A novel approach for inventory problem in the pharmaceutical supply chain

Transcription

1 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 DOI /s y RESEARCH ARTICLE Open Access A novel approach for nventory problem n the pharmaceutcal supply chan Gökçe Candan * and Harun Reşt Yazgan Abstract Background: In pharmaceutcal enterprses, keepng up wth global market condtons s possble wth properly selected supply chan management polces. Generally; demand-drven classcal supply chan model s used n the pharmaceutcal ndustry. In ths study, a new mathematcal model s developed to solve an nventory problem n the pharmaceutcal supply chan. Method: Unlke the studes n lterature, the shelf lfe and product transton tmes constrants are consdered, smultaneously, frst tme n the pharmaceutcal producton nventory problem. The problem s formulated as a mxed-nteger lnear programmng (MILP) model wth a hybrd tme representaton. The objectve s to maxmze total net proft. Effectveness of the proposed model s llustrated consderng a classcal and a vendor managed nventory (VMI) supply chan on an expermental study. Results: To show the effectveness of the model, an expermental study s performed; whch contans 2 dfferent supply chan polcy (Classcal and VMI), 24 and 30 months plannng horzon, 10 and 15 dfferent cephalosporn products. Fnally the mathematcal model s compared to another model n lterature and the results show that proposed model s superor. Concluson: Ths study suggest a novel approach for solvng pharmaceutcal nventory problem. The developed model s maxmzng total net proft whle determnng optmal producton plan under shelf lfe and product transton constrants n the pharmaceutcal ndustry. And we beleve that the proposed model s much more closed to real lfe unlke the other studes n lterature. Keywords: Pharmaceutcal supply chan, Shelf lfe, MILP, Vendor managed nventory Background Pharmaceutcal ndustry apples a supply chan polcy that allows the contnuaton of a wde varety of materals wth large quanttes n a very fast flow. Wthn pharmaceutcal supply chans, the product varety s a huge problem to manage wthn short tme wndows. Nevertheless, dependng on the medcne drugs, amounts can be a bg problem to trade wth costs. In here, the requrements of small batches are partcularly hard to handle. The producton of pharmaceutcal products has two stages as prmary and secondary level. Prmary producton ncludes the producton of basc molecules actve components or pharmaceutcal actve ngredents. The secondary producton also ncludes the processes of beng formulated of these actve components and the delvery to * Correspondence: gcandan@sakarya.edu.tr Industral Engneerng Department, Sakarya Unversty, Sakarya, Turkey the customers. Many operatons n pharmaceutcal producton occur n bulks called charge. Qualty control also takes place wth montorng each charge. On the producton lne, cleanng s a matter n the case of product change (transton) and ths stuaton s to prevent the contamnaton of dfferent products. Besdes, raw materals and products have a certan shelf lfe. All these constrants are reducng the effcency n the pharmaceutcal ndustry. Shelf lfe controls are performed for raw materals by subjectng to retest procedure at certan ntervals. Durng retest, raw materals are kept n quarantne; they are not defntely ncluded n the producton lne and f test results ndcate that the raw materals can already be used, they are taken from the quarantne and transferred to producton stores. In shelf lfe control for the products, expraton date s prnted on the packagng whle the 2016 Candan and Yazgan. Open Access Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton 4.0 Internatonal Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded you gve approprate credt to the orgnal author(s) and the source, provde a lnk to the Creatve Commons lcense, and ndcate f changes were made. The Creatve Commons Publc Doman Dedcaton waver ( apples to the data made avalable n ths artcle, unless otherwse stated.

2 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 2 of 16 product s on producton lne and the expry date starts from the date of producton. Compared wth supply chan of other products, pharmaceutcal supply chan s very complex. The factors such as long set-up tmes, resource-ntensve operatons, short shelf lfe and hgh producton of waste make the pharmaceutcal supply chan dfferent from other sectors. Pharmaceutcal producton s demand managed. Frms rarely delver the product to pharmacy or patent; nstead of ths, they delver products to the consumer through wholesalers (pharmaceutcal warehouses). In such a dfferent featured sector to mantan a presence n the market despte all these constrants s possble wth correctly selected supply chan management polces. To adapt to changng market condtons, sustanable supply chan polcy and to compete n global market, the pharmaceutcal supply chan should be carred out by mathematcal models based on scentfc formulas determned wth correct strateges [27]. In plannng, the mportance of nventory management has also great mportance. Consderng countless complcatons, t s very dffcult to obtan optmal schedules. However, mathematcal models help to take rght decsons. For an optmal producton plan n the pharmaceutcal ndustry, cleanng and preparaton tmes (these occur on product transton tmes), faclty mantenance tmes, testng and the producton of new chemcals, resource allocatons, manpower utlzaton and nventory management must be decded and planned n an ntegrated way. Ths case requres a producton plannng strategy evaluatng operatonal confguratons wth repeated consultatons wth several departments, process constrants, statstcal combnatons and busness scenaros. The producton must be planned at certan tme ntervals and n accordance wth a herarchcal approach [11]. In plannng, the mportance of nventory management has also great mportance. Also to compete n pharmaceutcal producton n the global market, t s requred to develop effectve nventory control polces. Companes want to meet customer demands at the hghest levels and prefer product storage to avod fallng below a safety stock level. In ths way, hgh amount of nventory cost occurs. Whle reducng the nventory level for mnmzng costs, frms cannot meet the demands, delvery dates delays, and there are some decreases n servce levels [30]. Wth the latest developments n nformaton technologes, the fast and easy nternet networks are used to make the nformaton sharng easer and ncrease securty across the supply network. Accordngly, VMI defned as cooperaton wth a customer and a suppler to optmze an nventory management for least-cost on both companes began to be used. Wth ths model, the suppler takes responsblty for the operatonal management of nventory wth agreed performance targets. These performance targets are contnuously montored and updated to ensure contnuous mprovement [12]. In order to optmze supply chan performance, the manufacturer takes the responsblty of dstrbutor s nventory levels. Dstrbutor also shares the demand forecast and sales data as well as nventory data. Manufacturer manages the dstrbutor s nventorywththsdata.themanufacturersresponsble for determnng the order quanttes and tme n ths model [31]. In ths study, n cephalosporn department of a factory makng secondary pharmaceutcal producton, a mxed nteger mathematcal model s developed to obtan the best producton plan whle maxmzng the total net proft n long term. Especally the presence of constrants related to shelf lfe, product transton tmes that are gnored n many studes about pharmaceutcal producton s also added to the model and an expermental study s mplemented. The proposed mathematcal model s appled on two dfferent types of supply chan (classcal supply chan and vendor managed nventory) and the results of both methods are compared n terms of the total supply chan cost. In addton, the proposed model s also compared wth another model from lterature to llustrate effectveness of model. Lterature revew Plannng and schedulng problems have been the subject of nnumerable studes n the mathematcal programmng lterature. Varous types ndustral sectors are consdered wth dfferent tme representatons n these studes. But some studes cover varous ndustral sectors for plannng and schedulng problem lke Fleschmann and Meyr [10]. Pharmaceutcal producton s a batch process and a type of chemcal producton. Chemcal productons are made n multproduct plants. The studes for plannng and schedulng n mult-product plants are Oh and Karm [28], Alle and Pnto [1], Dogan and Grossmann [9], Mendez and Cerda [25], Lu et al. [23], Chen et al. [6]. Some studes n lterature have handled producton and dstrbuton plannng together (Lee and Km [21], Blgen and Günther [4]). Also n ths part of the study, the studes n the lterature related to admnstratve ssues, plannng, schedulng and the cost optmzaton n the pharmaceutcal supply chan are lsted. The studes about optmzaton n pharmaceutcal supply chan wth mathematcal methods developed by usng mxed nteger programmng, are as follows; Papageorgou et al. [29] stdued to optmze the problems n strategc areas such as product development, promoton strategy, capacty plannng and nvestment strategy usng a mxed nteger programmng n the pharmaceutcal supply chan. Maravelas and Grossmann [24] dscussed smultaneous optmzaton problem for source constraned schedulng n pharmaceutcal

3 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 3 of 16 producton. They proposed MILP that maxmzes expected net present value n a mult-perod problem. Sundaramoorthy and Karm [35] developed a MILP ncludng a flexble approach ncreasng demand meetng rato aganst changng producton plans n a pharmaceutcal supply chan that s the outset of contract manufacturng and new producton. Levs and Papageorgou [22] proposed a mathematcal model for long-term capacty plannng n a mult-ste pharmaceutcal ndustry under uncertanty. The model s an mproved verson of the model prevously proposed by Papageorgou et al. [29]. All problems are formulated wth two-stage MILP model. Then, they developed a herarchcal algorthm for solvng large-scale problems. The accuracy of ther proposed method was dsplayed by comparng wth several examples. Km [18] appled an ntegrated approach to the pharmaceutcal supply chan n the health sector. The am was to reduce holdng cost and to optmze nventory costs. For ths, VMI was appled to reduce total supply chan cost. Amaroa and Barbosa [2] developed a plannng and schedulng approach n the management of reverse flow supply chan appled n a pharmaceutcal company. In ther study where optmal producton plans were obtaned, the economcal proft of the model was analyzed separately n terms of supply chan operatons and customer satsfacton. Lakhdar and Papageorgou [19] submtted a mathematcal programmng approach for medum-term producton plannng under uncertanty n bopharmaceutcal manufacturng. Uncertanty n the study s related to wth the fermentaton concentraton rato. All problems were dscussed n the two-stage mult-scenaro plannng problem and an algorthm was proposed for the problems n larger sze. Vendtt [39] developed a heurstc algorthm for producton plannng n the pharmaceutcal ndustry. Babol et al. [3] studed pharmaceutcal supply chan management wth two separate approaches as centralzed and decentralzed usng mathematcal programmng. They reached to the concluson that the centralzed method reduced the cost much more. Sousaa et al. [34] calculated the dynamc resource allocaton problem n the pharmaceutcal ndustry wth the delvery costs and the dfferent tax rates to maxmze the net proft of the company. Susarla and Karm [37] taken nto account the sequencedependent pattern change, resource usng, mantenance schedules and securty stocks usng the mathematcal model wth consderng ntegrated plannng and resources n the pharmaceutcal producton faclty. Susarla and Karm [36] studed to optmze supply chan costs about ntegrated supply chan plannng more than one producton plant for pharmaceutcal producton actvtes. Kelle et al. [17] developed a soluton wth MILP for demand pont n a hosptal pharmaceutcal supply chan organzed medcaton requrements plan. Chen et al. [7] used a smulaton-based optmzaton technque whle ncreasng customer servce level and reducng supply chan costs of pharmaceutcal clncal trals and they planned producton and dstrbuton actvtes wth MILP. Kelle et al. [17] developed a strategc and tactcal level of decson support models n ther work related to pharmaceutcal supply chan and nventory solutons n a hosptal. Kabra et al. [14] planned mult-stage and mult-producton processes n the bopharmaceutcal producton as long-term by usng MILP. The studes about admnstratve subjects that made extended lterature survey n pharmaceutcal supply chan can be lsted as follows; Shah [32] determned the key ssues and optmzaton strateges for pharmaceutcal supply chan n the study to determne the pharmaceutcal supply chan and optmzaton strateges. In the study, by mentonng all pharmaceutcal processes, from raw materal producton untl delvered to the customer were explaned and made some suggestons about how to ncrease customer servce level. Besdes, Shah [32] analyzed all stages one by one ensurng added value to the pharmaceutcal supply chan and emphaszed the mportant matters. Yu et al. [40] conducted a study makng an evaluaton for current ssues and health system reform about pharmaceutcal supply chan n Chna. Jaberdoost et al. [13] studed revealng strategc rsks of supply chan management n pharmaceutcal ndustry and they mentoned dfferent studes about ths area. Narayana et al. [26] dscussed the exstng studes on the pharmaceutcal supply chan n ther study. They classfed the studes n lterature accordng to the countres, research methods, termnology and the level of analyss. They made evaluatons about the future of the studes from the admnstratve perspectve. In addton the studes about the mplementaton of VMI model n the pharmaceutcal ndustry are lmted. These are; Danese [8] dscussed the project of the mplementaton of VMI to the entre producton and dstrbuton facltes and expressed how to manage the entre supply chan wth VMI model from one sde, data networks establshed and data systems supportng them and the performances of them n detal. Ths VMI model as seen n the study was a model applcable to the entre pharmaceutcal ndustry. Shen et al. [33] tred to dentfy economc producton amount under mnmum volume constrants n the producton of pershable products such as pharmaceutcals that s mportant for publc health. They developed an approach conssts of a mathematcal model and VMI whch was more economc n n terms of total supply chan cost. Kannan et al. [15] proposed a model revealng the benefts of VMI n pharmaceutcal ndustry. Kannan [16] tred to dentfy the most approprate supply polcy to stochastc demand

4 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 4 of 16 envronment dependng on the tme wth VMI n pharmaceutcal ndustry. All these studes summarzed as seen n Table 1. In ths study, a new mathematcal model s developed to solve an nventory problem n the pharmaceutcal ndustry. The mathematcal model contans shelf lfe and product transton constrants together and the model s much more dealng wth real lfe constrants unlke the studes n lterature. Besdes, the model contans parameters about general supply chan parameters such as costs of producton, nventory holdng, transton, waste product and unmet demand penalty. There are a few artcles about VMI method n pharmaceutcal sector. The model appled to classcal supply chan method and VMI, so ths study s mplemented VMI method and handled a new technc n pharmaceutcal supply chan. Methods The problem and detaled mathematcal formulaton The studes n the lterature dscuss a smplfed model of producton occurs n real lfe. In models, they take nto account only materals and machnery as resources and mathematcal models try to solve the model by makng crtcal assumptons about the case such as transt or nstallaton tmes of materal transfers, human resources, waste storage and treatment capacty. These assumptons prevent to be applcable of the models establshed n practce. However, the studes should nclude more comprehensve models to completely adapt to real lfe. To make a decson by combnng entre supply chan under unque plan n real lfe s very dffcult n dynamc market and envronment condtons. Some problems n lterature (Shah [32], Yu et al. [40], Jaberdoost et al. [13], Narayana et al. [26]) are studed soluton suggestons by takng nto account the supply, producton and dstrbuton processes. However, smple and flexble models are ensurng rapd soluton and beng approprate for the real lfe are much needed. Although t s generally gnored n lterature, pharmaceutcal raw materal and end product have a defnte expry date and t cannot be used after the expry date. If there s a presence of raw materal and product nventory n warehouse, they are turned nto waste product and they wll reflect to the supply chan as waste cost. For ths reason, the raw materals and product expry condtons must be taken nto account. In ths study, a long-term plannng model s developed n order to obtan the producton plan that optmally fulflls a net proft objectve. Ths crteron presents the trade between sales returns and costs ssues. The man contrbuton of ths study s to solve an nventory problem n the pharmaceutcal ndustry by proposng a new mathematcal model that contans shelf lfe and product transton constrants together. We beleve that the proposed model s much more dealng wth real lfe constrants unlke the studes n lterature. Besdes, the model contans general supply chan parameters such as costs of producton, nventory holdng, transton, waste product and unmet demand penalty. A hybrd tme representaton s appled over a plannng horzon, n whch the months of the plannng horzon are modeled and each month s represented by a contnuous tme formulaton. The most effectve characterstc of the problem s that, nventory amounts depend on the shelf lfe of the products. Also, transton condtons are handled that occur whle swtchng from one product to another. In the mathematcal model, constrants about transtons are adopted from the models of Lu et al. [23]. However, beng dfferent from them n our model, nventory amounts changes dependng on the shelf lfe of the product. And so; all nventory formulatons are novel. The cost crteron subtracted from the total sales revenue n the objectve functon s novel n ths model. Nomenclature of the proposed mathematcal model s gven at the Appendx 1. There s a lttle lterature about VMI method n pharmaceutcal sector. So ths study s mplemented VMI method and handled a new technc n pharmaceutcal supply chan. As close as a real lfe problem, a hypothetcal problem s consdered n cephalosporn department of a pharmaceutcal factory. Our mathematcal model s appled n order to obtan the best producton plan whle maxmzng total net proft n long term. The effcency of the model s shown on classcal supply chan and VMI method. Table 1 Studes about optmzaton n pharmaceutcal ndustry The subject of the study Method Authors Plannng, schedulng and cost optmzaton n pharmaceutcal ndustry Classcal supply chan model Vendor managed nventory model Papageorgou et al. [29], Maravelas and Grossmann [24], Sundaramoorthy and Karm [35], Levs and Papageorgou [22], Shah [32], Lakhdar and Papageorgou [19], Amaroa and Barbosa [2], Vendtt [39] Yu et al. [40], Babol et al. [3], Sousaa et al. [34], Susarla and Karm [37], Susarla and Karm [36], Kelle et al. [17], Chen et al. [7], Kabra et al. [14], Jaberdoost et al. [13], Narayana et al. [26] Danese [8], Shen et al. [33], Kannan et al. [15], Kannan [16]

5 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 5 of 16 Objectve functon The total net proft s maxmzed to obtan from sales revenue mnus supply chan costs, nvolvng the total, producton cost, product transton costs, the unmet demand costs, nventory holdng cost, product transportaton cost and the cost of waste products. NP ¼ PS c S ct P t CP c t t j t Z jt j ZF jt j t T f1gcc CUD c c t UD ct CI SM t TC t c t S ct CW W t t CC j ð1þ Product assgnment constrants F t ¼ 1 t T ð2þ L t ¼ 1 t T ð3þ In each perod one product s assgned as frst or last product to be processed and these two equatons show whether they are the frst product or last product. F t E t I; t T ð4þ L t E t I; t T ð5þ When the relevant product s not produced n ths perod, t assumes as E t =0. Product transton constrants Z jt ¼ E jt F jt I ; j J t T ð6þ j Z jt ¼ E t L t I ; j J t T ð7þ j Whle Z jt bnary varables are representng the product transtons occurrng n a perod, ZF jt varable represents the product transton between two consecutve perods. If there s a product transton wthn a perod, they are the varables ndcatng that there wll be no product before the frst product produced and t s not the frst product, other products wll gve prorty to ths product. Smlarly, f there s a product transton wthn a perod, there wll not be any product producton after the last product produced and f t s not the last product, ths product wll be followed by the producton of other products. ZF jt ¼ F jt I ; j J t T f 1g ð8þ ZF jt ¼ L t 1 I ; j J t T f 1g ð9þ If there s a product transton between two consecutve perods and f the producton of a product begns n that perod for the frst tme, there wll certanly be a product transton a perod before the relevant perod. If a product s not the frst or the last one processed, then there s not a changeover nvolvng the product between two perods. Travellng salesman problem formulaton based subtour preventon constrants β jt β t þ 1 β t M E t M 1 Zjt I ; t T I ; j J ; t T; j ð10þ ð11þ β t varable can be called as demand ndex or producton row. The am of wrtng these constrants s to determne row of the product n a perod and to take the product transton cases under control. If th product s produced before j th product, producton sequence number of th product wll be at least one more than j th product. If that product has never been produced, demand ndex wll be zero. These constrants are smlar to the constrants preventng the sub-tours n classcal Travellng Salesman problem (TSP) [23]. In TSP problem bnary varables are used to represent transton one cty to another. As smlar n ths model to maxmze net proft there should be mnmum number of transton n producton sequence. And Z jt and ZF jt varables are added to model the product transton n a perod and between t-1 and t perods respectvely. F t β t j E jt I ; t T ð12þ Ths constrant enables the demand ndex to take at least the value of 1 and to take value up to the maxmum product number. Tmng constrants θ L E t O t θ U E t I ; t T ð13þ For each product produced n a perod, the hghest and lowest tme lmts are gven.

6 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 6 of 16 O t þ O t þ Z jt þ ZF jt TZjt θ U t T f1g Z jt TZ jt θ U t f1g ð14þ ð15þ The total of the producton n a perod and product transton tmes cannot exceed the exstng tme gven for the shft. Producton constrants P t ¼ rr O t I ; t T ð16þ The product amount produced n a perod s as much as the multplcaton of the producton rato and producton tme. Demand constrants UD ct ¼ RD ct S ct c C; I ; t T ð17þ The amount of the unmet demand from a product s as much as the dfference between the realzed demand wthn that perod and the product amount delvered to the customer (satsfed demand) wthn that perod. S ct RD ct c C; I ; t T ð18þ Sales amount may be lower than or equal to demand amount that was realzed; n ths model the unmet demands n a perod are not delvered to the customer n the next perod (no backlogs). Shelf lfe and nventory constrants SM t ¼ SM t 1 þ P t c SM t ¼ t 1 S ct f t < α I ; t T ð19þ tþ1 α SM t 1 þ P t f t α I ; t T ð20þ α s shelf lfe and depends on products characterstcs and t s defned as an nteger multple of t. Inventory quantty vares dependng on the product shelf lfe. If the relevant tme s lower than the product s shelf lfe, that s to say, f the product s termhas Table 2 Expermental set Experment No Supply chan method Plannng horzon (months) 1 Classcal supply chan Classcal supply chan Classcal supply chan Classcal supply chan VMI VMI VMI VMI not been expred yet, the nventory amount of that product s as much as the dfference of the sales amount wthn that perod n the total of the stock amount transferred from the prevous perod and the productamountproducednthatperod. W t ¼ t α SM t ; f t α I ; t T ð21þ t¼1 Product amounts But f the relevant tme s longer than the product s shelf lfe, the products whose term s expred wll be waste product. W t ¼ 0 ; f t < α ð22þ Numercal nvestgaton Around the proposed mathematcal model, our man research focus s addressed n numercal nvestgaton and the followng questons are answered: Does ths mathematcal model provde reasonable results for a long term plannng horzon? Does the proposed mathematcal model offer cost advantages? How does the proposed model run for dfferent demand profles and dfferent numbers of products? Does ths mathematcal model run for dfferent knd of supply chan methods? Whch supply chan method s more proftable wth ths mathematcal model? When compared other studes n lterature, does ths model provde advantage? Fg. 1 Factory s transportaton system and warehouses

7 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 7 of 16 To answer these questons, an expermental study s consdered based on numercal experments and comparsons. Expermental set s summarzed n Table 2. To llustrate the applcablty of our mathematcal model, we consder a hypothetcal pharmaceutcal plant. In ths case, long term producton schedulng problem n the pharmaceutcal secondary producton s dscussed. In the cephalosporn department of ths factory, njectable beta-lactam products are manufactured. In a separate faclty that s completely ndependent from non-beta - lactam producton felds, mcro powder refllng s conducted n aseptc condtons and the producton condtons are provded to be montored contnuously va computer aded producton systems. In our study, t s amed to satsfy the customer demands for 15 dfferent products produced n cephalosporn department of the factory n 24 and 30 months perod to fnd optmal producton plan maxmzng the total net proft and to show n whch type of supply chan (classcal or vendor managed). We hypotheszed that; the pharmaceutcal factory has agreements wth 5 pharmaceutcal warehouses. In Fg. 1 factory s transportaton system and warehouses scheme s gven. The factory delvers the products to pharmaceutcal stores and pharmaceutcal stores delver them to the pharmaces. Before the expry, all the products that are not delvered to the consumer return to the factory and ts dsposal s carred out by the factory. In ths way, t s seen that the producton, delvery and waste product costs (dsposal cost) belongng to the products whose Table 3 Cephalosporn products No Actve raw materal 1 Ceftraxone 1 g IM/IV 2 Cefotaxme 1 g IM/IV 3 Ceftzoxme 0,5 g IM/IV 4 Cefsulodn 1 g IM/IV 5 Cefoperazone 1 g IM/IV 6 Ceftazdme 0,5 g IM/IV 7 Moxalactam 1 g IM/IV 8 Cefuroxme 0,5 g IM/IV 9 Cephalothn 0,5 g IM/IV 10 Cephapyrne 1 g IM/IV 11 Cefdnr 0,5 g IM/IV 12 Cefprozl 1 g IM/IV 13 Ceftbuten 0,5 g IM/IV 14 Cefpodoxm Proxetl 0,5 g IM/IV 15 Cefaclor Monohydrate 1 g IM/IV term s expred and that wll be returned beng sold, creates serous cost damages to the factory and a mathematcal model s developed to mnmze these costs and the model s compared by beng appled n two separate types of supply chan. In ths study, product name s not specfed and 15 dfferent products are named accordng to the actve raw materals. These are shown n Table 3. A work flow chart belongng to cephalosporn producton ste s seen above n the Fg. 2. As shown here, the Fg. 2 Cephalosporn producton area work flow chart

8 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 8 of 16 producton s performed on a unque lne. Fllng machne s solated from the producton envronment and n a sterle manner. The actve materal s loaded nto the fllng machne; these raw materals are agan flled n pharmaceutcal bottles n a sterlzed way; the bottles flled are checked, labeled and boxed. The producton and the expry date determnng the shelf lfe of the product are prnted on the label and box when the product s on the lne durng relevant transtons. Key model parameters Demand types Demand forecast was made whle makng producton plan for the next two years. Forecasted demand and sales amounts were obtaned from the real old data belongng to a real pharmaceutcal company. The average of sales amounts (29000) can be seen to conform to normal dstrbuton havng standard devaton (10500). Snce normal probablty dstrbuton a wdely known type, n many studes related to nventory management n supply chan that demand structure s n accordance wth normal dstrbuton (Lau et al. [20]). FD t ¼ normal ð29000; 10500Þ ð23þ Equaton 23 gves the dstrbuton of forecasted demand amounts. In current and proposed stuaton, the average of customer demands s and t s assumed to comply wth the normal dstrbuton, the standard devaton of whch s The equaton 24, gves the dstrbuton of customer demands performed. Table 5 Unt product transportaton costs to warehouses Pharmaceutcal warehouses Transportaton costs for unt product A 0,005 B 0,02 C 0,017 D 0,015 E 0,045 RD t ¼ normal ð27500; 19000Þ ð24þ Producton capacty In lterature there are studes n accordance wth unform dstrbuted producton capactes [5, 38]. The am of the manufacturers s always to satsfy the demand completely. Maxmum producton capactes are lmted, but ths capacty vares accordng to the events to occur durng the processes (malfuncton or perodc mantenances, or even stops). The factory works 12 h a day. Total avalable processng tme n a month s 264 h. Producton capacty s up to maxmum 4500 boxes of product/hour. But ths capacty vary n real lfe because of deteroratons or stops n producton lnes. When t s statstcally analyzed, the capacty of cephalosporn department producton lne s unformly dstrbuted n the range of (0, 4500). Shelf lfe condtons The shelf lfe of each product s fxed and t s 12 months. The products whose terms are expred cannot sold wthn ths tme perod, t s assumed as waste products Table 4 Unt costs and sales prce data of products Product no Sales prce ($) Producton cost ($) Unmet demand cost ($) Transton cost ($) Product 1 7 1,2 0,2 TZj *10 Product 2 7 1,2 0,25 TZj *10 Product 3 7 1,16 0,18 TZj *10 Product 4 7 1,16 0,25 TZj *10 Product 5 7 1,2 0,2 TZj *10 Product 6 7 1,1 0,15 TZj *10 Product ,15 TZj *10 Product ,25 0,2 TZj *10 Product ,2 0,18 TZj *10 Product ,2 0,22 TZj *10 Product ,16 0,25 TZj *10 Product ,2 0,22 TZj *10 Product ,16 0,25 TZj *10 Product ,16 0,15 TZj *10 Product ,2 0,22 TZj *10 Table 6 The transton tme (hour) from to j \j

9 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 9 of 16 Fg. 3 Pharmaceutcal supply chan processes and the costs belongng to ths reflect as waste product cost (e $/unt). Product transton condtons Transton cost s proportonal to transton tmes by a factor of 10. Unt nventory holdng cost data are the values such as $/unt dentfed by the company for a package of product, unt sales prce and rest of the other costs are gven n Table 4. Product transportaton costs are vares to warehouses and gven n Table 5. The transton tmes from one product to another (cleanng and mold change) are varable and they are stated n Table 6 below. Results Detals of experments In ths part of study, some of the expermental results are gven for comparson. Frstly Experment Number 1 and 5 s detals are gven and compared. In Experment 1; factory has a classcal supply chan model and produced products transfer due to the orders from pharmaceutcal stores and delver to the end user from there. The products whch are expred before sold from the factory to the pharmaceutcal store are sent to dsposal faclty. Besdes, the products whch s expred n the pharmaceutcal store before sold to pharmacy, are sent to the producer company by the pharmaceutcal stores and when these products are reached to the producer company, t s taken to reject store and t s delvered to the company for dsposal facltes. Durng ths returnng process, all costs (transport + dsposal costs) are subject to the company. A scheme of pharmaceutcal supply chan processes can be seen n Fg. 3. The above example s modeled usng GAMS/CPLE 12 for the MILP optmzaton. When the model s run, maxmzed total net proft s $ for 24 months wth 10 products. The graphs ncludng demand amounts, producton amounts, stock amounts and unmet demand amounts belongngtothemodelaregvennfollowngfg.4. Producton schedule s gven n Fg. 5. Ths fgure shows how the transton tmes affects to the producton sequence. It s hard to show all plannng horzon (24 months) schedulng, so we llustrate for a part of two months plannng tme. In Experment 5, the nventory s vendor-managed. Accordng to the agreement, pharmaceutcal factory can see the nventory and sales nformaton n the pharmaceutcal stores onlne wth the establshed nformaton system. At the begnnng, a producton plan s created accordng to estmated demand amounts and wth the Fg. 4 The graph of producton, demand and the unsatsfed demand for Experment 1

10 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 10 of 16 Fg. 5 Producton schedule for Experment 1 nformaton obtaned from pharmaceutcal store, producton plans are updated and wthn the framework of these plans, delvery plans wll be made and the product wll be delvered. The amounts and tme nformaton wll be communcated wth the store. For each product, the level of safety stocks n the store s determned and the stocks wll be controlled contnuously n order not to fall under safety stock levels n the store. Safety stock levels are gven n Table 7. Equaton 16 n Exp. 1 turns nto the equaton 25 n Exp.5. P t ¼ FD ct þ SS İ SM t 1 I ; t T ð25þ S ct ¼ P t c C; I ; t T ð26þ In Experment 5, each product s sold to pharmaceutcal stores accordng to the agreement. For ths reason, n addton to the equaton 18 created for sales amounts, the equaton 26 above should be added. Accordng to Table 7 Safety stock levels Product Product actve tem Safety stock amount Product 1 Ceftraxone 1 g IM/IV 1000 Product 2 Cefotaxme 1 g IM/IV 2250 Product 3 Ceftzoxme 0.5 g IM/IV 350 Product 4 Cefsulodn 1 g IM/IV 500 Product 5 Cefoperazone 1 g IM/IV 175 Product 6 Ceftazdme 0.5 g IM/IV 1250 Product 7 Moxalactam 1 g IM/IV 350 Product 8 Cefuroxme 0.5 g IM/IV 175 Product 9 Cephalothn 0.5 g IM/IV 1450 Product 10 Cephapyrne 1 g IM/IV 1250 Product 11 Cefdnr 0,5 g IM/IV 250 Product 12 Cefprozl 1 g IM/IV 1000 Product 13 Ceftbuten 0,5 g IM/IV 750 Product 14 Cefpodoxm Proxetl 0,5 g IM/IV 700 Product 15 Cefaclor Monohydrate 1 g IM/IV 350 producton plans, the products produced n the factory are drectly sent to the pharmaceutcal store. That s to say, sales amount s equal to the producton amount. Then, the producton plans are revsed from month to month n the factory n accordance wth the demands. Here, the am s to prevent shortages and waste product costs and makng the supply chan more proftable. When the model s run, the maxmzed total net proft s $ for 24 months wth 10 products. The graphs ncludng demand amounts, producton amounts, stock amounts and unmet demand belongng to the Experment 5 are gven n Fg. 6. The result of comparson for these two experments s as follows n Table 8. The mathematcal model created to reveal the best producton plan whle mnmzng supply chan costs and maxmzng the total net proft. The model compared wth two experments. For the both stuatons, the common data and data dstrbutons are used. Two dfferent optmum results are obtaned accordng to supply chan types. When these results are compared, sales revenue n Experment 1 s less than n Experment 5. The sales revenue dfference between them s so much. Transton costs are also seen as more advantageous n Experment 5. The unmet demand amounts are less n Experment 5 and accordngly, ts cost s lower. Producton and transportaton costs n Experment 1 s less than Experment 5. Ths s because the sales amounts are less than Experment 5. Consderng waste product costs, n Experment 1, 1.72 % of the producton s waste product and n Experment 5, ths rate s 0.03 %. So we can say, VMI s more advantageous n terms of waste product cost and wastage amounts. Because, the producton plans advance n more controlled way n Experment 5. A comparson of these experments expred product amounts can be seen n Fg. 7. When total net proft s compared, VMI s more proftable as much as % than Classcal Supply Chan. Fnally, when two experments are compared, VMI s much better n all costs except for producton and transportaton costs.

11 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 11 of 16 Fg. 6 The graph of producton, demand and the unmet demand amounts for Experment 5 The model s run for all expermental set and the total net proft for all the experments are gven below n Table 9. As seen n Table 8, VMI Method s more proftable (nearly 8,8 %) than Classcal Supply Chan method. Producton plannng s a crucal ssue n pharmaceutcal supplychanntermsofmeetng customer demands just n tme. Because pharmaceutcals are pershable products, the shelf lfe constrants have to be consdered whle plannng, schedulng and all supply chan actvtes are organzed. Accordng to our lmted knowledge, some pharmaceutcal companes do not take nto account the shelf lfe constrants durng ther plannng processes. It s assumed that all produced tems wll be sold after reasonable watng tme n the nventory. In realty, n some cases, there can be long watng tme of products. So ther pershng day of products can be very close to shelf lfe because of long watng tme. Although the long wated products are stll consdered as nventory products from the planner, they must be consdered wasted nstead of nventory product. In ths study we consder shelf lfe constrants and product transton constrants together. In terms of the Table 8 Comparson of soluton results for experment 1 and 5 for 24 months wth 10 products Exp. 1 Exp. 5 Revenue ($) Sales revenue Costs ($) Producton cost Transton cost Unmet demand cost Inventory holdng cost Product transportaton cost Dsposal cost Total net proft ($) practcal mplcatons of ths work n real pharmaceutcal companes; the proposed model can be adapted to producton plannng actvtes n the pharmaceutcal supply chan. Because; the model produces real tme nventory nformaton through the shelf lfe constrants and deals wth long wated (waste) and nventory products whle the plannng s done. Ths stuaton has a great opportunty to cope wth wastage costs. The model balances the nventory levels, demands and lost sales. And also real tme nventory nformaton provdes to reduce rsks about market demands and effcent producton schedulng actvtes. Ths helps to reduce all supply chan costs and the model offers a collaboratve, plannng and schedulng system to pharmaceutcal companes whle managng shelf lfe of products. Dscusson Comparson wth another model In ths part of study, the effcency of our model s compared wth Chen et al. [6] model. To make a comparson, the Chen et al. [6] mathematcal model s modfed. Modfed and orgnal model are gven n Appendx 2 and Appendx 3 respectvely. The objectve functon of proposed model conssts of producton cost, product delvery cost and wastage cost and t s wrtten as follow: NP ¼ PS c S ct P t c t t CP CC j Z jt CUD c j t c t UD ct CI SM t TC c t c t S ct CW W t t There s no storage capacty lmt, so the (C12.) constrant s removed from the model. In addton, backlogs are not allowed, therefore we remove the constrant (C14) from the model. But we

12 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 12 of 16 Fg. 7 Expred product amounts for Experment 1 and 5 have to calculate unmet demand amount so a new constrant s added as gven below: UD ct ¼ RD ct S ct The stock amounts s wrtten wth consderng shelf lfe condtons, the constrant (C13) as follow: SM t ¼ SM t 1 þ P t c SM t ¼ t 1 S ct f t < α I ; t T tþ1 α SM t 1 þ P t f t α I ; t T Wastage cost s added to the model; W t ¼ t α SM t ; f t α I ; t T t¼1 W t ¼ 0 ; f t < α The model s run under 24 and 30 months producton perod, the CPU tmes were 856 and 4150 respectvely. The detals of comparson of these models are gven n Table 10. Table 9 Soluton results for all expermental set Experment no Supply chan method 1 Classcal supply chan 2 Classcal supply chan 3 Classcal supply chan 4 Classcal supply chan Plannng horzon (months) Product amounts Total net proft ($) VMI VMI VMI VMI Models were run for 24 and 30 months under classcal supply chan. Sales revenues and nventory holdng costs are more proftable n our model. And the total net profts are n average %0,8 much more n our model. Concluson In ths study, a new mathematcal model was developed to solve nventory problem and maxmzng total net proft whle determnng optmal producton plan under shelf lfe and product transton constrants n the pharmaceutcal ndustry. The proposed MILP model contans shelf lfe and product transton tmes constrants together and we beleve that the proposed model has much more real lfe constrants unlke the other studes n lterature. Besdes, the model contans parameters such as costs of producton, nventory holdng, transton, transport, waste product and unmet demand penalty. As we defned at lterature revew secton of ths study; VMI method s not often used n the lterature of the pharmaceutcal sector. So ths study mplemented VMI method and handled a new technc for the pharmaceutcal supply chan. To show the effectveness of the model, an expermental study; whch contans 2 dfferent supply chan polcy (Classcal and VMI), 24 and 30 months plannng horzon, 10 and 15 dfferent cephalosporn products were chosen. The results llustrated that the VMI provded much better results n terms of total supply chan costs. Especally; the waste amount that was very mportant n pharmaceutcal sector and the cost was reduced n the VMI. The waste product amounts were 1.72 and 0.03 % of the products n experment 1 and experment 5 respectvely. In terms of total supply chan costs, % of an advantage was ganed by the proposed VMI model. As a result, we beleve that the proposed model should be adapted n the pharmaceutcal ndustry to reduce total supply chan cost. In addton that, the proposed model s compared wth a recently publshed study n lterature. And so the results are llustrated that the proposed model s better than the other.

13 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 13 of 16 Table 10 Comparson results for 24 months and 30 months 24 moths 30 moths Chen et.al. The proposed Chen et.al. The proposed Revenue ($) Sales revenue Costs ($) Producton cost Transton cost Unmet demand cost Inventory holdng cost 30056, Product transportaton cost Dsposal cost Total net proft ($) Appendx 1 Nomenclature Indces,j, products c, customers t, perod Sets I, J, product set C, customer set T, perods set Parameters CP, unt producton cost of product CUD c, unt unmet demand penalty cost of product to customer c CC j, product transton from product to product j. (change and cleanng cost on the lne whle passng from product to product j) CI, unt nventory holdng cost of product CW, unt waste product cost of product TC c, unt product delvery cost of product to customer c FD ct, forecasted demand of customer c, from th product, at perod t RD ct, the demand amount realzed by customer c, from th product, at perod t M, large number PS c, unt sellng prce product to customer c α, shelf lfe Ө L, the lowest producton rate n a perod Ө U, the hghest producton rate n a perod TZ,j, cleanng and mold changng tme whle passng from product to j product β t, demand ndex rr, producton rate Varables E t = 1, 0, product produced n t perod? F t = 1, 0, product the frst product n t perod? L t = 1, 0, product the last product n perod t? Z jt = 1, 0, product produced before product j? ZF jt =1,0 f there s any product transton between t-1 and t perod? P t, the producton amount from product n perod t S ct, sales amount from product to customer c n perod t O t, processng tme for product n perod t SM t, nventory amount of product n perod t SS, securty stock amount of product UD ct, unmet demand amount from product to customer c n perod t W t, waste product amount product n perod t NP, total net proft Appendx 2 Modfed Chen et. al. model NP ¼ PS c S ct P t CP c t t j t Z jt CUD c UD ct CI SM t c t t TC c S ct CW W t c t t y t ¼ 1 0 O t θ U y t O t θ L y t O t þ j Z jt ¼ y t 1 j Z jt ¼ y jt! TZ j Z jt θ U t 1 t 1 CC j

14 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 14 of 16 Z jtþ1 ¼ y t j Z jtþ1 ¼ y tþ1 P t ¼ rr O t SM t ¼ SM t 1 þ P t c UD ct ¼ RD ct S ct S ct RD ct SM t ¼ t 1 S ct f t < α I ; t T tþ1 α SM t 1 þ P t f t α I ; t T W t ¼ t α SM t ; f t α I ; t T t¼1 W t ¼ 0 ; f t < α Appendx 3 The proposed model by Chen et. Al. Nomenclature Indces c, customers,j, products k, tme slots w, weeks Sets C, customers I,J, products Kw, tme slots n week w W, weeks Parameters CBc, backlog cost of product to customer c CIw, nventory cost of product n week w CTj, transton cost of product to product j Dcw, demand of product from customer c n week w PSc, prce of product to customer c r, processng rate of product Vmax, maxmum storage of product Vmn, mnmum storage of product ӨL, lower bound for processng tme ӨU, upper bound for processng tme τj, changeover tme from product to product j Varables Pro, operatng proft Pw, producton of product n week w Scw, sales of product to customer c n week w Tkw, end tme of slot k n week w Vw, volume of product n week w Δcw, backlog of product for customer c n week w θkw, processng tme of product n slot durng week w Bnary varables Ew, 1 f product s produced n week w, 0 otherwse ykw, 1 f product s produced n tme slot k durng week w, 0 otherwse Zjkw, 1 f product (slot k-1) preceds product j (slot k) n week w, 0 otherwse Mathematcal formulaton Objectve functon Pro ¼ " ðps c S cw CB c Δ cw Þ w c!# CT j Z jkw þ CI w V w j k ðc1þ Assgnment constrants y kw ¼ 1 w W ðc2þ Tmng constrants T 0w ¼ 0 w W ðc3þ 0 θ kw θ U y kw I k K w W ðc4þ θ kw θ L E w I k K w W ðc5þ k T kw T k 1 w ¼ θ kw þ τ j Z jkw! k K w W ðc6þ Transton constrants Z jkw ¼ y k 1w I k K f1g w W ðc7þ j Z jkw ¼ y jkw j J k K f1g w W ðc8þ j Z j1wþ1 ¼ y jkw I w W ðc9þ j

15 Candan and Yazgan DARU Journal of Pharmaceutcal Scences (2016) 24:4 Page 15 of 16 Z j1wþ1 ¼ y j1wþ1 j J w W ðc10þ Process and storage capacty constrants P w ¼ r k θ kw I w W ðc11þ V mn V w V max I w W ðc12þ V w ¼ V wþ1 þ P w c S cw Δ cw ¼ Δ cw 1 þ D cw S cw c C I w W ðc13þ ðc14þ Degeneracy preventon constrants y kw E w þ ðk w 1Þ y Kw I w W ðc15þ k E w y Kw I w W ðc16þ Z jkw þ Z jkw 2 ykw I w W j k Competng nterests The authors declare that they have no competng nterests. ðc17þ Authors contrbutons GC; revewed the lteratüre secton and developed the mathematcal model and performed experments and researched about pharmaceutcal ndustry and draft the manuscrpt. HRY; studed about supply chan types. (VMI and Classcal) and partcpated n manuscrpts desgn and coordnaton. Both authors read and approved the fnal manuscrpt. Acknowledgements Authors thank to DARU journals edtors and revewers. Receved: 2 December 2015 Accepted: 17 February 2016 References 1. Alle A, Pnto JM. 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