Buffering against lumpy demand in MRP environments: a theoretical approach and a case study

Buffering against lumpy demand in MRP environments: a theoretical approach and a case study Maria Caridi 1 and Roberto Cigolini Dipartimento di Economia e Produzione, Politecnico di Milano Piazza Leonardo da Vinci 32, 20122, Milano, Italy 1 Corresponding author: Phone: +39.02.2399.2787, fax: +39.02.2399.2700; e-mail: maria.caridi@polimi.it Abstract This paper is aimed at filling the gap between theory and practice in the area of safety stocks under MRP environments. It is focused on providing a new methodology for dimensioning an overall buffer against uncertainty in market demand, which often plagues SMEs that act as sub-contractors or suppliers within large projects or they have a reduced bargaining power and adversely affects their performances. The proposed methodology suggests to split the amount of safety stocks, as dimensioned according to the traditional methodology, in new safety stocks to face the usual demand variance and in strategic stocks, to face peaks in market demand. To this purpose, a set of recommended guidelines is reported to effectively dimension and position safety and/or strategic stocks within products bills of materials and manufacturing pipelines. Finally, a case study is reported, where the benefits for the company coming from the adoption of the new proposed methodology lie in achieving the 95% target service level even under peak demand conditions, being the value of safety stocks as a whole grown only by about 20%. Keywords: MRP, inventory management, variance control 1. Introduction In this paper the issue of buffering against lumpy demand in MRP environments is considered. In such environments, consumption of items belonging to the various bills of materials (BOMs) is planned on the basis of either customers orders or forecasted demand. As a consequence, actual demand pattern may remarkably differ from the stationary and not-seasonal one required by the traditional stock management approaches. In addition, under MRP environments, whichever the demand pattern is, safety stocks are required not to face demand variance, but procurement time uncertainty, process yield uncertainty and forecast errors. Forecast errors on which this paper is mainly focused basically occur whenever demand forecasts reliability is low, which in turn is a commonplace of many SMEs that act as sub-contractors or suppliers within large projects or they have a reduced bargaining power. Starting from the pioneering masterwork of Orlicky (1975), many researchers over two decades deeply investigated the area of safety stocks dimensioning under MRP. To this purpose, the state-of-art (Guide and Srivastava 2000) shows that in literature there are no broadly accepted methodologies, clearly identified as the most effective ones. Furthermore, the reduced real-life fitness is the most serious shortcoming in some works belonging to this area. Finally, for the parameters setting, seldom there are benchmarks for comparisons with industrial data coming from field. As a consequence, this paper is aimed at filling the gap between theory developed in many academic works and practice currently experienced by industrial practitioners in their dayby-day operations management in the area of safety stocks under MRP environments. The focus of the study is directed towards forecast errors managing, by providing a new 1

methodology for safety buffer dimensioning, which proposes to split the amount of safety stocks, as dimensioned according to the traditional methodology, in new safety stocks and in strategic stocks. Strategic stocks aim at facing peaks of forecast error, e.g. due to a promotion action or to an extraordinary unforeseeable ordered quantity. Error peaks push to increase safety stock dimension because (i) they increase error standard deviation and (ii) service level required for extraordinary orders is usually higher than that one for normal demand. For these reasons, the authors propose in this paper a separate management of safety stock (for normal demand) and strategic stocks (for coping with error peaks). The sum of safety stock and strategic stock is similar to the traditionally-dimensioned safety stock, although the emerging performance of service level should improve. A case study is reported, where the benefits for the company coming from the adoption of the new proposed methodology lie in achieving the 95% target service level even under peak demand conditions, being the value of safety stocks as a whole grown only by about 20%. 2. Problem setting The guidelines considered for developing the new methodology are aimed at giving answer to questions very popular among production managers whenever stocks are to be considered, i.e.: (i) which items either finished products or components should be endowed with safety buffers; (ii) how should the buffers be sized; (iii) when a replenishment order for safety stocks should be released. The proposed methodology assumes that the inventory policy of the company has been already stated, i.e. it is known whether each item is managed according to a push or pull policy. The reasons of the choice may be different: some standpoints for inventory policy assessment are related to the ratio of delivery time out of the pipeline lead time, the available capacity etc. Whichever the reason for the choice between push and pull policy which goes beyond the scope of the paper pull managed items are provided with a regular (i.e. stationary, notseasonal) pattern of consumption over time. Anyway, both push and pull managed items are managed by MRP procedure: pull managed items are automatically replenished according to the specific lot-sizing policy, while orders of push managed items are issued according to a lotfor-lot (or similar) policy on the basis of the actual net requirements, with the aim of keeping the stocks as low as possible, apart for the practice of stock keeping for speculative purposes, treated here as an exception. For the notation purposes, the Requirements Chain Time (RCT) of pull managed items is defined as the length over time of the deepest branch of the BOM made up of push managed items (see figure 1); as a consequence, under a given inventory policy, each pull managed item is provided with its own RCT value. B A D C E RCT A Aside, in the BOM, A, B, D, E are pull managed items, whereas C is push managed. RCT A is showed by the row = pull managed item. Figure 1. Example of Requirements Chain Time determination. Moreover once the inventory policy is stated for a given end item, the set of the highest level pull managed items in the pipeline can be determined: items belonging to this set are called items in pull with the market, since their consumption is connected in a straightforward manner i.e. it is pegged to a forecasted demand or to a specific customer order, but their 2

consumption does not refer to a stock replenishment. Under a make-to-stock production policy (see figure 2), only finished products belong to the set of items in pull with the market, while under a purchase-to-order production policy, there are no items in pull with the market. Both the definitions quoted above and the remarks considered in problem setting, will greatly help in developing the new proposed methodology for the safety stocks dimensioning purposes, as shown in the following sections. 3. Safety stocks dimensioning When handling the problem of safety stocks sizing and positioning along the pipeline in MRP environments, safety stocks kept to face demand uncertainty should be positioned on pull managed items. Positioning safety stocks on push managed items can reveal itself to be expensive for companies either because these items are customised (e.g. standard gears marked with customers trademarks) or they are hard to keep as stock (e.g. large-size or fragile products, perishable goods etc.). Moreover, safety stocks are to be placed on items in pull with the market. This positioning allows the manufacturing system to react on time whenever a forecast error occurs. If safety stocks are positioned on lower levels of BOMs, they are useless when a forecast error occurs since the lead time required to manufacture finished product starting from components kept as safety stocks is longer than the delivery time required by the market. To this purpose, make-tostock environments offer a clear example: buffers against uncertainty have to be placed at the finished product level. Under assembly-to-order production policies, safety stocks can be placed either at the level of items in pull with the market or at the higher level in the pipeline (in both cases delivery lead time is respected). However, the latter option leads to place safety stocks on push managed items, which is not recommended, as stated before. Make to stock Assemble to order Make to order Purchase to order = pull managed item = item in pull with the market. Figure 2. Items in pull with the market under different production policies Let now consider the lowest level items in the BOMs. While push managed items are not provided with safety stocks, pull managed ones do not require to be provided with their own safety stocks on condition that the amount of safety stocks placed at the finished product level usually called end item level by MRP practitioners is so high to completely absorb forecast errors along the whole pipeline. However, when a safety stocks replenishment is required (e.g. demand has been repetitively underestimated), the related production orders can miss the needed components. The due date set for the replenishment orders is usually equal to the end item manufacturing lead time, so generating a today s withdrawal of first level codes. This unexpected withdrawal is normally uncovered by appropriate inventory levels. This means that safety stocks replenishments introduce nervousness in production planning, especially during MRP procedure running, thus leading to stock-outs at the lower level items of BOMs (Ho and Carter 1996, Ho and Ireland 1993, Ho, Law and Rampal 1995, Portioli 1997); in this case, safety stocks are needed even at lower levels. 3

A simple way of avoiding MRP nervousness lies in setting replenishment orders due dates far in the future. When orders due dates equal the length of the pipeline over time, there is no impact on the lower levels of BOMs, since the allotted time fence for the replenishment orders allows to manufacture the items unavailable due to inventory shortages. Nevertheless, this way of doing is costly, in that end items require a significant amount of safety stocks since they have to cope with forecast error for a time fence as long as safety stocks replenishment time. As a consequence, we can state that safety stocks sizing and managing are two issues to be solved together. In particular, an important item to be considered lies in finding the best compromise between two alternative scenarios. On the one hand, replenishment orders due dates can be set equal to end item lead times. This introduces nervousness in production plans, but it allows to keep reduced amounts of safety stocks at the lower levels of BOMs (notice that safety stocks have to be positioned even on lower level, in this case). On the other hand, replenishment orders due dates can be set equal to the overall length of the pipeline. This lowers MRP nervousness, but it forces to keep huge amounts of safety stocks at the end item level. Figure 3 shows two different alternatives in safety stocks sizing under a make-to-stock production policy. Alternative called A keeps safety stocks only at the end item level and the amount is proportional to the length of the whole pipeline (i.e. LT x1 in figure 3). Alternative called B keeps at the end item level safety stocks proportional to the finished products assembly lead time (i.e. LT X2 in figure 3), and at the lower levels of BOM proportional to the respective lead times (i.e. LT Y and LT Z in figure 3). Neither alternative has a significant edge over the other one a priori. The optimum compromise results from many elements such as cost structures and forecasting error patterns whose combination is often complex and unpredictable, thus recommending a simulation campaign in real-life case studies. Alternative A Alternative B X X Y Z LT X2 LT X1 LT Y LTZ = pull-managed item = item endowed with safety stocks. Figure 3. Alternative courses of action in safety stocks sizing and setting replenishments orders. Furthermore, referring to the safety stocks dimensioning technique, the optimum delay in releasing replenishment orders is to be considered. Literature studies (e.g. Johnston and Boylan 1996, Salameh 1997, Salameh and Jaber 1997) referred to pull environments recommend to replenish safety stocks as soon as they are drawn to face unexpected demand. However in MRP environments, due to the previous master production scheduling planning phase, demand error distribution is expected to be quasi symmetric around zero (Gupta and Brennan 1995, Murty and Ma 1991). In this case, positive forecasting errors (i.e. demand greater than forecasts) are balanced, on average, by negative ones and safety stocks replenishments could be avoided at all, thus betting they will be automatically replenished by negative forecasting errors (i.e. forecasts greater than actual demand). Also in this case a trade-off is to be evaluated. On the one hand, replenishment orders can be released as soon as safety stock are used, so as to guarantee the appropriate service level of the company, but once again this introduces nervousness into the production plan. On the other hand, safety stocks can be never replenished, so as to smooth down MRP nervousness, but it runs the risk of stock-out. Although this latter case does not fit very well real-life 4

manufacturing environments, the alternative is clearly stated and the optimum compromise highly depends on the specific production system considered, which requires to be evaluated through simulation. The previously discussed issues and remarks are summarised by the set of recommended guidelines reported in the followings. (i) Whichever the manufacturing environment, items in pull with the market should be endowed with safety stocks. Also the lower level items can be endowed with safety stocks: this decision impacts on the safety stocks dimensioning and it is system specific, so it should be treated via simulation, which also helps in defining the replenishment policy (i.e. orders due date and release date). (ii) Only pull managed items should be considered as candidates for safety stocks positioning. (iii) Safety stocks sizes are proportional to requirements chain time (rather than to the traditional lead time) to avoid stockout on the lower level push managed items. (iv) The algebraic formula for safety stocks dimensioning recalls that of Wilson (e.g. see Hill 1991) with the main difference that, in MRP environments, demand error is used instead of demand itself, as early suggested by Orlicky (1975). Moreover, the actual demand error distribution is to be considered, instead of the traditional Normal distribution assumed by Wilson but seldom encountered in real-life manufacturing environments. 4. Strategic stocks dimensioning Whenever companies face a lumpy demand pattern, the strategic stocks (also called strategic inventory, see Brandolese and Cigolini 1999) can help to manage the risk of stock-out, in that peaks of forecast error represent errors remarkably greater than average errors, thus introducing a relevant bias effect in the error distribution time series (Bradford and Sugrue 1997). These peaks of forecasting errors may be either related to an extraordinary unforeseeable quantity required by a single customer in make-to-order or assembly-to-order manufacturing system or they correspond to a selling promotion by distributors not communicated in fair advance to manufacturing and logistics manager. If not detected in advance, peaks can create great disturbance to the manufacturing system and peak orders can not be fulfilled within the delivery date required by the market. This becomes even more critical since SMEs often offer a better service level in case of large orders than in case of small ones, since these customers are considered strategic from the turnover point of view. According to Orlicky (1975), safety stocks in MRP environment should be sized on the basis of forecast error distribution. If error distribution is calculated even considering the peaks of error, its standard deviation will result considerably higher than the value representing the majority of the distribution. This leads to higher safety stock, which are costly and unfortunately unable to face the peaks of error whenever they happen. Moreover, supposing SL the usual service level (i.e. that one defined for normal orders) and SL the service level for large/peak orders. Since usually SL > SL, by considering only safety stocks, they can be dimensioned either on the basis of SL service level, which however means over-estimating the buffer actually needed to face uncertainty, or on the basis of SL, which however means that the buffer will not grant SL in case of unforeseen peaks of order (i.e. peaks of errors), thus allowing stock-outs. As a consequence, the proposed methodology suggests to keep two different kinds of buffer for two different kinds of objectives: (i) safety stocks for normal demand error; (ii) strategic stocks for high errors in strategic orders. The concept of strategic stocks was early conceived with reference to pull environments (Brandolese and Cigolini 1999) to face peaks of demand. In MRP environment, strategic stocks represent a buffer to face peaks of forecast error. The previously reported remarks referred to strategic stocks in MRP environments are summarised by the set of recommended guidelines reported in the followings. (i) In a similar way to what assessed about safety stocks and for the same reasons, also strategic stocks are to be placed on items in pull with the market: in a make-to-stock environment, end item should 5

be endowed with strategic stocks; in an assembly-to-order environment subassemblies should do etc. (ii) Strategic stocks are to be dimensioned on the basis of the statistical distribution of the peaks of demand error, in order to reach a given service level. To this purpose, the original definition of strategic stocks for pull environment (Brandolese and Cigolini 1999) assumed a 100% service level for demand peaks, so setting strategic stocks proportionally to the difference between the maximum peak and the mean value. In MRP environments, service level is below 100%, so strategic stocks are dimensioned referring to the actual error peaks statistical distribution (instead of demand distribution), so as to provide the required service level. Table 1 provides the reader with an overall view of the guidelines proposed for both safety and strategic stocks. Safety stocks Issue Items that should be endowed with safety stock Safety stocks buffer size Replenishment order for safety stock release time Manufacturing environment Make-to-stock Assemble-to-order Make-to-order - Subassembly: always - Lower levels down-to - Components/ra components/raw w materials materials: to be evaluated via simulation - End items: always - Lower levels down-to components/raw materials: to be evaluated via simulation Proportional to: - actual demand error distribution and (for lower level, if any) actual requirements error distribution - RCT down to pipeline length (depending on simulation results) From as soon as possible to never, depending on simulation results Proportional to: - actual requirements error distribution - RCT down to pipeline length (depending on simulation results) From as soon as possible to never, depending on simulation results Proportional to: - actual requirements error distribution - RCT down to pipeline length (depending on simulation results) From as soon as possible to never, depending on simulation results Strategic stocks Items that should be endowed with safety stock Safety stocks buffer size Replenishment order for safety stock release time End items Proportional to the actual distribution of demand error peaks Subassemblies Proportional to the actual distribution of requirements error peaks Components/raw materials Proportional to the actual distribution of requirements error peaks As soon as possible As soon as possible As soon as possible Table 1. Overall view of the guidelines proposed for both safety and strategic stocks. 5. Case-study The guidelines reported in the previous sections lead to a new methodology of buffering against lumpy demand in MRP environment. The proposed methodology consists in the following steps. (i) Forecast error estimation. (ii) Strategic stocks sizing according to the guidelines shown in section 4. (iii) Forecast error correction (elimination of error peaks from the series). (iv) Safety stocks sizing according to the guidelines shown in section 3. (v) Testing of alternative courses of action in safety stocks positioning and replenishment orders setting. This methodology has been applied to an Italian company, leader in the electro-mechanical components branch of industry. Depending on the volume and the delivery lead time, that company manages products according to either a make-to-stock or assembly-to-order or make- 6

to-order policy. The stock redesign project focused on make-to-stock products, whose target service level was 95%. During project execution, the following steps have been carried out: (i) data collection; (ii) definition of the simulation campaign, in terms of the alternative ways of safety stocks allocation, different replenishment criteria etc. (iii) determination of safety and strategic stocks for each simulation experiment; (iv) analysis of results. Table 2 highlights the comparison between the pre-project condition (called as-is ) and that one after buffer redefinition. As a consequence of buffering redefinition, stock-keeping costs has increased on average, however the achieved benefits lie in a reduced stock-out occurrence (in accordance to company s target service level) and in an improved plan nervousness, due to both a reduction of replenishment orders and a lower variance of production orders size. Table 2. As-is After buffer redefinition Safety stocks (in monetary units) 100 51,25 Strategic stocks (in monetary units) 0 65,86 Global buffering against uncertainty (in monetary units) 100 117,11 Number of stock-outs 10 0 Stock-out units 1523 0 Number of replenishments 24 7 Mean 100 112,74 Inventory level (units) Minimum 0 5,92 Maximum 186,12 203,13 Mean 100 100,00 Production orders (units) Minimum 0 0 Maximum 265,48 105,26 Results of the case-study; except for stockout, indicators are expressed as a percentage of the as-is indexes (in bold style). 6. Concluding remarks and future research paths In this paper, a new methodology for safety buffer dimensioning and managing has been proposed. In developing the methodology, the following research issues have been treated: (i) the type of buffer to be used (i.e. strategic and/or safety stocks); (ii) the size of buffer to be used, dimensioned on the basis of forecast error distribution and requirements chain time; (iii) the way of managing safety stocks replenishment. The contributions of the proposed methodology to the research body of knowledge can be briefly summarised as follows. (i) Strategic stocks are introduced as a buffer against uncertainty in MRP environments, while they were originally conceived for pull environments. (ii) Safety stocks are to be dimensioned on the basis of the actual, empirical, distribution of forecast error, rather than on the basis of a hypothesised normal statistical distribution. (iii) Safety stocks are to be dimensioned on the basis of the Requirements Chain Time, rather than manufacturing lead time, as traditionally stated in literature. The proposed methodology has been successfully implemented in an Italian manufacturing company, leader within its branch of industry, with the appreciation of the CEO and of the production and logistics management team. Nevertheless, some other issues have not yet been considered neither in the conceptualisation nor in terms of the benefits assessed by a field implementation. They can be considered here as future promising research directions and they basically refers to the following remarks. (i) The impact of forecast processing frequency on the dimension of safety and strategic stocks has not been investigated, especially when combined with a variable frozen period in production planning. It can only be argued that the first-processed forecast is to be taken into account, under the implicit hypothesis that forecast reliability improves as time horizon become shorter. 7

(ii) The impact of the MRP procedure running frequency on the dimension of safety and strategic stocks has not been analysed in detail. It seemingly can be modelled as a wider frozen period due to MRP, but its effects are actually unknown and well worth to be studied. (iii) While the proposed methodology assumes deterministic lead times, in case of stochastic lead times, each item should be anyway endowed with safety stocks, as suggested in literature. However, this safety buffer should never be replenished since a replenishment order would be probably a late order. Nevertheless, the presence of a balancing effect between safety stocks to face demand uncertainty and those ones to face lead time uncertainty has not been investigated, even though some benefits in terms of cost reduction are expected. Acknowledgements The authors wish to thank Prof. Andrea Sianesi, of Università Carlo Cattaneo, for having provided many helpful suggestions. References Bradford J W and Sugrue P K (1997). Estimating the demand pattern for C category items, Journal of the Operation Research Society, 48: 530-532 Brandolese A and Cigolini R (1999). A new model for the strategic management of inventories subject to peaks in market demand, International Journal of Production Research, 37(8):1859-1880 Guide V D R and Srivastava R (2000). A review of techniques for buffering against uncertainty with MRP systems, Production Planning and Control, 11(3): 223-233 Gupta S M and Brennan L (1995). MRP systems under supply and process uncertainty in an integrated shop floor control environment, International Journal of Production Research, 33: 205-220 Hill T (1991). Production / Operations Management, Prentice-Hall, New York Ho C and Carter P L (1996). An investigation of alternative dampening procedures to cope with MRP systems nervousness, International Journal of Production Research, 34:137-156 Ho C and Ireland T C (1993). A diagnostic analysis of the impact of forecast errors on production planning via MRP system nervousness, Production Planning and Control, 4: 311-322 Ho C, Law W K and Rampal R (1995). Uncertainty-dampening methods for reducing MRP system nervousness, International Journal of Production Research, 33: 483-496 Johnston F R and Boylan J E (1996) Forecasting for items with intermittent demand, Journal of the Operational Research Society, 47: 113-121 Murty D N P and Ma L (1991) MRP with uncertainty: a review and some extensions, International Journal of Production Economics, 25: 51-64 Orlicky J (1975). Materials Requirements Planning, Mc. Graw-Hill, USA Portioli A (1997). Investigation on the impact of component commonality on MRP system nervousness. Proceedings of the International conference on industrial engineering and production management, France, Lyon, October 1997, 1: 315-325 Salameh M K (1997). Buffer stock under the effect of fluctuating demand, Production Planning and Control, 8(1): 37-40 Salameh M K and Jaber M Y (1997). Reserve stock and transhipment in hierarchical inventory systems, Production Planning and Control, 8(5): 469-474 8