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Analyzing and evaluating product demand interdependencies
Computers in Industry 61 (2010) 869–876
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Computers in Industry journal homepage: www.elsevier.com/locate/compind
Analyzing and evaluating product demand interdependencies Peter Nielsen *, Izabela Nielsen, Kenn Steger-Jensen Department of Production, Aalborg University, Fibigerstrede 16, DK 9220 Aalborg, Denmark
A R T I C L E I N F O
A B S T R A C T
Article history: Available online 21 August 2010
Demand-driven manufacturing is an extremely unstable planning environment compared to forecastdriven manufacturing. This requires preparation and makes knowledge of demand behaviour even more important for planning and control. The basic assumptions of pre-ante allocation based on forecast of independent end-products demand are critical for manufacturing planning and control in general. However, the importance is higher for demand-driven manufacturing than forecast-driven manufacturing. This is due to the sensitivity of demand-driven manufacturing to demand fluctuations, e.g. time and interdependency of demand rates, due to the customer order decoupling point. This paper presents a method to establish time and interdependency of demand rates (the Time- and Interdependent Demand Rate Method), which can improve the planning and control performance as well as the order management performance in a MTO environment. The method is tested on data from two cases. For both cases results and demand planning implications are presented. Use guidelines for the method are also presented along with avenues of further research. ß 2010 Elsevier B.V. All rights reserved.
Keywords: Make-to-order Demand planning Master Production Scheduling Time- and Interdependent Demand Rate Method
1. Introduction Manufacturing companies differ in the way they meet their demand. Some deliver products to their customers from finished goods inventories as their production anticipates customers’ orders; others, however, manufacture only in response to customers’ orders. A company in the demand-driven make-toorder (MTO) manufacturing environment has to supply a wide variety of products, usually in small quantities, ranging from standard products to all orders requiring a customized product [1,2]. MTO companies primarily compete on delivery time and reliability in meeting due dates and flexibility to adapt (to product mix and volume) [3]. Likewise MTO companies, like all companies, are subject to competition on price. In recent years it has however become increasingly normal to produce a wide range of products (some more or less customized) entirely to order [4,5]. A vital part of the ability to compete in this environment is the MTO manufacturer’s order management approach. However, to a large extend this still depends on the MTO manufacturer’s ability to allocate resources and materials prior to actually receiving customer orders. Only in extreme cases it is unnecessary for MTO manufacturers to plan based on forecasts. This means that especially the demand-driven manufacturers will benefit from increased insight into customer ordering behaviour.
* Corresponding author. Tel.: +45 9940 8932. E-mail addresses: [email protected] (P. Nielsen), [email protected] (I. Nielsen). 0166-3615/$ – see front matter ß 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.compind.2010.07.012
In this paper a method is presented that contributes to this insight by establishing (1) time dependence of demand rates, and (2) interdependence of demand rates. This increased insight can be used to improve planning and order management. The paper is structured as follows. First, planning issues in a MTO-environment are discussed, finding that an unresolved critical aspect of demand planning in a MTO environment is handling demand rate fluctuations within a planning period and interdependent demand rates of products. Second, a method called the Time- and Interdependent Demand Rate Method, for establishing demand rate profiles and interdependencies of demand between products, is presented. Following this, the method is tested on data from two MTO manufactures, the results are interpreted and the demand planning implications of the particular demand behaviour is discussed. This section also includes guidelines for utilizing the method. Finally, conclusions and avenues of further research are presented. 2. Critical planning issues in a MTO-environment Demand planning impacts all areas of operations. The further up-stream the internal supply chain the Customer Order Decoupling Point is placed, the more demand-driven are operations, the more sensitive and complicated the demand planning process becomes to fluctuations in demand both aggregate and disaggregate volume and mix of products. Demand planning is in general integrated both vertically (the hierarchical planning approach, the basic assumptions of which are pre-ante allocation of independent end-products
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demand, based on forecast) and horizontally (the order management approach where the major part of the daily operations will be initiated and defined by the customer) in planning and operations. Vertically the challenges in a MTO environment is to pre-ante allocate the right capacity and the right materials [6–9]. This is primarily addressed at the sales and operations planning (SOP) level and at the Master Production Scheduling (MPS) level. For future reference in this paper, the period for which materials and capacity is allocated for on the MPS level is referred to as the MPS planning period. This period is considered as a fixed time bucket in which aggregate needs for material and capacity are allocated based on forecasts and received customer orders for the entire time bucket. If capacity and materials are not allocated pre-ante to actual customer demand, the manufacturer will incur increased costs of operations to achieve a short delivery time due to, e.g. rush orders from suppliers and use of overtime. The desired delivery time to customers is typically shorter than the actual lead time (purchasing lead time + manufacturing lead time). A consequence of shorter lead time than desired delivery time is the need to forecast demand to make allocations and to plan. This can be done in different ways [7,8] but in general capacity and material allocations are conducted based on forecasts of aggregate product demand (or customer orders) which are subsequently disaggregated for MPS planning purposes by the use of some sort of variant distribution key [7,10]. On the SOP level there are options to influence both the demand side (e.g. pricing, advertising and promotion, etc.) and the supply side (e.g. hiring and firing, using overtime and undertime, carrying inventory, etc.). However, these options are difficult to use if the assumptions of independences of product demand used for planning on both SOP and MPS levels are not valid. The allocation of capacity and materials for the MPS planning period is typically based on the following assumptions of customer ordering behaviour [7,11]:
Horizontally the challenge is to integrate the order management process with the planning process on the MPS level. The issue then becomes if the customer ordering behaviour experienced during the order management process matches the assumptions on which the MPS is based. So what can the customers actually be expected to do? Firstly, within MPS planning periods the timing of orders is likely to be influenced by:
This seems to indicate that the demand for individual products is not independent as assumed, but can potentially be interdependent. Both issues have not been addressed directly in current-state simultaneously, but some approaches to influence and improve the planning foundation have been presented. These approaches can roughly be categorized as collaboration/market manipulation schemes or coping with the givens. Collaboration includes supply chain planning and supply chain integration that by their very nature of sharing information integration and collaboration with customers on demand planning gives superior results [12,13]. Another proactive approach is demand management [14,15]. The underlying assumption in demand management is that changing some product characteristic (usually price or delivery time) manipulates customer behaviour in a way that benefits the manufacturer. Supply chain integration measures have frequently shown to give the best performance of the demand planning process with regards to cost and on-time-delivery, but it is not a viable option for all MTO manufacturers. Demand management will likewise be problematic to implement for most MTO manufacturers due to the typical size of the product portfolio. These MTO manufacturers must instead cope with the given situation of a market/production process/product-combination. Coping with the givens includes using advanced planning and scheduling systems [5] to ensure efficient utilization of resources, decreasing lead times through lean initiatives [11] and other measures to improve responsiveness. The fact is that most of the costs of operations are allocated prior to knowing demand. The quality and type of forecasted demand information used for allocation is therefore critical for the demand planning process performance. Getting a higher quality of demand information can only improve the performance of plans. Through the years many forecasting techniques have been presented with the purpose of supplying demand forecasts for planning purposes [16–18]. Forecasts are usually grouped into three categories qualitative methods, time series methods and causal methods [19]. The whole aim of the forecasting procedure is however still based on delivering forecasts covering a particular planning period. Methods as presented in Doganis et al. [18] for non-linear time series forecasting, Chen and Wang‘s [19] hybrid model or methods combining intuitive and quantitative methods such as expert systems [20] or Bayesian models [21] seem to be unable to address these issues. Wall et al. [22] present a prototype Decision Support System for supporting varying demand within certain periods of the MPS planning period. However, the method fails to support the day-to-day requirements of the dynamic planning environment in MTO manufacturing as well as it fails to support the interdependencies of demand. The conclusion is that there is a need for better knowledge/ models of demand behaviour prior to making pre-ante allocations of materials and capacity. Two critical issues present themselves:
customers’ own inventory policies, giving cyclic ordering patterns, credit conditions from the manufacturer encourage ordering certain products or quantities at certain times, and transportation rationalities, minimizing transportation cost, encourage ordering a full load or quantities at certain times.
1. Is the demand rate within the MPS planning period time dependent, i.e. does the customer have ordering preferences due to, e.g. credit conditions? 2. Are the demand rates of products within a MPS planning period interdependent, i.e. do customers order several products for simultaneous delivery due to, e.g. shipping or usage?
Contrary to the assumptions it seems likely that demand rates within a MPS planning period are time dependent. Secondly, it is likely that customers:
This paper provides a method, the Time- and Interdependent Demand Rate Method, to alleviate the uncertainty of timing of demand in a given planning period. The presented method furthermore establishes the level of interdependency between the demands of individual end-products. Based on this knowledge it is possible to improve the planning and control performance as well as the order management performance in a MTO environment.
1. The aggregate demand rate for a product family (group) is stable (law of big numbers – independent end-product demand). 2. Material and capacity consumption can be handled by disaggregation of product family (groups) demand (stable product mix). 3. That products within the same family (group) have similar load profiles on resources (insensitivity to product mix variation).
purchase products based on operating characteristics, and batch orders for multiple products for simultaneous delivery to minimize shipping costs.
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3. Time- and Interdependent Demand Rate Method The presented method, called the Time- and Interdependent Demand Rate Method (TIDRM), is based on multivariate analysis (Everitt [23], Krzanowski [24]) of demand patterns. Like all methods for statistical analysis the TIDRM’s performance depends on the quality of the data input. The higher the quality of data (i.e. many observations, high reliability of observations) the better the output model. The TIDRM is based on the assumptions that a pattern in ordering behaviour does not depend on the total demand of the MPS planning period, i.e. focus is not on absolute demand rates but relative demand rates. This implies that the demand rate profiles are independent of seasonality and trend. It is also assumed that the ordering behaviour has not changed significantly over the time period covered in the data set used to develop the model. The proposed TIDRM of analysis contains two distinct parts: 1. Establishing time dependent demand rate patterns. 2. Analyzing interdependencies between products based on output from the time dependent demand rate patterns. In the first part a multivariate density distribution is numerically fitted to historical demand data using the kernel method (Krzanowski [24], Silverman [25]). The kernel used is the standard bivariate normality density function [25]. The second part involves using these fitted demand rate patterns to establish whether interdependencies exist between products’ demand rates. This is done using Pearson’s test for Correlation (Krzanowski [24], Wasserman [26]) on the demand rates profiles established in the first part of the TIDRM. The first part of the TIDRM can stand by itself and the output of this analysis can be used without any further analysis. The second part of TIDRM however depends on the [(Fig._1)TD$IG] output of the first part.
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The proposed method is limited to an environment where demand occurs at frequent intervals, i.e. an environment with relatively many orders. This is typically also the environment that has the greatest need for planning tools and optimization of schedules. If demand for individual items is very sporadic but still has a significant impact on resource load and material consumption then other alternatives such as demand management or supply chain integration measures will be worth pursuing instead. To ensure that the applied analytical statistical methods can be used, the data is transformed from discrete to continuous. This is done for the demand rates by using the relative demand rates for the periods rather than the absolute, e.g. daily demand rates. This means that the demand rates will range from 0 to 1 on a continuous scale. This also serves another purpose, if demand is seasonal but demand rate patterns are not, then using absolute rather than relative demand rates will cause over fitting to data from periods of historical high demand. This is undesirable if the demand profiles should be used for future planning purposes. In this case the current volume (e.g. from sales forecasts) rather than historical importance of a given product should be used to determine the relative impact of a product on the manufacturing system. The second aspect is time. Making time continuous rather than discrete potentially poses some more significant problems. Several approaches seem valid: Making a mixed model including both continuous and discrete variables, making demand rate profiles, for e.g. each particular date, or finally looking at sufficiently long period so time can be treated as continuous rather than discrete. Due to the nature of the problems faced in a MTO planning environment (allocation of resources and materials prior to knowing demand) and the time horizons faced the latter approach seems to be appropriate. A full overview of the TIDRM is presented in Fig. 1. The first part of the TIDRM – establishing time dependent demand rate patterns (illustrated in Fig. 1) – contains the following steps:
Fig. 1. Proposed method for analyzing time dependency and interdependency of demand rates in the TIDRM.
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A. First, an initial treatment of the input data takes place. This involves choosing the length of the period for which demand rate patterns should be fitted, sorting the input data (i.e. order lines with requested delivery date and quantity) and calculating relative demand rates for all orders in all the recorded periods (i.e. periods of the chosen length). The output data now contains a list of dates and the relative demand rates experienced on these dates. B. Second, a multivariate density function is fitted to the data using the kernel method. C. Third, based on the fitted multivariate density function, confidence levels for largest expected relative demand rates are calculated. This can be done for any desired level of confidence. The output of this step is a number of demand rate profiles, expressing the maximum expected relative demand rate under the specified levels of confidence, e.g. a timedependent profile indicating the 98% confidence level for largest expected relative demand rates.
D.
E.
F.
G.
[(Fig._2)TD$IG]
The second part of the TIDRM – analyzing interdependencies between products’ demand rates – contains the following steps: The first step is to register the demand rate profiles for the products to be checked for interdependencies. This is done on the individual end products’ demand rate profiles found in the first part. The number of products included and the confidence levels of demand rates analyzed will depend on user preference. The second step is to determine which interdependencies between products are to be checked. Usually this will involve the mean demand rate (i.e. the 50%-confidence level demand rate profile) and the peaks (e.g. 95% confidence level demand rate profile). The third step is to check for interdependencies. This is done using Pearson-correlation where demand rate profiles (stored numerically from previously) are checked for combinations of start times and period lengths, e.g. the start time as well as the length of the period checked is varied with steps of 1 day. This approach is taken since the demand rate profiles may change interdependencies over the time period both based on start time and length of the period checked. The longer the period checked, the more one would expect the interdependencies between demand rate profiles to be a negative correlation (i.e. levelling) or no correlation (i.e. total independence of demand). However, even if this is the case, longer periods of positively correlated demand rates can cause problems in the planning process. The fourth step is to evaluate if the demand rate profiles in general can be considered to be interdependent, i.e. are demand rates significantly correlated. This is done by: Calculating the number of significant correlated start time and time horizon combinations. Any level of significance can be chosen; Finding the ratio of significant correlated start time and time horizon combinations compared to the total number of start time and time horizon combinations.
The ratio will indicate if further analysis is trivial—i.e. if too few of the start time and time horizon combinations are correlated. H. The fifth step is (if sufficient evidence for interdependency is found in the previous step) to establish whether the significant interdependency is either amplification (positive correlation) of demand rates or levelling of demand rates (negative correlation). This is done by calculating the ratio of positive correlated (start time, time horizon demand rate combinations) to negative correlated. A value larger than 1 means that the positive correlated time periods (i.e. start time, time horizon combinations) outnumber the negative correlated time periods. The lower this ratio is the more levelling of demand takes place. The larger (i.e. than 1) this ratio is, the more demand amplification occurs. This ratio is calculated for both the significantly correlated demand rates and for all values of correlation. In each of the steps F, G and H a ratio of interdependence is calculated giving a total of three ratios used to evaluate the interdependency of demand rates. 4. Examples and discussion The following section presents examples of application of the TIDRM. The TIDRM is implemented in R (Everitt [23]), an open source environment primarily for statistical analysis. 4.1. Time dependency vs. time independency The first part of the TIDRM (see Fig. 1 in Section 3) is to establish time dependent demand rate profiles. To illustrate this aspect of the TIDRM, demand data has been obtained from a MTO company for two products (A and B). The products are from two separate product families and interdependency of sales is not expected. The products are manufactured-to-order, but capacity and materials need to be allocated prior to knowing demand due to lead time on materials and desired short delivery time to customers. The products are produced on separate production lines, but have some similar/common components. The main competitive priority in the company is to deliver on-time in-full, with as short a delivery time as possible. For product A, a total of 485 orders for 35 months were used to fit the models, for product B 462 orders for the same period were used. Neither of the products exhibit trend nor seasonality, and the mean order size for the two products only differs 2%. Hence on paper the demand profiles for the two products are very similar. The MPS planning period in the company is 1 month, so the period fitted by the TIDRM is of this length. In Fig. 2 the time dependent demand rate profiles for the two products are illustrated. The lines in Fig. 2 for products A and B indicate
Fig. 2. Time dependent demand rate profiles for two products. The curves on the two graphs from the bottom up indicate the 50%, 90%, 95%, 98% and 99% biggest likely demand.
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respectively the 50%, 90%, 95%, 98% and 99% largest expected demand rate at any given time. The demand rates are standardized so that 1 corresponds to a level demand rate, and 10, e.g. indicates that the demand rate is 10 times the level demand. An example from the graphs in Fig. 2 is e.g. around time 20 for product A, with 99% likelihood the company will not experience sales more than 10 times bigger than could be expected. This can be directly translated to mean that the company will not sell more than 30% of the month’s sales for that product in a single day. Having applied the first part of the TIDRM to both sets of demand data and fitted demand rate profiles, the results indicate that the demand rate profile for product A has a uniform likelihood of achieving a given demand rate on any given date during the MPS planning period. This means that the demand rate for product A can be considered to be time independent. This demand rate profile is, as theory proscribes, nice and level, at no point (except for i.e. the 99% largest expected demand rate profile) there seems to be an indication of time dependent demand rates. For product B the story is however the opposite. In the beginning and end of the month product B exhibits a tendency for larger demand rates for the higher confidence levels. The demand rate profile of product B is from the illustration in Fig. 2 clearly time dependent. For product A, where demand rates are clearly independent of time, no issues present themselves when making allocations of capacity and materials previous to knowing demand. At any given time the probability of receiving a given order size is basically the same for product A. This corresponds perfectly with the assumptions underlying the demand planning approaches used today. As a result the company can simply calculate a time independent distribution of demand rates, and use this to estimate the need for volume flexibility. For product B however the implications are more daunting. The product B demand rate profile shows clear tendencies of time dependency. This means that using a standard planning approach and assuming that the probability of demand is uniform over the MPS planning period gives the following problems: At the timeslots where the confidence level for the demand rates are higher than average, the company finds it difficult to adhere to their delivery times due to the lack of capacity. Since the company uses a standard demand planning approach assuming level demand rates and uniform probability of achieving higher than average daily demand, the company occasionally suffers longer than necessary delivery times and higher than required costs of inventory and capacity. In the timeslots where the confidence levels for demand rates are lower than the average expected demand rate, the company often has un-utilized capacity and lower than expected delivery times. This over-capacity is however often used to catch up with unmet demand from periods of higher than expected demand rates. The consequences of assuming that demand rates are independent of time is of course more severe the stronger the time dependency. Furthermore, the more the MTO company competes on delivery times and low cost and the more capacity and materials have to be allocated previous to knowing customer demand, the greater the consequences for the costs of manufacturing and meeting a given delivery time.
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equipment which are manufactured in a dedicated job shop. The three products constitute around 80% of the total demand of the product family, the rest of the products in the family were sold infrequently. The products are manufactured to customer order and have a desired delivery time of 2 weeks. Since the products are sold on the same markets, to the same customers and have similar capabilities, it is likely that some sort of interdependency exists in the demand rates. The data used is the following: For product I: 1649 orders, product II: 340 orders and for product III: 384 orders are used. The information used has been gathered over a period of 38 months. So, there is an aggregate number of orders of 2373 for the 38 months. The company determines capacity and material needs for the whole MPS planning period based on forecasts of aggregate demand for the product family which is subsequently broken down through distribution keys and a MRP break-down to determine individual material requirements for the whole MPS planning period. The product mix distribution is relatively stable for the major products; this should mean that the approach chosen by the company seems valid. Even when following this approach the company experiences fluctuating delivery times to customers, problems adhering to due dates and occasional underutilization of resources. Furthermore, the company uses multiple replenishments of materials during the MPS planning period – and even when buffering the safety stock for the whole period the company still experiences stock-outs of crucial shared components. The planning time horizon for allocation of capacity and materials (due to long lead times) is 1 month, so this is the time period of analysis. The first part of the method is to make the time dependent demand rate profiles. These are illustrated in Fig. 3 for all three products. A demand rate profile fitted to the aggregate demand rate for the three products in also included in Fig. 3. The lines in Fig. 3 for products I, II, III and the aggregate demand indicate respectively the 50%, 90%, 95%, 98% and 99% largest expected demand rate at any given time. The demand rates are standardized so that 1 corresponds to a level demand rate, and 10, e.g. indicates that the demand rate is 10 times the level demand. From Fig. 3 it is apparent that all the products exhibit time dependent demand rates. The question is now whether this time dependency is somehow interdependent among products. A visual inspection of Fig. 3 indicates that the aggregate demand rate profile seems to exhibit smoother behaviour than the demand rate profiles for the individual products. Even though the aggregate demand rate profile seems smoother, the aggregate demand rates still appear to be time dependent. This indicates that the individual product demand rate profiles tend to amplify each other. To check this, the second part of the method is applied. This is done for the 50%, 95% and 99% largest expected demand rates, i.e. for the mean expected demand rate, and for confidence levels often used in industry to establish material and capacity needs. To evaluate the interdependency, several KPIs were calculated:
4.2. Interdependencies of demand rates
1. Ratio of significant/non-significant correlated observation for each confidence level. 2. Ratio of positive/negative correlated observations for each confidence level, a value above 1 would indicate that positive observations outnumber the negative by this factor. 3. Ratio of significant positive/negative correlated observations for each confidence level, a value above 1 would indicate that positive observations outnumber the negative by this factor.
To illustrate the second part of the TIDRM (see Fig. 1 in Section 3) – the check for interdependencies – a new case is presented where, due to the nature of the products, interdependency of demand among products is likely to be present. Demand information was obtained from another MTO manufacturer for three products from the same product family of electronic
The confidence level used to check if the demand rate profiles are significantly correlated is 95%. The demand rates are checked for correlation so that all combination of start dates from day 1 till 23 and all period lengths from 8 to 31 days are checked. This means that, e.g. the period starting at day 3 lasting 10 days is checked for correlation of demand rates between products on the chosen levels
[(Fig._3)TD$IG]
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Fig. 3. Demand rate profiles fitted for three products and fitted to all orders for all products.
of confidence. Since the length of period checked varies, so does the level of significance since this depends on the number of observations. For the demand rate profiles shown in Fig. 3, the corresponding ratios are presented in Table 1. From the results presented in Table 1 it is evident that the demand rate profiles are significantly correlated for between 30% and 51% of the start time/time horizon combinations tested. This indicates that there is indeed reason to assume that the demand rates for the products are interdependent. Moreover, it is evident that in particular the 50% level demand rate profile exhibits a very clear interdependency, so strong in fact that there are no significantly negative correlated start time/time horizon combinations. This indicates that what little variation there is for all the products in the 50%-level, demand rate profiles are positively correlated. From the aggregate demand rate profile, seen in Fig. 3, this however seems to have a limited impact, due to relative small deviations from a stationary mean demand rate. The 50% likely demand in this case appears to be almost completely level. However, this is due to the nature of the examined data set rather than a mechanism of the method. Deviations from this can be expected if a very clear demand rate pattern is present. The 95% and 99% confidence level profiles for maximum expected demand rates exhibit both positive, negative and uncorrelated behaviour. The ratios of positive correlated observations to negative correlated observations show that the demand rates for these confidence levels are positively correlated almost as much as negatively correlated. This means that there are periods in the demand rate profiles where the demand rates level each other out, Table 1 Table of ratios for check of interdependencies.
Ratio 1 Ratio 2 Ratio 3
50%-level
95%-level
99%-level
0.51 56.6 Infinite
0.31 0.55 0.93
0.30 0.90 0.98
but also periods where demand rates amplify each other. This is also evident from the aggregate demand rate profile shown in Fig. 3, if levelling (i.e. negatively correlated demand rates) or independence was present, then the demand rate profiles for the aggregate demand rates should be stationary, like the behaviour shown for product A in Fig. 2. The demand rates for all three products are clearly time dependent in nature. The product specific demand rate profiles are however not the issue here, the interdependencies between products are. Three situations can be encountered when looking at the interdependencies of demand rates among products; the demand rates can be uncorrelated, negatively correlated or positively correlated: 1. When the demand rates for the three products are uncorrelated, the aggregate demand rate is stationary. From a demand planning perspective this situation implies that the demand for one product is independent of the demand for another product. 2. When the demand rates for the three products are in general negatively correlated, the aggregate demand rate should be stationary. However, in this situation the product mix changes in a systematic manner not anticipated by the system. If products have different Bill-of-Materials or load profiles on resources this causes significant problems. On the resource side this can cause a shifting bottleneck to be present or uneven load of a fixed bottleneck. On the material side, the consumption of components shared by products but in product dependent numbers can cause shortages when the demand rate for a product consuming a larger than average number of components goes up; while the demand rate for products consuming less than average of the components goes down (e.g. one product uses ten bolts of a given type and dimension another only two, when demand for the first product goes up demand for the other goes down proportionally, however the consumption of the bolts in fact increases by a factor of five).
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3. When the demand rates for the three products are positively correlated, the aggregate demand rate is not stationary. This behaviour is seen from Fig. 3, in particular for the timeslots [day 1–day 5] and [day 20–day 27]. For these two timeslots the maximum expected demand rates are clearly lower than the average expected largest daily demand rate. When the aggregate demand rate profile is low, the company has less need to buffer on capacity and materials to achieve the desired delivery performance. When the demand rates for the products amplify each other we get the behaviour seen for the timeslot [day 7–day 15], where the largest expected aggregated demand rates are high. The demand implications of this are clear; when the maximum expected demand rate for one product is large, it is likewise for the other products. If the demand rates for products are large at the same time, so is the potential load on resources. This is also true for the consumption of materials. If it is assumed that the daily aggregate demand rate is stable and the inventory is replenished in this case in weekly intervals, material shortages occur. The combination of periodic insufficient capacity and the risk of stock outs of components means that in this timeslot, delivery time will be longer if overtime or rush orders on materials are not used. These observations correspond well with the observed behaviour of the manufacturing system, with varying delivery times and unstable utilization of resources.
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correlated. Vertically capacity profiles based on demand rate profiles can be used for the MPS planning period. This should stabilize the delivery time and the utilization of capacity. This scenario has interesting implications: (1) the cost of capacity is lower the earlier the capacity is allocated (e.g. the use of overtime can be avoided); (2) the MTO manufacturer can increase the ability to deliver on-time in-full even when products have time and interdependent demand rates. The TIDRM can be integrated in several levels of the planning hierarchy. On strategic levels the method can be used to establish strategies towards delivery capabilities. On operational levels the method can be used to change inventory and capacity profiles to better match the actual demand situation faced by companies. Practical implementation of the method in companies would probably be best as part of a Decision Support System, supporting planning. By implementing the method in a Decision Support System the chosen approach to handling the issues of time and interdependent demand rates will depend on the particular circumstances encountered at MTO manufacturers. The presented method significantly deviates from the current approaches available, since current approaches focus mainly on the timing of orders and ignore the vital aspect of interdependence of demand between products. The TIDRM remedies this by proposing a method for establishing the degree of interdependence between demand rates for products.
4.3. Guidelines for the use of the TIDRM 5. Conclusion and further research MTO manufacturers may find that the volume and mix for the whole MPS planning period are stable and still they have problems adhering to due dates, too long delivery time and higher than expected costs of operations. This is due to the fact that while aggregate demand behaviour is stable, the planning foundation on a lower level is unstable due time and interdependent demand rates. The TIDRM can in its current form be used to identify time and interdependency of demand rates and through this analysis establish: which product exhibit time dependent demand rates, and which products’ demand rates are interdependent. If the TIDRM analysis shows that several products have time dependent demand rate profiles and furthermore that the demand rate profiles are interdependent, this can explain why the demand planning performance with regard to utilization and delivery time is low even though the aggregate demand behaviour is stable. The problems identified by the TIDRM will have a particularly hard impact on planning performance in the following situations: 1. One main product exhibits time dependent demand behaviour within the MPS planning period. This gives an uneven load on resources over the planning period and varying delivery times. 2. Several products exhibit time dependent demand behaviour and the demand rates of the products are negatively correlated. This is only a problem if the products consume materials and/or load resources in a uneven manner. 3. Several products exhibit time dependent demand behaviour and the demand rates of the products are positively correlated. When the demand rate for one product increases the demand rate for one or more other products increases as well—and vice versa with decreasing demand rates. The TIDRM can be used to identify all the presented situations so that appropriate planning precautions can be taken. Horizontally these precautions can be demand management to try to level demand of certain products, or to change customer ordering behaviour so the demand rates of products are no longer
A review of demand planning approaches shows the need for methods: (1) to determine if demand rates for individual products are time dependent within a MPS planning period; (2) to establish whether time dependent demand rate profiles of individual products are interdependent. To address this issue the Timeand Interdependent Demand Rate Method (TIDRM) was developed and presented. The TIDRM uses estimations of multivariate density distributions to model time dependent demand rate profiles. These profiles are subsequently used in the TIDRM to establish whether demand rates for individual products are interdependent. The TIDRM was tested on data from two MTO manufacturers. In the first case the findings were both a time independent demand rate profile and a time dependent one. In the second case the finding was that three products within a product family exhibited time dependent demand rates, and that the demand rate for the three products are to some extend significantly correlated. In both cases demand planning implications connected with the demand rate profiles were inferred. Furthermore, guidelines for the use of the TIDRM are presented, emphasizing the need to focus on particularly the situation of positively correlated demand rates (demand amplification). The conclusion is that it is possible to develop time dependent demand rate profiles and to use these to establish whether demand rates for individual products are correlated. The conclusion is also that the very nature for grouping products will ensure that some form of correlation of demand rates exists. Using the TIDRM will enable MTO manufacturers to develop time dependent consumption and capacity profiles within MPS planning periods. These profiles should lead to lower delivery time and more consistent service levels of in-process inventories. The next step is to interpret the demand rate profiles and translate these into capacity profiles and demand profiles for material consumption. No quantitative method has been developed for this in the current research. However, this must be the logical next step. Moreover, benchmarking the performance of planning systems using time independent demand rate profiles and time dependent profiles must be conducted to validate the impact on demand planning performance.
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References [1] L.C. Hendry, B.G. Kingsman, Production planning systems and their applicability to make-to-order companies, European Journal of Operational Research 40 (1989) 1–15. [2] A.S. Marucheck, M.K. Mcclelland, Strategic issues in make-to-order manufacturing, Production and Inventory Management 27 (1986) 82–96. [3] F. Easton, D. Moodie, Pricing and lead time decisions for make-to-order firms with contingent orders, theory and methodology, European Journal of Operational Research 116 (1999) 305–318. [4] M. Holweg, F.K. Pil, The Second Century—Reconnecting Customer and Value Chain through Build-to-Order, The MIT Press, Cambridge, MA, 2005. [5] K. Steger-Jensen, C. Svensson, Issues of mass customisation and supporting ITsolutions, Computers in Industry 54 (2004) 83–103. [6] W.L. Berry, T. Hill, Linking systems to strategy, International Journal of Operations & Production Management 12 (1992) 3–15. [7] T.E. Vollmann, W.L. Berry, D.C. Whybark, F.R. Jacobs, Manufacturing Planning and Control for Supply Chain Management, McGrawHill, Singapore, 2005. [8] M.A. Carravilla, J.P. de Sousa, Hierarchical production planning in a Make-ToOrder company: a case study, European Journal of Operational Research 86 (1995) 43–56. [9] K.N. Mckay, F.R. Safayeni, J.A. Buzacott, A review of hierarchical production planning and its applicability for modern manufacturing, Production Planning & Control 6 (1995) 384–394. [10] A.C. Hax, H.C. Meal, Hierarchical Integration of production planning and scheduling, in: M.A. Geisler (Ed.), Studies in Management Science, vol. 1, Logistics, Amsterdam, 1975, pp. 53–69. [11] J. Nicholas, Competitive Manufacturing Management: Continuous Improvement. Lean Production and Customer-focused Quality, McGrawHill, New York, 1998. [12] F. Chen, Z. Drezner, J.K. Ryan, D. Simchi-Levi, Quantifying the Bullwhip effect in a simple supply chain: the impact of forecasting, Lead Times, And Information, Management Science 46 (2000) 436–443. [13] J.W. Forrester, Industrial Dynamics, first ed., The MIT Press, Cambridge, Massachusetts, 1961. [14] J.T. Mentzer, M.A. Moon, Sales Forecasting Management—A Demand Management Approach, second ed., Sage Publications, London, 2005. [15] L.R. Weatherford, S.E. Bodily, A taxonomy and research overview of perishableasset revenue management: yield management, overbooking, and pricing, Operations Research 40 (1992) 831–844. [16] J. Korpela, M. Tuominen, Inventory forecasting with a multiple criteria decision tool, International Journal of Production Economics 45 (1996) 159–168. [17] J.R. Stock, D.M. Lambert, Strategic Logistics Management, Richard D. Irwin Inc., USA, 1987. [18] P. Doganis, A. Alexandridis, P. Patrinos, H. Sarimveis, Time series sales forecasting for short shelf-life food products based on artificial neural networks and evolutionary computing, Journal of Food Engineering 75 (2006) 196–204. [19] K.Y. Chen, C.H. Wang, A hybrid SARIMA and support vector machines in forecasting the production values of the machinery industry in Taiwan, Expert Systems with Applications 32 (2007) 254–264. [20] F. Collopy, M. Adya, J.S. Armstrong, Expert systems for forecasting, in: J.S. Armstrong (Ed.), Principles of Forecasting—A Handbook for Researchers and Practitioners, Kluwer Academic Press, Norwell, MA, 2001, pp. 283–300. [21] M. West, P.J. Harrisson, Bayesian Forecasting and Dynamic Models, 2nd ed., Springer, NY, USA, 1997. [22] B. Wall, P. Higgins, J. Browne, G. Lyons, A prototype system for short-term supply planning, Computers in Industry 19 (1992) 1–19.
[23] B.S. Everitt, An R and S-Plus Companion to Multivariate Analysis. Springer Texts in Statistics, Springer-Verlag, 2005. [24] W.J. Krzanowski, Principles of Multivariate Analysis—A User’s Perspective. Volume 3 of Oxford Statistical Science Series, Oxford University Press, 1988. [25] W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall, 1986. [26] L. Wasserman, All of Statistics: A Concise Course in Statistical Inference, Springer, 2004.
Peter Nielsen is an assistant professor at the Centre for Logistics, Department of Production, Aalborg University in Denmark. He attained his Ph.D. Production Technology with a specialization in Demand Planning from Aalborg University in 2008. He has published approximately 20 peer-reviewed papers and is currently involved in two research projects focusing on planning and diagnostics of planning performance. His primary focus of research is Hierarchical Planning, Diagnostics of Planning Performance and Demand Pattern Analysis.
Izabela Nielsen is an assistant professor at the Department of Production in the Centre for Logistics, Aalborg University in Denmark. In 2005 she obtained a Ph.D. with honours from Warsaw University of Technology (Faculty of Production Engineering). Her research includes project management, production planning, scheduling and optimization problems for which she has developed methods/models further implemented as diagnostic tools or Decision Support Systems. In 2006 she obtained an award from Polish Ministry of Science and Higher Education for her research. She has published more than 50 peerreviewed publications.
Kenn Steger-Jensen gained a Ph.D. in Enterprise Resource Planning (ERP) and Advanced Planning and Scheduling (APS) Information Systems at Aalborg University in 2004 and a M.Sc. degree in Industrial Management from Aalborg University in 2000. He has been Associate Professor of Supply Chain Integration at Aalborg University since 2004. His research interests are within supply chain planning and manufacturing planning and control theory in general. Working areas are within modelling and solving inter-organizational decision and KPI, planning, scheduling and optimization problems; Information systems as APS, ERP, SFC, MES and integration. Lecturing across different master programmers in areas as, manufacturing planning and control theory, scheduling theory, shop floor control theory and systems, ERP-systems, APS-systems, IT-systems development, Design of IT-systems, Management Sciences and Operational Research.
Contents lists available at ScienceDirect
Computers in Industry journal homepage: www.elsevier.com/locate/compind
Analyzing and evaluating product demand interdependencies Peter Nielsen *, Izabela Nielsen, Kenn Steger-Jensen Department of Production, Aalborg University, Fibigerstrede 16, DK 9220 Aalborg, Denmark
A R T I C L E I N F O
A B S T R A C T
Article history: Available online 21 August 2010
Demand-driven manufacturing is an extremely unstable planning environment compared to forecastdriven manufacturing. This requires preparation and makes knowledge of demand behaviour even more important for planning and control. The basic assumptions of pre-ante allocation based on forecast of independent end-products demand are critical for manufacturing planning and control in general. However, the importance is higher for demand-driven manufacturing than forecast-driven manufacturing. This is due to the sensitivity of demand-driven manufacturing to demand fluctuations, e.g. time and interdependency of demand rates, due to the customer order decoupling point. This paper presents a method to establish time and interdependency of demand rates (the Time- and Interdependent Demand Rate Method), which can improve the planning and control performance as well as the order management performance in a MTO environment. The method is tested on data from two cases. For both cases results and demand planning implications are presented. Use guidelines for the method are also presented along with avenues of further research. ß 2010 Elsevier B.V. All rights reserved.
Keywords: Make-to-order Demand planning Master Production Scheduling Time- and Interdependent Demand Rate Method
1. Introduction Manufacturing companies differ in the way they meet their demand. Some deliver products to their customers from finished goods inventories as their production anticipates customers’ orders; others, however, manufacture only in response to customers’ orders. A company in the demand-driven make-toorder (MTO) manufacturing environment has to supply a wide variety of products, usually in small quantities, ranging from standard products to all orders requiring a customized product [1,2]. MTO companies primarily compete on delivery time and reliability in meeting due dates and flexibility to adapt (to product mix and volume) [3]. Likewise MTO companies, like all companies, are subject to competition on price. In recent years it has however become increasingly normal to produce a wide range of products (some more or less customized) entirely to order [4,5]. A vital part of the ability to compete in this environment is the MTO manufacturer’s order management approach. However, to a large extend this still depends on the MTO manufacturer’s ability to allocate resources and materials prior to actually receiving customer orders. Only in extreme cases it is unnecessary for MTO manufacturers to plan based on forecasts. This means that especially the demand-driven manufacturers will benefit from increased insight into customer ordering behaviour.
* Corresponding author. Tel.: +45 9940 8932. E-mail addresses: [email protected] (P. Nielsen), [email protected] (I. Nielsen). 0166-3615/$ – see front matter ß 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.compind.2010.07.012
In this paper a method is presented that contributes to this insight by establishing (1) time dependence of demand rates, and (2) interdependence of demand rates. This increased insight can be used to improve planning and order management. The paper is structured as follows. First, planning issues in a MTO-environment are discussed, finding that an unresolved critical aspect of demand planning in a MTO environment is handling demand rate fluctuations within a planning period and interdependent demand rates of products. Second, a method called the Time- and Interdependent Demand Rate Method, for establishing demand rate profiles and interdependencies of demand between products, is presented. Following this, the method is tested on data from two MTO manufactures, the results are interpreted and the demand planning implications of the particular demand behaviour is discussed. This section also includes guidelines for utilizing the method. Finally, conclusions and avenues of further research are presented. 2. Critical planning issues in a MTO-environment Demand planning impacts all areas of operations. The further up-stream the internal supply chain the Customer Order Decoupling Point is placed, the more demand-driven are operations, the more sensitive and complicated the demand planning process becomes to fluctuations in demand both aggregate and disaggregate volume and mix of products. Demand planning is in general integrated both vertically (the hierarchical planning approach, the basic assumptions of which are pre-ante allocation of independent end-products
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demand, based on forecast) and horizontally (the order management approach where the major part of the daily operations will be initiated and defined by the customer) in planning and operations. Vertically the challenges in a MTO environment is to pre-ante allocate the right capacity and the right materials [6–9]. This is primarily addressed at the sales and operations planning (SOP) level and at the Master Production Scheduling (MPS) level. For future reference in this paper, the period for which materials and capacity is allocated for on the MPS level is referred to as the MPS planning period. This period is considered as a fixed time bucket in which aggregate needs for material and capacity are allocated based on forecasts and received customer orders for the entire time bucket. If capacity and materials are not allocated pre-ante to actual customer demand, the manufacturer will incur increased costs of operations to achieve a short delivery time due to, e.g. rush orders from suppliers and use of overtime. The desired delivery time to customers is typically shorter than the actual lead time (purchasing lead time + manufacturing lead time). A consequence of shorter lead time than desired delivery time is the need to forecast demand to make allocations and to plan. This can be done in different ways [7,8] but in general capacity and material allocations are conducted based on forecasts of aggregate product demand (or customer orders) which are subsequently disaggregated for MPS planning purposes by the use of some sort of variant distribution key [7,10]. On the SOP level there are options to influence both the demand side (e.g. pricing, advertising and promotion, etc.) and the supply side (e.g. hiring and firing, using overtime and undertime, carrying inventory, etc.). However, these options are difficult to use if the assumptions of independences of product demand used for planning on both SOP and MPS levels are not valid. The allocation of capacity and materials for the MPS planning period is typically based on the following assumptions of customer ordering behaviour [7,11]:
Horizontally the challenge is to integrate the order management process with the planning process on the MPS level. The issue then becomes if the customer ordering behaviour experienced during the order management process matches the assumptions on which the MPS is based. So what can the customers actually be expected to do? Firstly, within MPS planning periods the timing of orders is likely to be influenced by:
This seems to indicate that the demand for individual products is not independent as assumed, but can potentially be interdependent. Both issues have not been addressed directly in current-state simultaneously, but some approaches to influence and improve the planning foundation have been presented. These approaches can roughly be categorized as collaboration/market manipulation schemes or coping with the givens. Collaboration includes supply chain planning and supply chain integration that by their very nature of sharing information integration and collaboration with customers on demand planning gives superior results [12,13]. Another proactive approach is demand management [14,15]. The underlying assumption in demand management is that changing some product characteristic (usually price or delivery time) manipulates customer behaviour in a way that benefits the manufacturer. Supply chain integration measures have frequently shown to give the best performance of the demand planning process with regards to cost and on-time-delivery, but it is not a viable option for all MTO manufacturers. Demand management will likewise be problematic to implement for most MTO manufacturers due to the typical size of the product portfolio. These MTO manufacturers must instead cope with the given situation of a market/production process/product-combination. Coping with the givens includes using advanced planning and scheduling systems [5] to ensure efficient utilization of resources, decreasing lead times through lean initiatives [11] and other measures to improve responsiveness. The fact is that most of the costs of operations are allocated prior to knowing demand. The quality and type of forecasted demand information used for allocation is therefore critical for the demand planning process performance. Getting a higher quality of demand information can only improve the performance of plans. Through the years many forecasting techniques have been presented with the purpose of supplying demand forecasts for planning purposes [16–18]. Forecasts are usually grouped into three categories qualitative methods, time series methods and causal methods [19]. The whole aim of the forecasting procedure is however still based on delivering forecasts covering a particular planning period. Methods as presented in Doganis et al. [18] for non-linear time series forecasting, Chen and Wang‘s [19] hybrid model or methods combining intuitive and quantitative methods such as expert systems [20] or Bayesian models [21] seem to be unable to address these issues. Wall et al. [22] present a prototype Decision Support System for supporting varying demand within certain periods of the MPS planning period. However, the method fails to support the day-to-day requirements of the dynamic planning environment in MTO manufacturing as well as it fails to support the interdependencies of demand. The conclusion is that there is a need for better knowledge/ models of demand behaviour prior to making pre-ante allocations of materials and capacity. Two critical issues present themselves:
customers’ own inventory policies, giving cyclic ordering patterns, credit conditions from the manufacturer encourage ordering certain products or quantities at certain times, and transportation rationalities, minimizing transportation cost, encourage ordering a full load or quantities at certain times.
1. Is the demand rate within the MPS planning period time dependent, i.e. does the customer have ordering preferences due to, e.g. credit conditions? 2. Are the demand rates of products within a MPS planning period interdependent, i.e. do customers order several products for simultaneous delivery due to, e.g. shipping or usage?
Contrary to the assumptions it seems likely that demand rates within a MPS planning period are time dependent. Secondly, it is likely that customers:
This paper provides a method, the Time- and Interdependent Demand Rate Method, to alleviate the uncertainty of timing of demand in a given planning period. The presented method furthermore establishes the level of interdependency between the demands of individual end-products. Based on this knowledge it is possible to improve the planning and control performance as well as the order management performance in a MTO environment.
1. The aggregate demand rate for a product family (group) is stable (law of big numbers – independent end-product demand). 2. Material and capacity consumption can be handled by disaggregation of product family (groups) demand (stable product mix). 3. That products within the same family (group) have similar load profiles on resources (insensitivity to product mix variation).
purchase products based on operating characteristics, and batch orders for multiple products for simultaneous delivery to minimize shipping costs.
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3. Time- and Interdependent Demand Rate Method The presented method, called the Time- and Interdependent Demand Rate Method (TIDRM), is based on multivariate analysis (Everitt [23], Krzanowski [24]) of demand patterns. Like all methods for statistical analysis the TIDRM’s performance depends on the quality of the data input. The higher the quality of data (i.e. many observations, high reliability of observations) the better the output model. The TIDRM is based on the assumptions that a pattern in ordering behaviour does not depend on the total demand of the MPS planning period, i.e. focus is not on absolute demand rates but relative demand rates. This implies that the demand rate profiles are independent of seasonality and trend. It is also assumed that the ordering behaviour has not changed significantly over the time period covered in the data set used to develop the model. The proposed TIDRM of analysis contains two distinct parts: 1. Establishing time dependent demand rate patterns. 2. Analyzing interdependencies between products based on output from the time dependent demand rate patterns. In the first part a multivariate density distribution is numerically fitted to historical demand data using the kernel method (Krzanowski [24], Silverman [25]). The kernel used is the standard bivariate normality density function [25]. The second part involves using these fitted demand rate patterns to establish whether interdependencies exist between products’ demand rates. This is done using Pearson’s test for Correlation (Krzanowski [24], Wasserman [26]) on the demand rates profiles established in the first part of the TIDRM. The first part of the TIDRM can stand by itself and the output of this analysis can be used without any further analysis. The second part of TIDRM however depends on the [(Fig._1)TD$IG] output of the first part.
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The proposed method is limited to an environment where demand occurs at frequent intervals, i.e. an environment with relatively many orders. This is typically also the environment that has the greatest need for planning tools and optimization of schedules. If demand for individual items is very sporadic but still has a significant impact on resource load and material consumption then other alternatives such as demand management or supply chain integration measures will be worth pursuing instead. To ensure that the applied analytical statistical methods can be used, the data is transformed from discrete to continuous. This is done for the demand rates by using the relative demand rates for the periods rather than the absolute, e.g. daily demand rates. This means that the demand rates will range from 0 to 1 on a continuous scale. This also serves another purpose, if demand is seasonal but demand rate patterns are not, then using absolute rather than relative demand rates will cause over fitting to data from periods of historical high demand. This is undesirable if the demand profiles should be used for future planning purposes. In this case the current volume (e.g. from sales forecasts) rather than historical importance of a given product should be used to determine the relative impact of a product on the manufacturing system. The second aspect is time. Making time continuous rather than discrete potentially poses some more significant problems. Several approaches seem valid: Making a mixed model including both continuous and discrete variables, making demand rate profiles, for e.g. each particular date, or finally looking at sufficiently long period so time can be treated as continuous rather than discrete. Due to the nature of the problems faced in a MTO planning environment (allocation of resources and materials prior to knowing demand) and the time horizons faced the latter approach seems to be appropriate. A full overview of the TIDRM is presented in Fig. 1. The first part of the TIDRM – establishing time dependent demand rate patterns (illustrated in Fig. 1) – contains the following steps:
Fig. 1. Proposed method for analyzing time dependency and interdependency of demand rates in the TIDRM.
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A. First, an initial treatment of the input data takes place. This involves choosing the length of the period for which demand rate patterns should be fitted, sorting the input data (i.e. order lines with requested delivery date and quantity) and calculating relative demand rates for all orders in all the recorded periods (i.e. periods of the chosen length). The output data now contains a list of dates and the relative demand rates experienced on these dates. B. Second, a multivariate density function is fitted to the data using the kernel method. C. Third, based on the fitted multivariate density function, confidence levels for largest expected relative demand rates are calculated. This can be done for any desired level of confidence. The output of this step is a number of demand rate profiles, expressing the maximum expected relative demand rate under the specified levels of confidence, e.g. a timedependent profile indicating the 98% confidence level for largest expected relative demand rates.
D.
E.
F.
G.
[(Fig._2)TD$IG]
The second part of the TIDRM – analyzing interdependencies between products’ demand rates – contains the following steps: The first step is to register the demand rate profiles for the products to be checked for interdependencies. This is done on the individual end products’ demand rate profiles found in the first part. The number of products included and the confidence levels of demand rates analyzed will depend on user preference. The second step is to determine which interdependencies between products are to be checked. Usually this will involve the mean demand rate (i.e. the 50%-confidence level demand rate profile) and the peaks (e.g. 95% confidence level demand rate profile). The third step is to check for interdependencies. This is done using Pearson-correlation where demand rate profiles (stored numerically from previously) are checked for combinations of start times and period lengths, e.g. the start time as well as the length of the period checked is varied with steps of 1 day. This approach is taken since the demand rate profiles may change interdependencies over the time period both based on start time and length of the period checked. The longer the period checked, the more one would expect the interdependencies between demand rate profiles to be a negative correlation (i.e. levelling) or no correlation (i.e. total independence of demand). However, even if this is the case, longer periods of positively correlated demand rates can cause problems in the planning process. The fourth step is to evaluate if the demand rate profiles in general can be considered to be interdependent, i.e. are demand rates significantly correlated. This is done by: Calculating the number of significant correlated start time and time horizon combinations. Any level of significance can be chosen; Finding the ratio of significant correlated start time and time horizon combinations compared to the total number of start time and time horizon combinations.
The ratio will indicate if further analysis is trivial—i.e. if too few of the start time and time horizon combinations are correlated. H. The fifth step is (if sufficient evidence for interdependency is found in the previous step) to establish whether the significant interdependency is either amplification (positive correlation) of demand rates or levelling of demand rates (negative correlation). This is done by calculating the ratio of positive correlated (start time, time horizon demand rate combinations) to negative correlated. A value larger than 1 means that the positive correlated time periods (i.e. start time, time horizon combinations) outnumber the negative correlated time periods. The lower this ratio is the more levelling of demand takes place. The larger (i.e. than 1) this ratio is, the more demand amplification occurs. This ratio is calculated for both the significantly correlated demand rates and for all values of correlation. In each of the steps F, G and H a ratio of interdependence is calculated giving a total of three ratios used to evaluate the interdependency of demand rates. 4. Examples and discussion The following section presents examples of application of the TIDRM. The TIDRM is implemented in R (Everitt [23]), an open source environment primarily for statistical analysis. 4.1. Time dependency vs. time independency The first part of the TIDRM (see Fig. 1 in Section 3) is to establish time dependent demand rate profiles. To illustrate this aspect of the TIDRM, demand data has been obtained from a MTO company for two products (A and B). The products are from two separate product families and interdependency of sales is not expected. The products are manufactured-to-order, but capacity and materials need to be allocated prior to knowing demand due to lead time on materials and desired short delivery time to customers. The products are produced on separate production lines, but have some similar/common components. The main competitive priority in the company is to deliver on-time in-full, with as short a delivery time as possible. For product A, a total of 485 orders for 35 months were used to fit the models, for product B 462 orders for the same period were used. Neither of the products exhibit trend nor seasonality, and the mean order size for the two products only differs 2%. Hence on paper the demand profiles for the two products are very similar. The MPS planning period in the company is 1 month, so the period fitted by the TIDRM is of this length. In Fig. 2 the time dependent demand rate profiles for the two products are illustrated. The lines in Fig. 2 for products A and B indicate
Fig. 2. Time dependent demand rate profiles for two products. The curves on the two graphs from the bottom up indicate the 50%, 90%, 95%, 98% and 99% biggest likely demand.
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respectively the 50%, 90%, 95%, 98% and 99% largest expected demand rate at any given time. The demand rates are standardized so that 1 corresponds to a level demand rate, and 10, e.g. indicates that the demand rate is 10 times the level demand. An example from the graphs in Fig. 2 is e.g. around time 20 for product A, with 99% likelihood the company will not experience sales more than 10 times bigger than could be expected. This can be directly translated to mean that the company will not sell more than 30% of the month’s sales for that product in a single day. Having applied the first part of the TIDRM to both sets of demand data and fitted demand rate profiles, the results indicate that the demand rate profile for product A has a uniform likelihood of achieving a given demand rate on any given date during the MPS planning period. This means that the demand rate for product A can be considered to be time independent. This demand rate profile is, as theory proscribes, nice and level, at no point (except for i.e. the 99% largest expected demand rate profile) there seems to be an indication of time dependent demand rates. For product B the story is however the opposite. In the beginning and end of the month product B exhibits a tendency for larger demand rates for the higher confidence levels. The demand rate profile of product B is from the illustration in Fig. 2 clearly time dependent. For product A, where demand rates are clearly independent of time, no issues present themselves when making allocations of capacity and materials previous to knowing demand. At any given time the probability of receiving a given order size is basically the same for product A. This corresponds perfectly with the assumptions underlying the demand planning approaches used today. As a result the company can simply calculate a time independent distribution of demand rates, and use this to estimate the need for volume flexibility. For product B however the implications are more daunting. The product B demand rate profile shows clear tendencies of time dependency. This means that using a standard planning approach and assuming that the probability of demand is uniform over the MPS planning period gives the following problems: At the timeslots where the confidence level for the demand rates are higher than average, the company finds it difficult to adhere to their delivery times due to the lack of capacity. Since the company uses a standard demand planning approach assuming level demand rates and uniform probability of achieving higher than average daily demand, the company occasionally suffers longer than necessary delivery times and higher than required costs of inventory and capacity. In the timeslots where the confidence levels for demand rates are lower than the average expected demand rate, the company often has un-utilized capacity and lower than expected delivery times. This over-capacity is however often used to catch up with unmet demand from periods of higher than expected demand rates. The consequences of assuming that demand rates are independent of time is of course more severe the stronger the time dependency. Furthermore, the more the MTO company competes on delivery times and low cost and the more capacity and materials have to be allocated previous to knowing customer demand, the greater the consequences for the costs of manufacturing and meeting a given delivery time.
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equipment which are manufactured in a dedicated job shop. The three products constitute around 80% of the total demand of the product family, the rest of the products in the family were sold infrequently. The products are manufactured to customer order and have a desired delivery time of 2 weeks. Since the products are sold on the same markets, to the same customers and have similar capabilities, it is likely that some sort of interdependency exists in the demand rates. The data used is the following: For product I: 1649 orders, product II: 340 orders and for product III: 384 orders are used. The information used has been gathered over a period of 38 months. So, there is an aggregate number of orders of 2373 for the 38 months. The company determines capacity and material needs for the whole MPS planning period based on forecasts of aggregate demand for the product family which is subsequently broken down through distribution keys and a MRP break-down to determine individual material requirements for the whole MPS planning period. The product mix distribution is relatively stable for the major products; this should mean that the approach chosen by the company seems valid. Even when following this approach the company experiences fluctuating delivery times to customers, problems adhering to due dates and occasional underutilization of resources. Furthermore, the company uses multiple replenishments of materials during the MPS planning period – and even when buffering the safety stock for the whole period the company still experiences stock-outs of crucial shared components. The planning time horizon for allocation of capacity and materials (due to long lead times) is 1 month, so this is the time period of analysis. The first part of the method is to make the time dependent demand rate profiles. These are illustrated in Fig. 3 for all three products. A demand rate profile fitted to the aggregate demand rate for the three products in also included in Fig. 3. The lines in Fig. 3 for products I, II, III and the aggregate demand indicate respectively the 50%, 90%, 95%, 98% and 99% largest expected demand rate at any given time. The demand rates are standardized so that 1 corresponds to a level demand rate, and 10, e.g. indicates that the demand rate is 10 times the level demand. From Fig. 3 it is apparent that all the products exhibit time dependent demand rates. The question is now whether this time dependency is somehow interdependent among products. A visual inspection of Fig. 3 indicates that the aggregate demand rate profile seems to exhibit smoother behaviour than the demand rate profiles for the individual products. Even though the aggregate demand rate profile seems smoother, the aggregate demand rates still appear to be time dependent. This indicates that the individual product demand rate profiles tend to amplify each other. To check this, the second part of the method is applied. This is done for the 50%, 95% and 99% largest expected demand rates, i.e. for the mean expected demand rate, and for confidence levels often used in industry to establish material and capacity needs. To evaluate the interdependency, several KPIs were calculated:
4.2. Interdependencies of demand rates
1. Ratio of significant/non-significant correlated observation for each confidence level. 2. Ratio of positive/negative correlated observations for each confidence level, a value above 1 would indicate that positive observations outnumber the negative by this factor. 3. Ratio of significant positive/negative correlated observations for each confidence level, a value above 1 would indicate that positive observations outnumber the negative by this factor.
To illustrate the second part of the TIDRM (see Fig. 1 in Section 3) – the check for interdependencies – a new case is presented where, due to the nature of the products, interdependency of demand among products is likely to be present. Demand information was obtained from another MTO manufacturer for three products from the same product family of electronic
The confidence level used to check if the demand rate profiles are significantly correlated is 95%. The demand rates are checked for correlation so that all combination of start dates from day 1 till 23 and all period lengths from 8 to 31 days are checked. This means that, e.g. the period starting at day 3 lasting 10 days is checked for correlation of demand rates between products on the chosen levels
[(Fig._3)TD$IG]
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Fig. 3. Demand rate profiles fitted for three products and fitted to all orders for all products.
of confidence. Since the length of period checked varies, so does the level of significance since this depends on the number of observations. For the demand rate profiles shown in Fig. 3, the corresponding ratios are presented in Table 1. From the results presented in Table 1 it is evident that the demand rate profiles are significantly correlated for between 30% and 51% of the start time/time horizon combinations tested. This indicates that there is indeed reason to assume that the demand rates for the products are interdependent. Moreover, it is evident that in particular the 50% level demand rate profile exhibits a very clear interdependency, so strong in fact that there are no significantly negative correlated start time/time horizon combinations. This indicates that what little variation there is for all the products in the 50%-level, demand rate profiles are positively correlated. From the aggregate demand rate profile, seen in Fig. 3, this however seems to have a limited impact, due to relative small deviations from a stationary mean demand rate. The 50% likely demand in this case appears to be almost completely level. However, this is due to the nature of the examined data set rather than a mechanism of the method. Deviations from this can be expected if a very clear demand rate pattern is present. The 95% and 99% confidence level profiles for maximum expected demand rates exhibit both positive, negative and uncorrelated behaviour. The ratios of positive correlated observations to negative correlated observations show that the demand rates for these confidence levels are positively correlated almost as much as negatively correlated. This means that there are periods in the demand rate profiles where the demand rates level each other out, Table 1 Table of ratios for check of interdependencies.
Ratio 1 Ratio 2 Ratio 3
50%-level
95%-level
99%-level
0.51 56.6 Infinite
0.31 0.55 0.93
0.30 0.90 0.98
but also periods where demand rates amplify each other. This is also evident from the aggregate demand rate profile shown in Fig. 3, if levelling (i.e. negatively correlated demand rates) or independence was present, then the demand rate profiles for the aggregate demand rates should be stationary, like the behaviour shown for product A in Fig. 2. The demand rates for all three products are clearly time dependent in nature. The product specific demand rate profiles are however not the issue here, the interdependencies between products are. Three situations can be encountered when looking at the interdependencies of demand rates among products; the demand rates can be uncorrelated, negatively correlated or positively correlated: 1. When the demand rates for the three products are uncorrelated, the aggregate demand rate is stationary. From a demand planning perspective this situation implies that the demand for one product is independent of the demand for another product. 2. When the demand rates for the three products are in general negatively correlated, the aggregate demand rate should be stationary. However, in this situation the product mix changes in a systematic manner not anticipated by the system. If products have different Bill-of-Materials or load profiles on resources this causes significant problems. On the resource side this can cause a shifting bottleneck to be present or uneven load of a fixed bottleneck. On the material side, the consumption of components shared by products but in product dependent numbers can cause shortages when the demand rate for a product consuming a larger than average number of components goes up; while the demand rate for products consuming less than average of the components goes down (e.g. one product uses ten bolts of a given type and dimension another only two, when demand for the first product goes up demand for the other goes down proportionally, however the consumption of the bolts in fact increases by a factor of five).
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3. When the demand rates for the three products are positively correlated, the aggregate demand rate is not stationary. This behaviour is seen from Fig. 3, in particular for the timeslots [day 1–day 5] and [day 20–day 27]. For these two timeslots the maximum expected demand rates are clearly lower than the average expected largest daily demand rate. When the aggregate demand rate profile is low, the company has less need to buffer on capacity and materials to achieve the desired delivery performance. When the demand rates for the products amplify each other we get the behaviour seen for the timeslot [day 7–day 15], where the largest expected aggregated demand rates are high. The demand implications of this are clear; when the maximum expected demand rate for one product is large, it is likewise for the other products. If the demand rates for products are large at the same time, so is the potential load on resources. This is also true for the consumption of materials. If it is assumed that the daily aggregate demand rate is stable and the inventory is replenished in this case in weekly intervals, material shortages occur. The combination of periodic insufficient capacity and the risk of stock outs of components means that in this timeslot, delivery time will be longer if overtime or rush orders on materials are not used. These observations correspond well with the observed behaviour of the manufacturing system, with varying delivery times and unstable utilization of resources.
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correlated. Vertically capacity profiles based on demand rate profiles can be used for the MPS planning period. This should stabilize the delivery time and the utilization of capacity. This scenario has interesting implications: (1) the cost of capacity is lower the earlier the capacity is allocated (e.g. the use of overtime can be avoided); (2) the MTO manufacturer can increase the ability to deliver on-time in-full even when products have time and interdependent demand rates. The TIDRM can be integrated in several levels of the planning hierarchy. On strategic levels the method can be used to establish strategies towards delivery capabilities. On operational levels the method can be used to change inventory and capacity profiles to better match the actual demand situation faced by companies. Practical implementation of the method in companies would probably be best as part of a Decision Support System, supporting planning. By implementing the method in a Decision Support System the chosen approach to handling the issues of time and interdependent demand rates will depend on the particular circumstances encountered at MTO manufacturers. The presented method significantly deviates from the current approaches available, since current approaches focus mainly on the timing of orders and ignore the vital aspect of interdependence of demand between products. The TIDRM remedies this by proposing a method for establishing the degree of interdependence between demand rates for products.
4.3. Guidelines for the use of the TIDRM 5. Conclusion and further research MTO manufacturers may find that the volume and mix for the whole MPS planning period are stable and still they have problems adhering to due dates, too long delivery time and higher than expected costs of operations. This is due to the fact that while aggregate demand behaviour is stable, the planning foundation on a lower level is unstable due time and interdependent demand rates. The TIDRM can in its current form be used to identify time and interdependency of demand rates and through this analysis establish: which product exhibit time dependent demand rates, and which products’ demand rates are interdependent. If the TIDRM analysis shows that several products have time dependent demand rate profiles and furthermore that the demand rate profiles are interdependent, this can explain why the demand planning performance with regard to utilization and delivery time is low even though the aggregate demand behaviour is stable. The problems identified by the TIDRM will have a particularly hard impact on planning performance in the following situations: 1. One main product exhibits time dependent demand behaviour within the MPS planning period. This gives an uneven load on resources over the planning period and varying delivery times. 2. Several products exhibit time dependent demand behaviour and the demand rates of the products are negatively correlated. This is only a problem if the products consume materials and/or load resources in a uneven manner. 3. Several products exhibit time dependent demand behaviour and the demand rates of the products are positively correlated. When the demand rate for one product increases the demand rate for one or more other products increases as well—and vice versa with decreasing demand rates. The TIDRM can be used to identify all the presented situations so that appropriate planning precautions can be taken. Horizontally these precautions can be demand management to try to level demand of certain products, or to change customer ordering behaviour so the demand rates of products are no longer
A review of demand planning approaches shows the need for methods: (1) to determine if demand rates for individual products are time dependent within a MPS planning period; (2) to establish whether time dependent demand rate profiles of individual products are interdependent. To address this issue the Timeand Interdependent Demand Rate Method (TIDRM) was developed and presented. The TIDRM uses estimations of multivariate density distributions to model time dependent demand rate profiles. These profiles are subsequently used in the TIDRM to establish whether demand rates for individual products are interdependent. The TIDRM was tested on data from two MTO manufacturers. In the first case the findings were both a time independent demand rate profile and a time dependent one. In the second case the finding was that three products within a product family exhibited time dependent demand rates, and that the demand rate for the three products are to some extend significantly correlated. In both cases demand planning implications connected with the demand rate profiles were inferred. Furthermore, guidelines for the use of the TIDRM are presented, emphasizing the need to focus on particularly the situation of positively correlated demand rates (demand amplification). The conclusion is that it is possible to develop time dependent demand rate profiles and to use these to establish whether demand rates for individual products are correlated. The conclusion is also that the very nature for grouping products will ensure that some form of correlation of demand rates exists. Using the TIDRM will enable MTO manufacturers to develop time dependent consumption and capacity profiles within MPS planning periods. These profiles should lead to lower delivery time and more consistent service levels of in-process inventories. The next step is to interpret the demand rate profiles and translate these into capacity profiles and demand profiles for material consumption. No quantitative method has been developed for this in the current research. However, this must be the logical next step. Moreover, benchmarking the performance of planning systems using time independent demand rate profiles and time dependent profiles must be conducted to validate the impact on demand planning performance.
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Peter Nielsen is an assistant professor at the Centre for Logistics, Department of Production, Aalborg University in Denmark. He attained his Ph.D. Production Technology with a specialization in Demand Planning from Aalborg University in 2008. He has published approximately 20 peer-reviewed papers and is currently involved in two research projects focusing on planning and diagnostics of planning performance. His primary focus of research is Hierarchical Planning, Diagnostics of Planning Performance and Demand Pattern Analysis.
Izabela Nielsen is an assistant professor at the Department of Production in the Centre for Logistics, Aalborg University in Denmark. In 2005 she obtained a Ph.D. with honours from Warsaw University of Technology (Faculty of Production Engineering). Her research includes project management, production planning, scheduling and optimization problems for which she has developed methods/models further implemented as diagnostic tools or Decision Support Systems. In 2006 she obtained an award from Polish Ministry of Science and Higher Education for her research. She has published more than 50 peerreviewed publications.
Kenn Steger-Jensen gained a Ph.D. in Enterprise Resource Planning (ERP) and Advanced Planning and Scheduling (APS) Information Systems at Aalborg University in 2004 and a M.Sc. degree in Industrial Management from Aalborg University in 2000. He has been Associate Professor of Supply Chain Integration at Aalborg University since 2004. His research interests are within supply chain planning and manufacturing planning and control theory in general. Working areas are within modelling and solving inter-organizational decision and KPI, planning, scheduling and optimization problems; Information systems as APS, ERP, SFC, MES and integration. Lecturing across different master programmers in areas as, manufacturing planning and control theory, scheduling theory, shop floor control theory and systems, ERP-systems, APS-systems, IT-systems development, Design of IT-systems, Management Sciences and Operational Research.