The impact of component commonalityin an assemble-to-order environment under supplyand demand uncertainty

Omega 33 (2005) 472 482 www.elsevier.com/locate/omega The impact of component commonalityin an assemble-to-order environment under supplyand demand uncertainty E. Mohebbi, F. Choobineh Department of Industrial and Management Systems Engineering, University of Nebraska-Lincoln, 175 Nebraska Hall, Lincoln, NE 68588-0518, USA Received 6 August 2003; accepted 7 July2004 Available online 15 September 2004 Abstract A material requirements planning simulator with a two-level bill-of-material is used to studythe impact of introducing component commonalityinto an assemble-to-order environment when demand is subject to random variations, and component procurement orders experience random delays. By using simulated data, our ANOVA results show that component commonality significantlyinteracts with existence of demand and supplychain uncertainties, and benefits of component commonalityare most pronounced when both uncertainties exist. 2004 Elsevier Ltd. All rights reserved. Keywords: Component commonality; Lead-time uncertainty; Demand uncertainty; Assemble-to-order environment 1. Introduction The assemble-to-order (ATO) strategyemerges in manufacturing environments where manyfinished products are assembled from a relativelysmall set of standard components and subassemblies. In a typical ATO manufacturing environment, components and subassemblies are acquired according to a forecast, while finished products are assembled onlyafter actual customers orders have been received. In other words, component and subassemblies are replenished in a make-to-stock (MTS) fashion, but finished products are assembled in a make-to-order (MTO) manner. Such a hybrid planning approach is particularlyadvantageous in situations where the assemblytime of a product is considerably shorter than the procurement and/or manufacturing time of its components and subassemblies; thus, making a tradeoff Corresponding author. E-mail address: emohebbi@unlnotes.unl.edu (E. Mohebbi). between inventoryholding cost, product variety, and deliverytime achievable [1]. Examples of ATO systems can be found in various industries producing consumer goods such as automobiles and personal computers where customers are offered a varietyof product options with a relativelyshort deliverytime. It is well known that the on-time deliveryof assemblysystem in general is diminished bythe shortages of components. Experiencing such shortages often results in production capacitylosses and/or customers goodwill loss induced bymissing planned product deliverydates. The primarycause of component shortage is the inherent uncertaintyassociated with procurement and/or suppliers manufacturing lead times, which can be attributed to a varietyof reasons ranging from unexpected delays in shipping, transportation, and receiving times to variable setup, processing and inspection times. Yano [2], Hopp and Spearman [3], and Hegedus and Hopp [4], among others, discuss the issue of lead-time uncertaintyin assemblysystems. Another factor that is known to influence the performance of an assemblysystem is the commonalityof components 0305-0483/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.omega.2004.07.011

2 E. Mohebbi, F. Choobineh / Omega 33 (2005) 472 482 among products. Unlike the element of lead-time uncertaintywhich is an operating characteristic of a manufacturing/supplysystem, the commonalityof components is an attribute of product design decisions. For instance, one wayfor increasing component commonalityis bydesigning multiple-feature components that can be used in different products. Often all products do not need all the features and each product requires onlya subset of the designed features. A car dashboard, for example, can be designed with multiple features to fit a varietyof models without increasing the number of stock keeping units (SKUs) and the associated ordering and holding costs. It should be noted that increasing the number of components features mayincrease their production costs; however, the resulting productivitygains from the economyof scale in procurement as well as from cost savings in warehousing and manufacturing operations in most cases offset the potential increase in production costs [5]. This paper investigates the desirabilityof increasing component commonalityin ATO systems when product demand and component procurement lead times are random variables. We conduct a comprehensive simulation studyto reveal the level of complex interactions among factors affecting the performance of an ATO system. Our findings provide significant insights in managing component inventories in ATO systems. The organization of the paper is as follows. In Section 2, we identifythe research gap in the literature that motivates our study. Section 3 contains a detailed description of our simulation experiment. The experimental results are presented in Section 4, followed bya summaryof our findings in Section 5. Section 6 outlines the limitations of the present studyand proposes a few related directions for future research. 2. Past research Component commonalityhas been studied from various standpoints in the literature. A large portion of research in the area is concerned with the impacts of introducing commonalityamong components on various performance measures (e.g., inventoryand service levels, total cost or total profit, etc.) of assemblysystems. More specifically, most of the existing analytical models in the inventorycontrol literature are focused on studying the benefits of risk-pooling and order-pooling effect of component commonalityon reducing inventorylevels and procurement costs solelyin relation to the variabilityof demand (e.g., see Baker et al. [6], Gerchak et al. [7], Eynan and Rosenblatt [8], Agrawal and Cohen [9], among others). As such, an underlying assumption in all these studies is that the procurement lead time for components is either zero (negligible) or constant. In recent years, the increasing popularity of mass customization and postponement of product differentiation in manufacturing environments has motivated new analytical models in areas of component commonality and ATO systems (e.g., Ma et al. [10], Song and Yao [11], Cheng et al. [12]). However, a review of the relevant literature indicates that the impacts of component commonalityin assemblysystems where both product demand and component procurement lead time are random variables remains largelyunexplored. Indeed, this is due to the fact that analytical treatment of such systems is an exceedingly difficult task which requires detailed tracking of outstanding procurement orders (curse of dimensionality) and explicit knowledge of demand during lead time. As in similar circumstances, simulation provides an effective tool for gaining insights into the performance of complex systems which appear to be analytically intractable. Most manufacturing environments face multiple sources of uncertainties including product demand, procurement lead times, production yield, and product quality, to name a few. A simulation studyof material requirements planning (MRP) systems by Brennan and Gupta [13] established the significance of demand and supply channels uncertaintyfactors for various product structures with a single finished product and fixed number of unique components (i.e. no commonalityfactor was considered). Other simulation studies that have incorporated the product structure as a design factor in investigating the MRP performance include Grasso and Taylor [14], Benton and Srivastava [15], Lee and Adam [16], and Gupta and Brennan [17], among others. Benton and Krajewski [18] conducted a simulations study that showed component commonalitydampens the effect of lead-time uncertaintyin MTS environments with variable demands. Sheu and Wacker [19] treated the manufacturing lead time as a performance measure and carried out a simulation studyto investigate the effect of purchased components commonalityand commonality imbalances on manufacturing lead time in a two-stage manufacturing and assemblyenvironment. However, none of these studies have addressed the combined impact of component commonality, random product demand, and random procurement lead time as experimental factors in a single operational setting for ATO systems. Hence, in contrast with the existing simulation studies, this research focuses on ATO environments where demand and supplyare both uncertain and explores new aspects of the component commonalityfactor in manufacturing systems. 3. Simulation environment We consider a two-level ATO environment that produces three finished products, F j,j=1, 2, 3. Each product is considered with several two-level bill-of-material (BOM) structures to reflect various degrees of component commonality (Fig. 1). The main characteristics of the simulated environment are discussed below.

E. Mohebbi, F. Choobineh / Omega 33 (2005) 472 482 3 PS1 (DCI=1; TCCI=0) C 41 C 42 C 43 PS 2 (DCI=1; TCCI=0) C 4 PS5 (DCI=1.5; TCCI=0.4) C 41 C 42 C 43 C 4 C 51 C 52 C 53 C 5 PS3 (DCI=1; TCCI=0) PS6 (DCI=1.8; TCCI=0.5) C 41 C 42 C 43 C 4 C 51 C 52 C 53 C 5 C 61 C 62 C 63 C 6 PS4 (DCI=1; TCCI=0) PS7 (DCI=2; TCCI=0.55) DCI: Degree of Commonality Index TCCI: Total Constant Commonality Index Basic Components Replaceable Components Common Components Fig. 1. Product structures (PS).

4 E. Mohebbi, F. Choobineh / Omega 33 (2005) 472 482 3.1. Assembly environment The simulation model represents an ATO environment that is identified bythe following characteristics: 1. A rolling planning horizon forecast for each finished product is generated from a known pattern throughout each simulation run. 2. The actual demand for each finished product in anygiven period is a random variable. 3. The actual and planned assemblylead time for all assemblyorders is one period. 4. The planned procurement lead time for all components is fixed at four periods. 5. The actual procurement lead time for each component is a random variable. 6. A lot-for-lot (L4L) policyis used to determine the sizes of components procurement orders. 7. The components time-phased net requirements, planned order releases, and planned order receipts are generated through the BOM explosion in everyperiod, using planned lead times and the lot-sizing policy. 8. All unmet demands for finished products are backordered. 9. There are no provisions for safetystocks or safetylead times in the system. 10. There are no production capacity/storage constraints. At the beginning of everyperiod, inventoryrecords are updated, and actual demands for finished products are generated. The updating process adds procurement orders to inventoryaccording to their actual lead times and sets the finished products inventoryto zero (i.e., components procurement orders are received and finished products are shipped to the customers). Next, similar to MRP logic, a BOM explosion is carried out to determine time-phased net requirements and planned order releases for all components. Finally, actual lead times are determined by random sampling from lead time probabilitydistributions as orders are released. Note that in this ATO environment, components are ordered according to the their time-phased planned order releases, and finished products are assembled only to meet the customers actual demands and shortages are backordered if necessary. Therefore, given that the inventoryrecords are updated at the beginning of each period, all the components received at the beginning of each period are immediatelyavailable for allocation to the assembly of finished products. Taking into account the one-period assemblylead time, this simplymeans that in anygiven period, the system is assembling finished products to meet the actual demand for the next period plus anypossible backordered quantityfrom the current or previous periods. It should also be pointed out that the exclusion of anysafety stock or safetylead time from the simulation model stems from the main focus of our experimental study. That is, the research question that the simulation studyattempts to address is solelyconcerned with whether or not increasing the commonalityof components (without interacting with anysafeguarding measures such safetystock or safetylead time) will have anyimproving effect on the performance of an ATO system when demand and lead time vary from their fixed estimates used for planning purposes. Furthermore, the choice between safetystock or safetylead time as well as the distinction between the aggregated impact of these two safetybuffers (if applied concurrently) when demand and lead time are both uncertain is generallyvery difficult and remains an open research question. As such, the issue of finding the proper method of safeguarding an ATO system against uncertainty (i.e., through the use of safetystock, safetylead time, component commonality, or some combination of these factors) extends beyond the scope of the present work, and provides a direction for future research and development. 3.2. Allocation policy Since our ATO system allows for shortages to be backordered, we note two extreme approaches toward filling backorders in anygiven period. In the first approach, the system aims at filling the backorders before satisfying the current demand; and in the second, the system attempts to fill the backorders onlyafter the demand orders for the current period are met in full. While the first approach is prevalent in situations involving time-dependent shortage cost, the second approach fits environments where the shortage cost is charged on a per order basis. We realize that perhaps a combination of the two extreme approaches is more likelyto occur in practice. In our current experimental study, however, we adopt the second approach that appears to be more in line with the main focus of this research. Furthermore, in case of components shortages, we applya rationing rule that is based on giving priorityto product requirements of smaller demand. That is, when determining the size of assemblyorders for finished products in anyperiod, component stocks are first allocated to meet the actual demand orders in a non-descending order. The remaining stock is then allocated to fill the backorders from the smallest quantityto the largest. Baker et al. [6] use a similar rule in their single-period model with no backorders. 3.3. Performance measures The simulation model collects period-by-period statistics on levels of components inventories, products backorders, and the proportion of products demand orders that are satisfied on time. These statistics are collected at the beginning of each period (after inventoryrecords are updated) and then used to calculate end-of simulation run statistics on three performance measures: the average total inventory of components per period, the average proportion of products demand orders per period that were fullysatisfied on time (service level), and the average total backorder of finished products per period. Note that the average proportion

E. Mohebbi, F. Choobineh / Omega 33 (2005) 472 482 5 of demand orders satisfied on time is particularlychosen as a measure of service level to reflect on the impact of uncertaintyin components planned availability. Also, similar to Baker et al. [6], we do not consider anycost attributes as the main focus of our studyis to understand the sheer impacts of lead-time and demand uncertainties on assemblysystems with/without component commonality. 3.4. Experimental factors and their levels The simulation experiments were designed to investigate the impacts of four main factors within the designated ATO environment. These factors and their corresponding levels are as follows. 3.4.1. Product structures A keyfocus of this research was to studythe impacts of increasing the number of common components on the assemblysystem performance. Hence, we considered seven different product structures. These structures (i.e. PS1,..., PS7) along with their corresponding Degree of CommonalityIndex (DCI) [20,21] and the Total Constant CommonalityIndex (TCCI) [22] are depicted in Fig. 1. All structures contain three finished products, each having a twolevel BOM with a on-for-one parent-sibling relationship. To simplifyfuture references, the components are classified under three distinct categories: basic components (,, and ) that are part of all seven structures; replaceable components (C 41,C 42,C 43,C 51 C 52,C 53,C 61,C 62, and C 63 ) that are onlypresent in PS2, PS3, and PS4; and common components (C 4,C 5, and C 6 ) that are included in structures PS5, PS6 and PS7. Observe that all basic and replaceable components are product-specific components. Also, note that the base structure considered in PS1 represents a simple three-product three-component structure with no commonality(i.e., all components are product specific). Accordingly, PS2, PS3, and PS4 exhibit similar three-product structures with no commonality, but with the number of components increased to 6, 9, and 12, respectively. In effect, structures PS1 through PS4 represent a scenario that involves increasing the number of product-specific components byan increment of 3. Clearly, such a scenario is of interest in investigating the impacts of increasing the number of product-specific components when procurement lead times are uncertain. On the other hand, PS5, PS6 and PS7 exhibit alternative product structures for the same finished products, each with three product-specific components (i.e. basic components), but allowing for 1, 2, and 3 common components, respectively. Hence, structures PS1, PS5, PS6, and PS7, in contrast with structures PS1 PS4, represent a scenario involving a systematic increase in the number of common components among all three finished products. For instance, while components,, and are present as basic components in both PS2 and PS5, replaceable components C 41,C 42,C 43 in PS2 are replaced with the common component C 4 in PS5. We call PS2 and PS5 an isomorphic pair of product structures. Similar analogies can be drawn between components C 51,C 52,C 53, and C 5 as well as between components C 61,C 62,C 63, and C 6 in structures PS3 and PS6, structures PS4 and PS7, respectively. 3.4.2. Forecast and actual demand for finished products The forecast for each finished product throughout the experiments was held constant at 100 units per period. However, the actual demand per period for each finished product was generated independentlyusing a uniform distribution over the interval [a,b]. Four levels of such demand intervals were considered: D1 with a = b = 100; D2 with a = 90 and b = 110; D3 with a = 80 and b = 120; and D4 with a =70 and b =130. Note that the case D1 simplyrepresents a perfect forecast with no errors. 3.4.3. Components procurement lead times The procurement lead times for all components (i.e. the time elapsed between the release of components procurement orders and the actual receipt of the material in inventory) in each experiment were assumed to be independent and identicallydistributed. Recall that the planned lead time for components procurement orders was set at four periods. In most assemblyenvironment where components are procured from external resources, the issue of earlydeliveryof replenishment orders is fairlyinsignificant as operation managers attempt to obtain accurate (non-inflated) estimates of replenishment lead times byworking closely with their suppliers. Nevertheless, random delays in deliveryof procurement orders in such settings can still occur due to unexpected disruptions in the supplyprocess (e.g., equipment breakdowns, traffic and weather conditions, etc.) Hence, in characterizing the lead time uncertainty, we ignored the possibilityof an earlydeliveryof a procurement order and allowed for the actual procurement lead time of each component to be subject to a random delay, l, where l is a non-negative random variable following a discrete distribution. Table 1 contains five cases of discrete probability distributions with increasing mean delay, E[l], and probabilityof lateness, P(l>0) that were considered to represent l in our experiments. We note that our chosen distributions in this case serve the main objective of this work byfocusing on the impact of late procurement order arrivals on assembling finished products with and without component commonality. 3.5. Initial inventories Initial inventories (i.e., at the beginning of period 1) for each item of finished products, product-specific basic and replaceable components, and common components were set at 100, 500 and 1500 units, respectively. We note that these quantities were set based on the forecast of each product demand per period (100 units), and the resulting requirements for product-specific (100 units/period) and common (300 units per period) components over a full replenishment

6 E. Mohebbi, F. Choobineh / Omega 33 (2005) 472 482 Table 1 Actual lead-time lateness distributions for components procurement orders Lateness l = 0 l = 1 l = 2 l = 3 l = 4 Mean E[l] P(l>0) Level LT1 1 0 0 0 0 0 0 LT2 0.60 0.25 0.1 0.05 0 0.60 0.40 LT3 0.45 0.25 0.15 0.10 0.05 1.05 0.55 LT4 0.30 0.25 0.20 0.15 0.1 1.50 0.70 LT5 0.20 0.20 0.20 0.20 0.20 2.00 0.80 cycle (i.e., planned lead time +1) to avoid severe stockouts at the start of the simulation runs. 3.6. Experimentation We considered a full factorial experimental design that required simulating 140 scenarios (four levels of demand, five levels of lead time, and seven levels of product structures). Since most companies report their performance metrics on an annual or quarterlybasis, and follow their trends accordingly, we conducted a terminating simulation analysis that was ended after collecting statistics for 50 periods (i.e. weeks) of operation. This amounts to annual reporting of the performance metrics. To nullifythe impact of initial conditions and ensure steadystate results, a run length of 70 periods was used in each experiment and the desired statistics were collected starting with period 21. Each scenario was replicated 10 times and the averages of the 10 replications are reported. We note that this approach was adopted after conducting a series of pilot simulation runs with various parameters settings. 4. Simulation results and analysis Our experimental results reveal interesting insights into the performance of the ATO system described above. In what follows, we first present a graphical view of resulting performance measures to provide a conceptual understanding of the system behavior. We then present statistical analyses of the simulation results pertaining to the full factorial experimental design described above. It should be noted that in presenting our graphical results pertaining to inventory levels, we chose to plot the average inventoryper component per period for better clarityand scaling purposes. Our statistical analysis of inventory results, however, is based on the average total inventoryof components per period. 4.1. Graphical view of simulation results Fig. 2 shows the behavior of average total inventoryper component per period as a function of product structures (PS) and actual components procurement lead times (LT) for cases 1 and 4 of actual demand (D1 and D4). We note that to calculate the average inventoryper component per period for creating these plots, replaceable components C 41,C 42, and C 43 were grouped together and counted as a single component. The same grouping scheme was applied to (C 51 C 52,C 53 ), and (C 61,C 62,C 63 ) where applicable. As such, the total number of components for PS1, PS2, PS3, PS4, PS5, PS6, and PS7 were considered as 3, 4, 5, 6, 4, 5, and 6, respectively. Recall that in D1, the actual demand is the same as forecast demand, and in D4, the actual demand can randomlyvaryfrom the forecast byup to 30%. Several observations can be made: (i) while the total number of components increases as the product structure varies from PS1 to PS4, or from PS5 to PS7, the average total inventory per component per period in both scenarios increases at a diminishing rate; (ii) when actual lead time is the same as the planned lead time (LT1), the average total inventoryper component per period is always the highest; and (iii) the presence of both demand and lead-time uncertainties tend to reduce average total inventoryper component per period. Fig. 3, in separate panels, displays the average total inventoryper component per period for basic, replaceable, and common components as a function of lead-time cases for relevant cases of product structures. It is clear from this figure that: (i) demand uncertaintyincreases the average inventoryfor both basic and common components; (ii) leadtime uncertaintytends to decrease the average inventoryof both basic and common components when demand is uncertain, however, this decreasing impact tends to diminish as the number of components increases; and (iii) lead-time uncertaintyhas mixed impacts on the average inventorywhen demand is deterministic. Fig. 4 shows that the average proportion of demand orders fullysatisfied per period decreases with demand uncertainty and this decrease is magnified as the lead-time uncertainty increases. Bythe same token, Fig. 5 exhibits that the average backorder per finished product per period increases with lead-time uncertaintyand this increase becomes more visible as the number of components increases. 4.2. Statistical analysis of simulation results As mentioned earlier, we conducted a full factorial ANOVA with dependent variables consisting of the average

E. Mohebbi, F. Choobineh / Omega 33 (2005) 472 482 7 Fig. 2. Plots of average total inventoryper component per period. Fig. 3. Plots of average inventoryof basic, replaceable, and common components per component per period.

8 E. Mohebbi, F. Choobineh / Omega 33 (2005) 472 482 Fig. 4. Plots of average proportion of demand orders fullysatisfied per period. Fig. 5. Plots of average backorders of finished products per product per period. total components inventoryper period, the average proportion of demand orders fullysatisfied per period (service level), and the average total backorder of products per period. In addition, we performed pair-wise statistical analyses between mean values of performance measures of isomorphic product structures. Recall that the isomorphic pairs of product structures are PS2 and PS5, PS3 and PS6, and PS4 and PS7. Hence, in conducting a pair-wise analysis between PS2 and PS5, for example, we investigate the desirability of replacing three replaceable components (i.e. C 41,C 42, and C 43 ) with one common component (C 4 ). We note that such pair-wise analyses are aimed at investigating the attractiveness of component commonalityas the total number of components increases in a stochastic ATO environment. The ANOVA results for the full factorial experimental design are depicted in Table 2. These results clearlyindicate that product structures, and lead-time and demand uncertainties significantlyimpact all three dependent variables. All two level interactions, except for the interaction between product structures and demand in the case of average total inventoryas the dependent variable, are also significant at the 0.05 level. Table 3 contains the mean values of performance measures for the isomorphic product structures. Several observations are worth mentioning. Note that irrespective of the degree of component commonality, the average total inventoryper period in our experiments increased with the total number of components used in product structures. However, the average total inventories for PS5, PS6 and PS7, respectively, were found to be lower than those of PS2, PS3, and PS4. This suggests that the average total inventoryper period in product structures with component commonalityis consistentlylower than in their isomorphic structures without component commonality. Furthermore, pair-wise comparisons of different categories of components inventories between isomorphic structures suggest that component commonalityreduces the average total inventoryof basic components. A similar pattern can be found when comparing the average total inventoryper period of common components and that of their corresponding replaceable components in isomorphic product structures. Entries in Table 3 also indicate that component commonalityappears to elevate the service level and reduce the average total backorders per period in the ATO system.

Table 2 ANOVA results for various performance measures E. Mohebbi, F. Choobineh / Omega 33 (2005) 472 482 9 Source df Inv SL BO F p F p F p PS 6 3319.6 0.000 * 28.3 0.000 * 34.3 0.000 * LT 4 232.4 0.000 * 990 0.000 * 1123.5 0.000 * D 3 98.0 0.000 * 176.4 0.000 * 38.0 0.000 * PS * LT 24 1.9 0.006 * 4.1 0.000 * 3.5 0.000 * PS * D 18 1.3 0.149 6.2 0.000 * 1.6 0.044 * LT * D 12 6.1 0.000 * 17.0 0.000 * 3.7 0.000 * PS * LT * D 72 0.3 0.999 0.7 0.989 0.3 0.999 Inv: Average total inventoryof components per period; BO: Average total backorder of finished products per period; SL: Average proportion of total demand orders fully satisfied per period (service level); PS: Product structure; LT: Lead-time uncertainty; D: Demand uncertainty; R-Squared: 0.944 (INV), 0.802 (SL), 0.799 (BO). Marks statistical significance at the 0.05 level. Table 3 Mean value of performance measures observed for different cases of product structures Performance measures Product structures PS2 PS3 PS4 PS5 PS6 PS7 Average total inventory1056.7 1697.8 2380.0 1041.7 1677.3 2340.3 (units/period) Total basic components a 526.4 566.4 595.7 525.6 549.6 570.4 Total replaceable components b 530.2 1131.6 1784.3 n/a n/a n/a Total common components c n/a n/a n/a 516.1 1127.6 1769.9 Average proportion of demand 0.7758 0.7548 0.7429 0.8030 0.7914 0.7953 fullysatisfied per period Average total backorders (units/period) 112.8 126.7 138.0 102.4 116.1 121.5 a + + for all cases of product structures. b C 41 +C 42 +C 43 for PS2; C 41 +C 42 +C 43 +C 51 +C 52 +C 53 for PS3; and C 41 +C 42 +C 43 +C 51 +C 52 +C 53 +C 61 +C 62 +C 63 for PS4. c C 4 for PS5; C 4 + C 5 for PS6; and C 4 + C 5 + C 6 for PS7. To examine the statistical significance of these observations, when comparing isomorphic product structures, the following alternative hypotheses were formulated. In all cases the null hypothesis corresponds to the scenario involving no significant difference between the performance measures. Hypothesis 1. The average total inventoryper period with component commonalityis lower than that without common components. Hypothesis 2. The average total inventoryof the common components per period is lower than that of their corresponding replaceable components. Hypothesis 3. The average total inventoryof the basic components per period with component commonalityis lower than without commonality. Hypothesis 4. The service level with component commonalityis higher than that without common components. Hypothesis 5. The average total finished products backorders per period with component commonalityis lower than that without common components. The results of our pair-wise-t-test for the above hypotheses are given in Table 4. These results show that the first three hypotheses cannot be accepted at the 0.05 level except for Hypothesis 3 which is accepted when comparing PS3 with PS6, and PS4 with PS7. These results suggest that component commonalitydoes not seem to significantlyreduce the total components inventoryin the ATO system. Nevertheless, the impact of component commonalityon reducing the average total inventoryof basic components per period appears to become more significant as the number of common components increases. In particular, the reduction in the average total inventoryof basic components in the case of comparing PS4 and PS7 is 50% more than when comparing PS3 and PS6. The results of the pair-wise t-tests for Hypothesis 4 demonstrates a similar relationship between the growing significance of component commonalityin improving the service level and number of common components. The service level improvement when comparing PS4 and PS7 is 43% more than when comparing PS3 and PS6. Finally, the advantage of component commonalityin reducing the average total backorders per period does not seem to

10 E. Mohebbi, F. Choobineh / Omega 33 (2005) 472 482 Table 4 Hypotheses testing on the impacts of component commonality on total inventory, service level, and backorders Hypothesis PS2&PS5 PS3&PS6 PS4&PS7 t Accept? t Accept? t Accept? 1 0.718 No 0.813 No 1.357 No 2 1.342 No 0.230 No 0.650 No 3 0.076 No 1.838 Yes 3.166 Yes 4 1.614 No 2.147 Yes 3.115 Yes 5 1.154 No 1.101 No 1.620 No Level of significance = 0.05. be significant as Hypothesis 5 cannot be accepted at the 0.05 level. 5. Summary We presented an extensive simulation studyof an ATO manufacturing environment with two-level product structures. The purpose of our simulation experiments was to studythe combined effects of component commonality, demand uncertainty, and late procurement-order arrivals on the system s performance. Our experiments consisted of three independent variables that included product structures, demand and lead-time probabilitydistributions. We chose seven product structures with increasing number of components three with, and four without component commonality. Also, four demand distributions with increasing variance and five procurement lead-time distributions with increasing probabilityof late deliverywere chosen. The insights gleaned from the experimental results are summarized as follows: Introduction of common components among products does not significantlydecrease the average total inventoryof components per period. Increasing component commonalitysignificantlyincreases the average percentage of products on-time order delivery. The impact of increasing component commonalityon reducing the average total backorder of products per period is not significant. Increasing component commonalityis more advantageous in environments that experience uncertaintyin both products demand and components procurement processes than those facing uncertaintyin onlyone of these processes. When replacing a number of product-specific components with a common component, the system on average will carrya lower inventoryof common components per component than that of the replaceable components. The inventoryof basic components is not significantlyaffected bychanges in the number of common components. 6. Limitations ofthe study and future research directions In general, the scope of conclusions drawn from any simulation studyis constrained bythe experimental design of the simulated environment. As such, the conclusions drawn from the present studyshould be viewed in light of the limitations of our experimental design. The first and foremost of such limitations is the simplicity of our BOM s; we onlyconsidered two levels for each BOM and set the quantityper product for all components to one. Sheu and Wacker [19] have shown that increasing the quantityper product values from one to larger values changes the balance within and between BOM s and hence, influences the commonalitymeasures to a great extent. Therefore, whether or not our conclusions stand for BOM s with more than two levels and/or larger values of quantityper product is a subject for future studies. In addition, our studyonly considered four products. While we conjecture that the impact of commonalitywill be more pronounced when component commonalityexists among a larger number of products, more research is required to investigate the issue. Finally, it should be noted that the insights provided in this study are based on operational analyses of an ATO system without anycost considerations. In practice, the costs of designing and manufacturing common components may outweigh the potential benefits of utilizing component commonality. Therefore, decisions regarding the introduction of common component into product structures, like other productivityimprovement initiatives, should be subject to economic justification. Acknowledgements The authors wish to thank three anonymous referees for their insightful comments and the programming support of Ms. Chun Fan, and Mr. Anupam Pattanayak. This research was supported bythe NSF grant EPS-0091900.

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