Online Appendix to: Implementing Supply Routing Optimization in a Make-To-Order Manufacturing Network

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1 Online Appendix o: Implemening Supply Rouing Opimizaion in a Make-To-Order Manufacuring Nework A.1. Forecas Accuracy Sudy. July 29, 2008 Assuming a single locaion and par for now, his sudy can be described by defining d ashedemandforhaparacuallyobservedinhalocaiononday, andf +δ as he corresponding demand forecas available a he beginning of day for day + δ, soha f 0 = d for 0 <. Because of he invenory balance equaion saed in Secion 4.1 of he paper, we were primarily ineresed in he cumulaive forecas error ε +δ d,+δ, P +δ k= d k (sum of demand observed from day o day + δ) and f +δ, d +δ,+δ f wih, P +δ k= f k (forecas of he same quaniy available a he beginning of day ). We firs colleced a large number of acual observaions of he cumulaive forecas error ε +δ for all par ypes, all locaions {Ausin, Nashville, Reno, Winson-Salem} and all values of δ lower han he lengh T of he relevan planning horizon for supply rouing decisions (abou 4 weeks). Considering observaions corresponding o disjoin ses of days (i.e. { ε kδ+δ kδ,k N}) inorder o avoid correlaion biases due o ime period overlaps, we hen consruced and sudied he associaed empirical disribuions of ε +δ. This sudy led o he following observaions: 1. These empirical disribuions were well fied by he normal disribuion, which is unsurprising in ligh of he cenral limi heorem given he definiion of ε +δ. In order o esablish his, we performed χ 2 and Kolmogorov-Smirnov goodness of fi essforhe hypoheses ha he empirical daa for he cumulaive forecasing error ε +δ had been generaed by normal, uniform and gamma disribuions, respecively. The ypical resuls of hese ess were ha he hypohesis of normaliy was acceped by boh ess for all bu he smalles values of he forecas horizon δ, whereas he hypoheses ha he daa had been generaed by eiher he uniform or he gamma disribuion were rejeced. To 1

2 illusrae his fi, Figure A.1 provides a plo of he cumulaive disribuion funcions of he empirical daa and he normal disribuion for a paricular par (a 17 inch fla panel) and locaion (Nashville), and δ =5days; Figure A.1: Empirical Cumulaive Disribuion of he Cumulaive Forecas Error ε +δ for Par HC545 in Nashville and δ = 5 days, and Normal Cumulaive Disribuion (Unis Disguised). 2. The sandard deviaions σ δ of hese disribuions for ε +δ were well prediced by a coefficien of variaion facor K δ imes he demand forecas f,wihk δ only depending on +δ he locaion and he number of days of demand prediced δ, and exhibiing a decreasing rend wih δ. 3. The expeced values E[ ε +δ ], represening he sysemaic forecasing bias, refleced wo effecs: (i) over he daa collecion period, he daily forecass provided o he supply rouing analyss were acually obained by dividing a weekly forecas equally among all days of each week. Because Dell s demand wihin he week does exhibi a seasonaliy paern, ha consrucion mehod for he daily forecass induced some bias; and (ii) Dell s demand exhibied a general downwards rend for some componens over a porion of he daa collecion period, which was slighly underesimaed by he forecasing eam in each one of is successive forecas revision seps. Because hese biases were relaively small overall and accouned for by he wo effecs jus described, we decided however o 2

3 ignore hem as par of our model. These resuls suggesed he srucure and provided he inpu daa for he sochasic model of cumulaive demand saed in Secion of he paper. A.2. Sofware Implemenaion The sofware implemening he opimizaion model described in secion 4 of he paper was developed using he environmen and modeling language Ilog OPL and relied on he ineger opimizaion engine Ilog CPLEX 9.1. The user inerface was embedded in several Microsof Excel spreadshees, which are illusraed in Figures A.2 o A.4 below, and Figure 3 in he paper. Specifically, Figure A.2 shows he spreadshee serving as a reposiory for conrol commands such as execuion of opimizaion runs, choice of mehod used o generae he forecasing daa, addiion and removal of pars, visualizaion and enacmen of decisions.figure A.3 shows a porion of he spreadshee developed o ener and modify he saic Figure A.2: Screen Copy of he Conrol Inerface (Disguised Daa) inpu daa, which includes coss, lead-imes and forecas coefficiens of variaion.figure A.4 3

4 Figure A.3: Screen Copy of he Inerface for Enering and Modifying Cos and Lead-Time Daa for Transfer Decisions (Disguised Daa) shows a porion of he inerface developed o visualize joinly some of dynamic inpu daa (invenory, incoming supply, forecas), as well as he oupu daa (ransporaion decisions, expeced invenory and resuling expeced shorages, denoed "Expeced Backlog" in Figure A.4). Noe ha he inerface shown in Figure A.4 was designed in order o represen he model oupu and is raionale in a forma ha would be familiar o he supply chain analyss, hence is similariy wih he Balance Tool described in Secion 3 of he paper.finally, we refer he reader o Figure 3 in he paper for a screen copy of he inerface developed o represen each individual supply rouing decision generaed by he opimizaion model runs. 4

5 Figure A.4: Screen Copy of he Oupu Visualizaion Inerface (Disguised Daa) 5