel tube manufacturer now evaluates rush orders against the optimal production schedule. If market factors permit extending the production cycle, special orders may be introduced into the production schedule. However, an extra setup fee is charged to the customer as a result of understanding the financial consequences of interrupting the production process.
Table 4

T-Test for Differences in Setup Hours Between Production Cycles
1-6 and Production Cycles 7-12

 Std
Groups Mean Dev T Statistic P-value

Production
Cycle 1-6 172 15.38

 3.887 .003

Production
Cycle 7-12 127 24.10


Cooper's hierarchy of overhead costs provides a theoretical framework to assist cost system designers in developing an activity-based cost system. The activity-based cost system is a significant departure from traditional overhead allocation systems using cost drivers that are exclusively volume-based. Cooper identified four levels of overhead drivers: unit-level, batch-level, product-sustaining, and facility-sustaining. The first level (unit level) resembles the traditional volume-based cost driver. The fourth driver (facility-level) often is allocated in an arbitrary manner because these costs are not directly traceable to a cost object. Thus, the major contributions made by Cooper in developing the hierarchy are the batch-level and product-sustaining costs. Product-sustaining costs are traceable to a cost object based on the unique resource demands of a product or product family. This article examined in finer detail the complexities associated with using batch-level cost drivers.

The ABC literature indicates a relationship exists between a batch activity and the units that demand the batch activity. In fact, causality is implied in this relationship. For example, raw material movement is required to initiate production of a new batch of products. Thus, in the logic of batch-level drivers, the new batch of products "caused" the activity "material movement" to occur. Material movement costs are attached to the batch of products following the movement. This article evaluates activities that occur prior to performing the batch activity. For example, the specifications of a previous product may make a subsequent setup more (or less) difficult. Examples in industry are common. A company that applies painted designs to metal sheets that ultimately are converted into coffee cans may have major and minor setups based on size changes (one-pound cans, two-pound cans, and three-pound cans) and color characteristics (red and white cans, blue and gold cans, green and white cans). A minor change may require changing from a one pound red and white can, to a one-pound blue and white can. Alternatively, a minor change may entail changing from a three-pound red and white can, to a one-pound red and white can. A major setup involves changing both color and size. According to Cooper's hierarchy of overhead costs, the setup (whether major or minor) should be assigned to the units that follow the setup.

As in the paper industry and steel tube production examples, batch-level costs for a particular production run of products may vary depending on existing machine settings when the product is scheduled. Why should a three-pound red and white can cost more to produce today (if it happens to follow the production of a one-pound blue and gold can) than when it happens to follow the production of a three pound blue and gold can? In other words, sometimes the setup is major (both color and size); sometimes the setup is minor (either color or size, but not both). The statistical results of this study provide evidence that batch level costs can be statistically different if actual production does not occur in a manner consistent with optimal production schedules. Thus, if differences exist, something other than products following a batch activity are affecting costs. Since batch-level costs are one of the most significant levels within the activity-based costing hierarchy, cost designers must consider further refining assumptions inherent in the application of batch costs to cost objects.

This article used the optimal production schedule as a baseline for comparing actual batch level activities. The purpose was to establish a best-case scenario from which to draw statistical inferences. If deviations occur, the model suggests that excess "batch-level" costs are incurred. However, control of batch-level costs is not the primary goal of a production manager. If demand does not exist for a product at the time of scheduled production, JIT principles suggest the product should not enter production. Holding costs, including financial carrying costs, damage, and obsolescence, may result from rigid adherence to an optimal production schedule that does not consider market demand.

The author wishes to acknowledge the following individuals for their helpful comments: Robin Cooper, Mike Dugan, Rob Ingram, Tom Lee, Jay Nichols, Harold Roth, William Samson, two anonymous reviewers, and the editor. In addition, the author wishes to acknowledge the Culverhouse School of Accountancy and the College of Commerce and Business Administration at the University of Alabama for providing a research grant in support of the project.

1 Though the setup cost per unit is lower for large batches, holding costs may be higher for large batches if insufficient market demand exists for output.

2 Siemens Motor Works is Harvard Business School Case # 191-006, copyright 1988.

3 John Deere Component Works A and B are Harvard Business School Case numbers # 9-187-107 and # 9-187-108, respectively, copyright 1987.

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Author:Albright, Thomas L.
Publication:Journal of Managerial Issues
Date:Sep 22, 1998
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