INVENTORY MANAGEMENT REVISED

Scence & Mltary 2/2011 INVENTORY MANAGEMENT REVISED Analyss of behavoral asects of decson makng wthn Sales & Oeratons Plannng rocess Peter JUREČKA Abstract: The urose of ths artcle s to extend the standard text-book statc nventory otmzaton model for the rocess vew by analyzng the antagonstc ncentves of dfferent lannng stakeholders that may lead to neffcences n nventory management. Two models are outlned to nvestgate the macts of such otentally contradctory behavor otmzaton model based on dualty known from the classc mcroeconomc theory of consumer reresentng more theoretcal smulaton and Value Based Management model followng recent trends n busness management. Keywords: nventory management, economc modelng, rocess otmzaton, sales and oeratons lannng, S&OP.. 1 INTRODUCTION Toc of nventory management s resent wth dfferent detal at every level of comany s lannng, ndeendent whether examnng manufacturng or servce rovdng rvate entty or ublc sector organzaton. Tocs of strategc management of resources, fnancal otmzaton of workng catal, volatlty n sales demand or flexblty n oeratons has a common denomnator - nventores. Most of the text-book nventory otmzaton models have been dealng wth the trade-off between two tyes of costs ) Orderng/Set-u costs often called also as Prearaton costs and ) Inventory Carryng costs. The outcome of the otmzaton of total costs of nventores s the calculaton of otmal order sze known as Economc Order Quantty (EOQ) 1. What has been mssng s more comlex vew that would nclude at least also the ) Costs of not havng the nventory when needed,.e. cost of mssed sales due roduct shortage on one sde and the v) Costs of surlus nventory on the other. Whle the frst two categores are rather objectve wth costs defned by the structure of comanes assets for ) or by the oston of market costs for related servces for ), categores ) and 1 Two man arts of rearaton costs ncludes ) Processng of Purchase Orders,.e. costs of urchasng, goods recevng, ncomng nsecton and accounts ayable and ) Manufacturng Set-u Costs ncludng all the costs of managng the works order, e.g. rearng the secfcaton, rasng and trackng the order or the costs of settng u the machne and ntal nsecton. Inventory Carryng costs results from the fact that the tem s n stock and ncludes: cost of catal, deteroraton, obsolesce, theft, nsurance and storage costs etc. For more nformaton see e.g. Brealey, Meyers, Allen (2010),. 758 759 for model wth certanty or Kslngerova (2007),. 474 483 for the model wth uncertanty. v) are rather subjectve and hghly deendant on the qualty and set-u of nternal lannng rocess. In the ucomng chaters, the focus wll be on the latter two categores and ther denomnaton consderng the roles and ower of dfferent busness functons wthn lannng rocess. In Chaters 2 and 3, antagonsm n ncentves wthn Sales and Oeratons Plannng (S&OP) rocess s exlaned va usng the mcroeconomc modelng. In Chater 4, Value Based Management aroach s aled to outlne the consequences of varous rocess set-us on value creaton of the frm. 2 ANTAGONISM IN SALES & OPERATIONS PLANNING The most tycal examle of comany s lannng rocess wth ossbly hghest mact on nventory levels s the rocess of Sales and Oeratons Plannng (S&OP). In general, S&OP s takng three key nuts; the busness lan, the antcated demand and the avalable resources that are used to create and mantan two fundamental lans for managng the busness n the medum and long term. Frst s the sales lan, whch s the agreed volume of exected future sales and second s the roducton lan, whch s the agreed volume of roducton requred to suort the sales lan. Based on the bref descrton of S&OP rocess, t s clear that the two man artes nvolved n ths rocess are the Sales and Suly chan (Oeratons) 2. Although the general goal of the 2 By Sales or Suly chan contrary to sales or suly chan would be for the dstnctve uroses meant the sales/suly chan deartment or functon n the comany. From the ersectve of nut, Marketng wth ts defnton of busness strategy and Fnance/Controllng wth fnancal valuaton of quanttatve lans lay also very mortant role. However, n the end t s manly the Sales and Suly chan/oeratons that should algn sales lans wth 40

Scence & Mltary 2/2011 comany s usually qute straghtforward, amng mostly on the sustanable roft growth and thus creatng value exceedng catal costs for ts stakeholders, secfc targets of dfferent artes nvolved n S&OP rocess mght dffer, even though they do not conflct or deally they suort the general target. The level and structure of nventores 3 s the ndrect outcome of S&OP rocess as t s the result of the roducton and dstrbuton lannng and sales. In general, nventory level and structure should be ket so, that the comany s able: a) to react effectvely on the demand fluctuatons on the market, b) at the lowest ossble costs. However, these two requrements have artally antagonstc effect on the total costs of nventores. Lookng closer at the motvaton of Sales, the sales reresentatves and managers are n most cases focused on the ncrease of sales erformance. The man contrbuton to the roft ncrease from Sales s thus reached through growth on the sde of revenues. From the vew of roduct avalablty, the two man rerequstes of reachng ther goals are: a) to have suffcent amounts of roduct avalable (.e. volume related flexblty), b) early enough before the antcated sales (.e. tmng related flexblty). Ths would ensure the total desred sales flexblty reresentng suffcent roduct avalablty so that Sales s able to react on the demand volatlty for comany s roduct. On the other hand, the core functon of Suly chan s to suly the Sales and eventually the customers at the lowest ossble costs under the assumton of mantanng certan agreed level of flexblty for Sales, defned usually n a certan form of Servce Level Agreement. Suly chan s thus rmarly tryng to contrbute to roft creaton through lowerng the costs, nstead of ncreasng the revenues. As can be seen, dfferent motvaton of Sales and Suly chan nfluences the level of nventores, and roducton caabltes. The Suly chan here s reresented manly by Demand lanners, Forecast managers, Suly chan managers etc. deendng on the organzatonal structure of each ndvdual comany. 3 For the uroses of ths text, under the term nventores, one should understand the fnshed goods (not assumng two other man nventory grous, raw materals and work-n-rogress, as the S&OP rocess relates manly to the art of suly chan from roducton to customers and not from sulers to roducton) thus eventually the costs n the ooste drecton. The request for flexblty buffer/safety stocks from the Sales ont of vew leads to the ncrease n the amounts and tme of roducts on stock, whch oostes the costs mnmzaton efforts of Suly chan. To sum u, the effcency of S&OP rocess can be vewed from two ersectves: - the ablty of Suly chan to meet the requrements of Sales regardng the amount and tme avalablty of roduct; or n other words, the satsfacton of Sales from havng at dsosal suffcent amounts of roduct soon enough on stock (named Product Avalablty PA ) - Costs of nventores related to ths roduct avalablty CoI. Both of these vews meet under the toc of nventory management that deals manly wth two ssues: What s the arorate level/mx of nventores? and How long n advance should be the roduct avalable on stock before the lanned sales? Both PA and CoI are generated by certan amount of nventores at stock for certan erod of tme. Therefore, for the modelng uroses the followng two varables needs to be defned:: - average level of nventores (measured n quanttatve unts of measure, named Q ), caturng the volume asect of nventory management, - average erod, for whch the nventores are at stock (measured n tme unt of measure, named T ), caturng the tme asect of nventory management. The hgher s each of the varables, the hgher are the CoI, as well as PA. 3 OPTIMIZATION MODEL MICROECONOMIC MODELING Lookng at the roblem of antagonsm n S&OP rocess through mcroeconomc lenses, t s ossble to recognze many common features of decson makers nvolved wthn ths rocess wth ratonal consumer from the classc mcroeconomc theory. Alyng mcroeconomc fndngs on busness rocesses can exlan the dfferent motvaton of nvolved artes and thus fnd the ossble gas n effcent settng and functonng of S&OP rocess. Lookng for the lnk to mcroeconomc Theory of consumer, we can say, that Sales are consumng certan levels of Q (S) and T (S) 4, whch form the 4 In ths work, wherever (S) or (SC) are used to dentfy, whether varable refers esecally to Sales (S) or 41

Scence & Mltary 2/2011 secfc level of PA. The utlty for Sales ncreases wth the ncrease of PA and the PA bundle 5 s denoted by the vector: PA m = (Q (S) m,t (S) m), where Q (S) m and T (S) m, m = 1,2,3 n, reresents the secfc quantty and tme of nventores 6 on stock. Moreover, the values of Q (S) and T (S) are not only not-negatve, but are also restrcted wthn secfc lmts: 0 < Q Mn < Q (S) < Q Max 0 < T Mn < T (S) < T Max Fg. 1 Oeratonal Area The ratonale for ths assumton s as follows: there s certan mnmum level of Q (S) and T (S) (called Q Mn and T Mn ), that reresents an unbased mnmal level of nventores acceted/agreed by both Sales and Suly Chan, under whch the normal functonng of the busness s mossble. Contrary to ths, we can assume also certan maxmum level of Q (S) and T (S) (called Q Max and T Max ), above whch keeng any addtonal nventores would have no ossble beneft for busness. Therefore, we can determne the Oeratonal area for nventory otmzaton wthn the area defned by these two onts [Q Mn ;T Mn ] x [Q Max ;T Max ], as llustrated on the Fgure 1. Sales ranks the bundles n the feasble set n order of reference and choose the one wth the hgher rankng. Further on, each level of PA brngs certan level of utlty to Sales, whch can be exressed as: Suly Chan (SC), e.g. Q(S)* means the otmal level of Inventory volumes from the ersectve of Sales. 5 Consumton bundle n the Theory of consumer 6 m stands for Stock Keeng Unt/ Artcle 0 us u = 0 S ( PA) us where s some gven number. Establshng the noton of Sales utlty functon (u S ) and wth regards to the assumtons of reference orderng descrbed above, we can redefne the roblem of fndng the most desred level of PA as the one of constraned maxmzaton of a strctly quasconcave functon 7. Each combnaton of Q and T not only brngs certan level of utlty for Sales, but also bear nventory related costs. The hgher the Q and T, the hgher amount of comany s catal s bounded n form of nventores, and thus hgher ts costs. All combnatons of Q and T that comes to the consderaton from the ersectve of Suly chan form the Feasble set. Each ont wthn the set reresents a secfc level of Costs of Inventores (CoI), whose mnmzaton belongs to rmal targets of Suly chan. Suly chan tres to manage the cost of nventores through effectve roducton and dstrbuton lannng n order not to exceed the certan maxmum target level of CoI, named CoI Max. The total level of CoI Max s usually determned through varous Key Performance Indcators (KPIs) n relaton to other varables, such as level of sales, e.g. t s common busness raxs that comany adots the target that the Average Inventory to Sales rato should not exceed certan ercentage. From budgeted or forecasted yearly level of sales, the level of average yearly nventores s calculated, and out of t usng exected/defned rces (Q) and (T) also the CoI Max. Formally, ths feasble set showng the total Cost of Inventores (CoI) can be calculated as follows: ( Q) Q ( T) T = CoI CoI max +, where P(Q ) stands for average unt rce of the unt of Inventory related to Quantty and P(T ) reresents the rce of the unt of nventory related to tme 8. As can be seen on the followng fgure, the Feasble set s a trangular area determned by the level of CoI Max from the to and Oeratonal area [Q Mn ;T Mn] x [Q Max ;T Max] descrbed above from the bottom. 7 For more nformaton about the features of utlty functon see e.g. Gravelle, Rees (2004),. 16-18. 8 P (Q) s the comound measure most commonly reresented by combnaton of the rces of transortaton, warehousng and handlng er square or cubc meter or alette based on the nature of the nventory. P (T) reresents the comound measure too, caturng the tme asect of the nventory, (e.g. for how long s the roduct stored), ncludng seed of transortaton (ar freght vs. ground shng), rce for the unt of tme the goods are stored, etc. 42

Scence & Mltary 2/2011 ths ont, sloe of ndfference curve s equal to the sloe of ICL 9 : dt dq dt = dq u const. CoI const. Fg. 2 Feasble set The uer boundary of the Feasble set, named Inventory Cost Lne (ICL) can be defned by the smle modfcaton of CoI defnton as: T = CoI and ts sloe thus as: dt dq Q max / ( T) ( Q) / ( T) = ( Q) CoI const. ( T) Taken nto consderaton the assumtons mentoned above, the roblem of choosng the most referred mx of Q and T can be formalzed as: maxu ( Q, T ); s. t. ( Q) ( Q, T ) [Q Q + ( T) Mn T,Q = CoI CoI Max ] x [T Mn Max,T ; Max Based on these assumtons, the Sales references about the otmal levels of PA are reresented by Sales utlty functon u(s) wth ndfference curves such as on the Fgure 3. As both Q and T are ostvely related to PA and thus have ostve margnal utlty for Sales, the combnatons of Q and T lyng on hgher ndfference curves wll be referred to those on lower ones. Ths, together wth assumton of Nonsataton of references wll result n usng the maxmal level of CoI by maxmzng u(s). The combnaton of Q and T on the ICL wll be chosen. In the Fgure 3, the otmal combnaton of Q* and T* s a tangency soluton, where the hghest attanable ndfference curve s tangent to ICL. In ] Fg. 3 Otmal soluton Sales So far, we have been dealng wth fndng the otmal mx of Q and T under assumton that Sales s the man decson makng authorty regardng the choce of the level of PA. In other words, we assumed that Sales drves the S&OP rocess. In theory t would mean that Sales take the maxmum level of CoI (CoI Max ) as gven, and move alongsde Inventory cost lne tryng to fnd the common ont on the hghest ndfference curve,.e. the hghest level of PA. The stuaton when commercal functons lke the Sales or Marketng are drvng forces of the S&OP rocess wll be more alcable for the comanes sellng hghly roftable roducts, where the fnancal mact of the loss of sales outweghs the rsk of hgher nventory costs, therefore there s hgher ressure on roduct avalablty. Dfferent aroach to the soluton of ths otmzaton roblem would be aled, f the man drvng art of S&OP rocess would not be Sales, but Suly chan. Ths wll be most robably the case for the cost drven ndustres wth relatvely small gross roft margns. Suly chan than take the reference orderng of Sales as gven, and t s 9 Usng the assumtons of strctly quas-concavty of utlty functon and the characterstc features of feasble set (convex, non-emty, closed and bounded), we can derve that the otmzaton roblem has a unque soluton and there are no other non global local solutons (For more nformaton see e.g. Gravelle, Rees (2004); Aendxes A-D) 43

Scence & Mltary 2/2011 lookng for the cheaest way, how to acheve certan level of PA. In other words, by fndng the otmal soluton, t would move alongsde the gven ndfference curve lookng for such level of PA as the combnaton of Q and T that s lyng at the lowest ossble Inventory cost lne. In ths case we are dealng wth dual otmzaton roblem to that descrbed above. Formally, we can wrte t as: mn 1) u ( Q + T ) S ( Q) ( SCF) u 2) ( Q, T ) [( Q ( T) S, Mn Q ; Max ),( T Mn, T Max )] R Analogcally to the stuaton when Sales was drvng the S&OP, solvng of these equatons would lead to smlar results,.e. that n otmum, the rato between margnal utlty of Q and T for equals to the rato of (Q ) and (T ): dt * dq * dt ( Q*) = =. ( T*) dq * CoI const u( SCF ) = u( SCF*) From the outcomes of the revous chaters t mght seem, that t does not make any dfference regardng the otmal level of PA and CoI, whether the man decson makng ower n S&OP s Sales or Suly chan. However, ths dfference wll become vsble: a) when we examne the mact of changes of rces (Q ) and (T ) on otmal choce of Q and T and (.e. when the sloe of ICL would change) b) when we look at the settng of constrans for otmzatons (when the whole ICL would shft as a result of dfferent CoI). It s obvous that the settng of S&OP rocess and the slt of decson makng ower between Sales and Suly chan can have substantal mact on the costs of nventores whch mght reresent sgnfcant orton of comany s total costs. Ths s vald esecally n the case of sellng organzatons where bg amount of catal s ted n form of fnshed, but not yet sold roducts. In raxs, such otmzaton s not ossble for examle because of dffcult attrbuton of cost down to the level of ndvdual stock keeng unt. Also, n most of the comanes where ncentves are not algned and each functon s rmarly focusng on ts own targets, the revalng busness functon wll shae the whole nventory management aroach,.e. n strongly Sales orented organzatons, the PA and related CoI wll be n extreme case determned by Q Max and T Max and * 2 n strongly cost orented comanes wth low roft margns, the PA and CoI wll be much closer towards levels defned by Q Mn and T Mn. The examles above also show the alcaton of classc mcroeconomc otmzaton models to real busness envronment. 4 OPTIMIZATION MODEL VALUE BASED MANAGEMENT As mentoned n revous chater, there are certan constrans for ractcal alcaton of theoretcal otmzaton models as descrbed above. One of the alternatve ways of how to aroach the otmal set-u of busness lannng rocess s to analyze how ts qualty contrbutes to generaton of value for comany s shareholders. Identfyng and focus on the man drvers of value creaton s one of the man targets of the concet of Value Based Management. The thnkng behnd Value Based Management (VBM) s qute straghtforward. As the value of a comany s determned by ts dscounted future cash flows, comany s creatng addtonal value only when returns from nvested catal exceed ts costs. The followng fgure shows the tycal Value drver tree decomosng EBIT after Cost of Catal (EaCC) nto ndvdual arts. Fg. 4 Value drver tree n general In order to demonstrate how can the set-u of lannng rocess from the ersectve of emowerment of ndvdual decson makers nfluences EaCC, we have to examne how t nfluences the ndvdual value drvers, or even more recsely, how t macts the KPIs that are assgned to these drvers. Secfc value drvers closely lnked to lannng erformance can be dentfed and ther mact on overall bottom lne erformance of the frm measured. In general, rght nventory structure resultng from roerly set S&OP rocess macts the EaCC twofold - ether ndrectly va suortng sales through roer resonse on sales demand volatlty 44

Scence & Mltary 2/2011 by havng the rght roduct at dsosal at the rght tme, or drectly va the costs of nventores 10. The followng fgure shows the value drvers that are essental for suly chan management related to lannng qualty 11, sulemented wth examles of some most frequently used KPIs. effcency of oeratons and consequently also fnancal erformance. Also n case of algned ncentves,.e. through sharng the common targets of forecast accuracy or average nventory levels by both Sales and Suly Chan, there s a need for a decson bass on whether the addtonal unt of roduct should be made avalable to suort otental sales on one hand or burden the catal costs n case f not beng sold on another. Ths s esecally vald for the Make-to-Stock oeratonal set-u, where the roducton s trggered by antcated or forecasted demand, not by actual confrmed orders. Generally, roduct should be made avalable f the otental value ganed from ts sales s hgher than costs n case that t would not be sold,.e. f: where: (GP m ) - (1-)(COGS m ) > 0, Fg. 5 Value drver tree Suly Chan KPIs As can be seen, reachng hgh levels of suly chan caablty, relablty and flexblty, wth ts drect lnk on logstcs related customer comlans are the key rerequste for delverng sales. Unless Suly chan kees ersstent hgh erformance levels, Sales and Marketng wll always be reluctant to showng transarently ther most realstc sales forecast and wll always be based ether towards earler roducton or to overestmaton of oeratons lannng n order to secure ther sales flexblty. If there s not enough transarency n lannng that would steer algnment of lannng rocesses and reconclatons between lans of Sales and Oeratons, t hts back negatvely the overall 10 Aart from the mact on Sales and Inventores, neffectve set-u of S&OP rocess mght also have negatve mlcatons for examle on some varable costs, e.g. through usage of ar-freghts as a frefghtng reacton of roduct shortages n some cases, but ths analyss s out of scoe of ths artcle. 11 There are also multle other value drvers related to suly chan wth effect manly on fxed costs or varable costs (e.g. logstc costs or lead tmes), but these are nor drectly macted by qualty of busness lannng, therefore are out of scoe of ths artcle. Although one could robably argue that n case of frefghtng reacton on the roblems related to wrongful lannng mght be for examle necessty of usage arlne shment n stead of vessels and thus drectly mactng logstc costs, but ths should be taken more as an excetonal case and therefore s not consdered further. lkelhood that roduct wll be sold (1-). lkelhood that roduct wll not be sold GP m.. Gross Proft of roduct m COGS m. Cost of Goods Sold for roduct m P m... Sales Prce of roduct m (=GP m +COGS m ) After numercal adjustment we get: P > COGS m /(COGS m -GP m ) P > COGS m /P m P > COGS m margn Ths easy examle can serve as rule of thumb method on the decson regardng addtonal requrement of sales on usde roducton. In case the robablty that the addtonal roduct s hgher than the Cost of goods margn, t s on average roftable to roduce addtonal volumes of ths roduct. The fndng also suorts the argument that the more roftable s the roducts (.e. havng hgher GP margn thus lower COGS margn), the lower the lkelhood of otental sales s requred to justfy addtonal roducton. Ths effect s even more obvous f the roduct can be resold later,.e. for the case of seasonal roducts wth more that one season of shelf lfe. Than the costs related to not sellng the roduct wll be lmted only to the costs of catal bounded n form of nventores for the tme tll the roduct s sold. The adjusted formula for such case would be as follows: (GP m ) - (1-)(COGS m )xcc > 0, where CC stands for Costs of Catal bounded n form of nventores. 45

Scence & Mltary 2/2011 5 CONCLUSIONS Standard text-book nventory otmzaton models often omt the rocess art of nventory management,.e. the behavoral factors and set-u of the nternal lannng rocess that n the end has major mact on the nventory levels. The artcle outlned the two alternatve aroaches towards further analyss of ths toc. Dualty known from mcroeconomc Theory of consumer was aled to demonstrate dfferent aroaches towards same roblem of fndng the otmal nventory mx from Sales and Oeratons ersectve. More ractcal aroach can be offered by alcaton of Value Based Management rncles through analyss of how the nventores mact the value that comany s generatng. Both of the aroaches can be aled to suort the dscussons about one of the most common trade-offs wthn Sales and Oeratons Plannng of the frm balancng addtonal benefts from more sales flexblty wth costs of addtonal nventores. References [1] GRAVELLE, H., REES, R.: Mcroeconomcs (3rd edton); Prentce Hall; 2004; 738.; ISBN- 0582404878 [2] BREALEYl, R.; MYERS, S.; ALLEN, F.: Prncles of Cororate Fnance (10th edton); McGraw-Hll/Irwn; 2010; 960.; ISBN-10: 0077356381 [3] KISLINGEROVÁ, E. a kol.: Mazažerské fnance; C. H. Beck; 2010; 745.; ISBN: 978-80-7179-903-0 Dl. Eng. Peter JUREČKA, M.A. Postgraduate student Deartment of Busness Economcs Faculty of Busness Admnstraton Unversty of Economcs, Prague Nám. W. Churchlla 4 130 67 Praha 3 Žzkov Czech Reublc E-mal: eter.jurecka@gmal.com 46