Bi-Objective Optimization for the Clinical Trial Supply Chain Management

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1 Ian David Lockhart Bogle and Michael Fairweather (Editor), Proceeding of the 22nd European Sympoium on Computer Aided Proce Engineering, June 2012, London Elevier B.V. All right reerved. Bi-Objective Optimization for the Clinical Trial Supply Chain Management Ye Chen, Joé Miguel Laínez, Joeph F. Pekny, Gintara V. Reklaiti * Purdue Univerity, Wet Lafayette, IN 47907, USA, reklaiti@purdue.edu Abtract In the pharmaceutical indutry, clinical trial contitute a critically important and very expenive part of the new drug development proce. A clinical trial upply chain will terminate after 1-2 year, and leftover at the end of clinical trial contitute an important financial cot ince all the unued material hould be dipoed after clinical trial completion. Normally, extra afety tock are kept in the upply chain ytem to increae the cutomer ervice level (CSL), however more leftover are introduced by increaing afety tock. By conidering a bi-objective optimization uing a weightedum approach, we build an approximation to the CSL v. leftover Pareto frontier. Thi will upport the evaluation of the trade-off between thee two performance metric and thu the election of a afety tock level that optimally balance CSL and leftover. The entire framework include four module: demand forecating, an integrated planning and optimization formulation, a dicrete event imulation model and an outer loop optimization proce. An indutrially motivated cae tudy i preented to demontrate the utility of thi propoed approach. Keyword: Clinical Trial, Supply Chain, Safety Stock, Bi-Objective Optimization 1. Introduction Clinical trial contitute a critically important and very expenive part of the new drug development proce due to their high failure rate and extended duration. It ha become more and more critical to have an optimized clinical trial management proce to accelerate the new drug development proce and reduce the total cot for a pharmaceutical company. A number of different approache are being purued to reduce clinical trial cot, including innovation in trial organization, randomization methodology election, and upply trategy election, a decribed in Peteron et al. (2004) work. However, thee approache do not contitute an actual optimization trategy ince their outcome are not ued to modify the prior trategie. Abdelkafi et al (2009) work i the tart point of applying optimization technique in the clinical trial upply chain management area: it trie to elect the bet upply plan by attempting to balance the cot and the rik of hort upply. However, it only focue on the drug upply part of clinical trial without conidering the production part. The entire clinical trial upply chain management problem i compoed of a et of interrelated planning and cheduling deciion which eek to better ynchronize all activitie, tranaction, operation and organization involved in the clinical proce. The key challenge of thi problem are to fully atify the need of clinical ite, avoid overupply and reduce leftover. Normally, afety tock i kept in the upply chain ytem a a hedge againt the tochatic demand and thu to increae CSL. For a clinical trial upply chain, leftover product remaining on hand at the end of the trial, contitute an important financial cot which increae with higher afety tock.

2 2 Y. Chen et. al Leftover mut be conidered a watage ince uch drug product cannot be rehipped to other clinical ite or reued, according to FDA regulation. Chen et al. (2010) propoed a imulation-bae optimization approach to deal with clinical trial upply chain management and thi paper preent an extenion of that work. Specifically, baed on the imulation-optimization computational framework, a biobjective baed weighted-um approach (Freita, 2004) i ued to build an approximation for the CSL v afety tock Pareto-frontier. Thi will allow the pharmaceutical company to elect the afety tock level which optimally balance the CSL and leftover performance. 2. Propoed Approach 2.1. Simulation-Optimization Computational Framework The computational framework propoed for thi work conit of tochatic demand forecating, determinitic planning and optimization, a dicrete event imulation of the entire upply chain, and an outer loop earching proce to optimize the afety tock level baed on bi-objective: CSL and leftover, a depicted in Figure 1. Figure 1 Simulation-optimization computational framework Stochatic demand forecating occur via a imulation model which repreent the patient enrolment proce at the clinical ite and erve to determine the number of drug package needed at the clinical ite. The forecated demand cenario can be generated baed on thee demand value. Given demand cenario and preet afety tock level, the planning and optimization part i executed to determine the manufacturing and hipping plan. Thi i accomplihed by olving an MILP formulation uing GAMS 23.2-CPLEX The reulting plan erve a the driver for the imulation model of the entire upply chain, which i built in the dicrete event imulation oftware ExtendSim 7, and which capture all activitie, operation and procee involved in thi clinical trial. The planning and imulation part are executed in the rolling horizon mode for each timeline and include ampling from the ditribution of the uncertainty parameter of the ytem. To capture the uncertaintie and effectively ae the performance of the entire upply chain, here repreented by the CSL and leftover, multiple optimization-imulation timeline are implemented by repeatedly ampling the uncertain parameter in the claical Monte Carlo mode. Baed on a erie of replication, an outer loop earch algorithm i ued to optimize the biobjective performance function by iterating on the afety tock level until convergence i achieved Planning and Optimization Traditionally, multi-purpoe batch plant are widely ued in the pharmaceutical indutry. Since thee batch facilitie are uually hared acro variou product, it i neceary to decide the order, amount and timing of the product to be produced on

3 Bi-objective Optimization for the Clinical Trial Supply Chain Management 3 thee hared production reource. A dicrete time MILP formulation method (Papageorgaki & Reklaiti, 1990) i ued to formulate the planning model, in which both production and ditribution procee are treated a one tak i, conducted on equipment j. Each tak operate in batch campaign mode. A ditribution campaign i repreented a a ingle batch without etup time but with a variable batch ize. Since the batch proceing time i a characteritic of the equipment ued, it value i treated a a given parameter Objective The objective of thi model i to minimize the total operation cot, including the fixed etup cot aociated with tarting a campaign, variable proceing cot, holding cot, watage cot for expired product and leftover, penalty cot for unatified afety tock level, and penalty cot for mied demand in clinical ite. d Min TotalCot Cijf X ijft C jff ' XD jff ' t i j f t jjdc f f ' t Setup cot p dp Cijf Pijft C jff ' PEjff ' te ii p jj p f t jjdc f f ' ii p t e Variable cot h w d C f S ft C f Eft S fh C penalty ( Dft SDft ) C penalty ( SS f Sft ) f t f t f t Inventory holding cot Watage and leftover Penalty cot Contraint Several contraint are included in thi MILP planning model to decribe the entire upply chain tructure. The model comprie different et of contraint related to the campaign-batch mode, ma balance, atified demand, helf life/expired material contraint, and inventory capacity. The entire MILP model i olved to generate the production campaign and ditribution plan, which erve a the driver for the imulation model which in turn i executed to evaluate the performance of entire upply chain Bi-objective Optimization in the Outer Loop One advantage of thi propoed imulation-optimization framework i that it can determine the optimal amount of afety tock level with repect to the bi-objective performance function uing an outer loop direct earch optimization method. The objective function for thi problem can be mathematically decribed in Eq. (1). MIN J ( SS) [ CSL LTR ] CSL = f t 1 2 atified _ demand ( f, t) Total _ Demand Tar CSL CSL CSL LTR = Leftover Total _ Demand Here CSL i the etimated CSL of material from current imulation, CSL Tar i the target CSL of material, and ΔCSL i the deviation of current CLS from the target CSL. LTR i the normalized leftover ratio, leftover of material divided by it total demand. ω 1 and ω 2 are the weight for the two objective. The combined objective i to minimize the weighted um of the deviation of target CSL and leftover ratio. (1)

4 4 Y. Chen et. al With preet ω 1 and ω 2 value and afety tock etting, the planning and imulation part work together to evaluate the performance for the entire upply chain: CSL and leftover ratio (LTR), which are ued to update the current afety tock level etting, hown in Eq. (2). The entire earching proce i driven by the weighted um of the deviation of target CSL and normalized LTR until the final optimization objective ( J(SS) n - J(SS) n-1 < ε 1 ) or afety tock level ( SS n - SS n-1 < Θ 2 ) converge. The final obtained afety tock level are optimal for that et of weighting factor, n1 n n n 1 2 ( CSL - LTR ) where n n1 n n n1 J( SS ) J ( SS) The afety tock level obtained for different ω 1 and ω 2 parameter value, erve to define an approximation for the CSL v. LTR Pareto frontier. The frontier erve to upport corporate trategic deciion regarding the appropriate balance between financial cot and cutomer ervice level. 3. Cae Study and Reult The utility of the propoed imulation-optimization approach and it bi-objective optimization proce i demontrated by mean of a cae tudy. The cae problem i drawn from Chen et al. (2010): the aociated clinical trial upply chain network i hown in Figure 2. Safety tock are kept in the US ditribution center and European intermediate ditribution center and optimized in the outer loop. Three cae tudie with different ω 1 and ω 2 value are invetigated to obtain the final converged afety tock and ued to contruct the CSL v LTR Pareto frontier. Figure 3 how the outer loop optimization proce for the afety tock in the EU ditribution center and the optimization objective, in which ω 1 =1 and ω 2 =0. We can note that after 8 iteration, the optimization objective tart to converge and the earch proce i terminated after 18 iteration. For different ω 1 and ω 2 etting, different converged afety tock level are obtained with correponding CSL and LTR value. Figure 4 how three point obtained from cae tudie for EU Drug 1: point A i obtained with ω 1 =0 and ω 2 =1, and the aociated converged afety tock i 0 package; point B i obtained with ω 1 =0.8 and ω 2 =0.2, and the aociated converged afety tock i 170 package; point C i obtained with ω 1 =1 and ω 2 =0, and afety tock i 913 package. The et of uch olution point can be ued to contruct the CSL v LTR Pareto frontier, which allow the pharmaceutical company to chooe an appropriate afety tock value on the bai of other trategic conideration. 4. Concluion The propoed multi-level imulation-baed optimization approach effectively allow treatment of the clinical trial upply chain planning problem. However, the approach i quite computationally intenive ince each iteration require around replication to converge and around 10 hour to finih. Thi i becaue each cycle through the outer optimization loop, require evaluation of the tochatic bi-objective function which in turn require ignificant number of replicate of the Monte Carlo imulation and imbedded planning problem olution. There are a number of way to reduce the computational burden, uch a through parallelization of the Monte Carlo timeline. Moreover, the ue of thi framework doe allow acce to more detailed level information about the conduct of the trail. For intance, the progreion of each patient (2)

5 Bi-objective Optimization for the Clinical Trial Supply Chain Management 5 can be tracked during the coure of the adminitration protocol. Conequently if a patient treatment i mied becaue there are not enough drug on hand when the patient arrive at the clinical ite to receive the drug package for the next week thi occurrence can be recorded. Such an occurrence not only invalidate that patient a a contribution to the clinical trial but a a reult the drug package previouly adminitered to thi patient are wated. Thi amount can be recorded and thu, the cot of underupply can be quantified in term of ineffectively ued drug package. While failure to upply the patient when needed alo reult in other cot, the reduction of under and overupply to a ingle metric of wated drug package ha attractive feature. Additional beneficial tudie baed on the ue of uch tracked patient information can be obtained from the imulation model. For intance one could examine progreively increaing incentive trategie which would encourage patient to perit in the treatment protocol. Figure 2 Clinical trial upply chain network Figure 3 Outer loop optimization proce Figure 4 CSL v LTR Reference 1. Peteron, M., B. Byrom, N. Dowlman, and D. McEntegart, 2004, Optimizing Clinical Trial Supply Requirement: Simulation of Computer-controlled Supply Chain Management, Clinical Trial, 1(4), Abdelkafi, C., B. Beck, B. David, C. Druck, and M. Horoho, 2009, Balancing Rik and Cot to Optimize the Clinical Supply Chain A Step Beyond Simulation, Journal of Pharmaceutical Innovation, 4(3), Freita, A. A., 2004, A Critical Review of Multi-objective Optimization in Data Mining: a Poition Paper, SIGKDD Exploration, 6(2), Papageorgaki, S., and G. V. Reklaiti, 1990, Indutrial & Engineering Chemitry Reearch, 29(10), Y. Chen, L. Mocku, S. Orcun, G. V. Reklaiti, 2010, Simulation-baed Optimization Approach to Clinical Trial Supply Chain Management, Proceeding of the 20th European Sympoium on Computer Aided Proce Engineering (ESCAPE20), v28, 14