Capital Investment Industrial Modeling Framework - IMPRESS
Capital Investment & Facilities Location, Industrial Modeling Framework (CIFL-IMF) J.D. Kelly1 & A. Vazacopoulos2 i n d u s t r IAL g o r i t h m s January, 2013Introduction to Capital Investment & Facilities Location, UOPSS and QLQPPresented in this short document is a description of what is typically known as a capitalinvestment or facilities location problem involving fixed-charge and economies-of-scale details(Williams, 1993 and Winston, 1994). It is also known as a long-range strategic capacityexpansion problem (Sahinidis et. al. 1989, Lui and Sahinidis, 1995, 1996 and Lui et. al., 1996).Figure 1 below depicts two processing unit-operations (batch and continuous) producingproduct stocks D and E from feed stocks A, B and C. Each feed and product has dedicatedstorage where product E is only produced if capital is expended to install a new continuous-process unit either consuming A or B but not both. The capacity of the batch-process unit canalso be expanded or extended where D is an intermediate product. Cash-flows are also shownconstrained by budgetary restrictions which represent both a fixed-charge amount and avariable-charge amount scaled by the throughput of the units i.e., batch, charge or lot-sizes. Figure 1. Capital Investment & Facilities Location Flowsheet Example. 1 email@example.com 2 firstname.lastname@example.org
A full description of the objects found in Figure 1 (as well as other objects not shown) can befound in Kelly (2004b) and Zyngier and Kelly (2009) and is based on our Unit-Operation-Port-State Superstructure (UOPSS) and our Quantity-Logic-Quality Phenomena (QLQP) (Kelly,2005). In UOPSS, the units represent physical equipment which can have one or moreprocedural operations assigned, attached or associated with it. The cross-product of a unit withan operation creates a projectional unit-operation which is sometimes referred to as a virtual,logical or hypothetical object. We impose symmetry with the projectional port-state where theport is physical and the state is procedural where the state characterizes the type of substancepassing through the port-state. Connectivity is modeled as paths between unit-operations andport-states and represents the flow of something. The key idea of UOPSS is its ability toexplicitly manage the fact that a single unit can have multiple operations each with a differentconfiguration of port-states (e.g., BATCH and CONTINUOUS in Figure 1) and allows for verycomplex flowsheets to be depicted graphically. An important notion that we exploit with respectto the QLQP is our novel phenomenological decomposition3 of logistics and quality. Logistics isthe combination of quantity and logic where quantities are flows, holdups, yields and rates andthe logic aspects are related to the setup, startup, switchover, shutdown, status, etc. (Kelly andZyngier, 2007) of unit-operations and is solved using mixed-integer linear programming (MILP),meta-heuristics (Genetic Algorithms, Simulated Annealing, etc.) and/or constraint programming(CP).The industrial shipping model presented above is MILP4 based but most process industryproduction or manufacturing problems also contain a quantity times quality (sub-)problem due tointensive variables such as densities, components, properties and conditions multiplied byextensive quantities such as flows and holdups and is solved using nonlinear programming(NLP). Furthermore, our modeling framework is based on a discrete-time time-indexedformulation which requires each time-period to have the same time duration. Other time-indexed formulations classed as continuous-time models are available and have severalvariations based on whether the asynchronous time-periods are defined for a global/commontime grid or local/specific to each unit. However, for our industrial planning and schedulingproblems we have found discrete-time to be not only computationally effective (Maravelias,2012) but also appropriate when dealing with the many nuances of the problem specificationespecially handling partially specified plans or schedules in the future i.e., manually locking orfixing certain future activities and solving around or between them. This is very important forindustrial decision-making problems where some level of transparency for the user, modeler oranalyst is required in terms of how the planning or scheduling solution is computed fromessentially black-box solvers5.Industrial Modeling Framework (IMF), IMPRESS and SIIMPLETo implement the mathematical model of this and other systems, Industrial Algorithms offers aunique approach and is incorporated into our Industrial Modeling and Pre-Solving System wecall IMPRESS. IMPRESS has its own modeling language called IML (short for IndustrialModeling Language) which is a flat or text-file interface as well as a set of APIs which can becalled from any computer programming language such as C, C++, Fortran, Java, C# or Python 3 Other decompositions are well known such as hierarchical, structural, spatial and temporal but the conceptof phenomenological decomposition is new at least in name for advanced planning and scheduling problems. 4 Although MH and CP as well as local search (LS) solvers can be integrated, at present they are not. 5 Most industrial scheduling applications are still simulation-based where the schedules are built manually andincrementally one decision at a time so feedback in terms of cause and effect is important to the user.
called IPL (short for Industrial Programming Language) to both build the model and to view thesolution. Models can be a mix of linear, mixed-integer and nonlinear variables and constraintsand are solved using a combination of LP, QP, MILP and NLP solvers such as COINMP, GLPK,LPSOLVE, SCIP, CPLEX, GUROBI, LINDO, XPRESS, CONOPT, IPOPT and KNITRO as wellas our own implementation of SLP called SLPQPE (successive linear & quadratic programmingengine) which is a very competitive alternative to the other nonlinear solvers.The underlying system architecture of IMPRESS is called SIIMPLE (we hope literally) which isshort for Server, Interacter (IPL), Interfacer (IML), Modeler, Presolver Libraries and Executable.The Server, Presolver and Executable are primarily model or problem-independent whereas theInteracter, Interfacer and Modeler are typically domain-specific i.e., model or problem-dependent. Fortunately, for most industrial planning, scheduling, optimization and controlproblems found in the process industries, IMPRESSs standard Interacter, Interfacer andModeler are well-suited and comprehensive to model the most difficult of production andprocess complexities allowing for the formulations of ubiquitous conservation laws, rigorousconstitutive relations, empirical correlative expressions and other necessary side constraints.User or adhoc constraints can be augmented or appended to IMPRESS when necessary inseveral ways. For MILP or logistics problems we offer user-defined constraints configurablefrom the IML file or the IPL code where the variables and constraints are referenced using unit-operation-port-state names and the quantity-logic variable types. It is also possible to import aforeign LP file (row-based MPS file) which can be generated by any algebraic modelinglanguage or matrix generator. This file is read just prior to generating the matrix and beforeexporting to the LP, QP or MILP solver. For NLP or quality problems we offer user-definedformula configuration in the IML file and single-value and multi-value function blocks writable inC, C++ or Fortran. The nonlinear formulas may include intrinsic functions such as EXP, LN,LOG, SIN, COS, TAN, MIN, MAX, IF, LE, GE and KIP, LIP, SIP (constant, linear and monotonicspline interpolation) as well as user-written extrinsic functions.Industrial modeling frameworks or IMFs are intended to provide a jump-start to an industrialproject implementation i.e., a pre-project if you will, whereby pre-configured IML files and/or IPLcode are available specific to your problem at hand. The IML files and/or IPL code can beeasily enhanced, extended, customized, modified, etc. to meet the diverse needs of your projectand as it evolves over time and use. IMFs also provide graphical user interface prototypes fordrawing the flowsheet as in Figure 1 and typical Gantt charts and trend plots to view the solutionof quantity, logic and quality time-profiles. Current developments use Python 2.3 and 2.7integrated with open-source Dia and Matplotlib modules respectively but other prototypesembedded within Microsoft Excel/VBA for example can be created in a straightforward manner.However, the primary purpose of the IMFs is to provide a timely, cost-effective, manageableand maintainable deployment of IMPRESS to formulate and optimize complex industrialmanufacturing systems in either off-line or on-line environments. Using IMPRESS alone wouldbe somewhat similar (but not as bad) to learning the syntax and semantics of an AML as well ashaving to code all of the necessary mathematical representations of the problem including thedetails of digitizing your data into time-points and periods, demarcating past, present and futuretime-horizons, defining sets, index-sets, compound-sets to traverse the network or topology,calculating independent and dependent parameters to be used as coefficients and bounds andfinally creating all of the necessary variables and constraints to model the complex details oflogistics and quality industrial optimization problems. Instead, IMFs and IMPRESS provide, inour opinion, a more elegant and structured approach to industrial modeling and solving so thatyou can capture the benefits of advanced decision-making faster, better and cheaper.
CIFL-IMF Modeling DetailsAt this point it is prudent to elucidate more of the modeling details found in Figure 1. Theproduction facility or plant is represented by a supply of raw materials A, B and C which can beused to produce finished product D in an existing batch-process unit-operation labeled BATCH,EXISTING. Batch-processes exhibit a distinct "fill-hold-draw" holdup or inventory profile overtime (Zyngier and Kelly, 2009) where the feeds can be filled or loaded into the batch vesseleither continuously or intermittently over the duration of the batch known as its cycle orprocessing-time. Finished product E is produced in a (future) continuous-process unit namedCONTINUOUS requiring D and A for operation INSTALLATION1 and D and B forINSTALLATION2. Continuous-processes exhibit no or negligible holdup during the processingand as such simultaneously produce E the instant D and A or B is available where the fill-hold-draw profile collapses to a concurrent fill-draw with no hold of course. The non-material or non-stock flow called CAPITAL is a pecuniary or currency resource and is located on what we call aport-state.Port-states allow flow into and out of a unit-operation and can be considered as flow-interfacessimilar to ports on a computer i.e., nozzles, spouts, spigots. Port-states also provide anunambiguous description of the flowsheet or superstructure in terms of specifically what type ofmaterials or resources are being consumed and produced by the unit-operation. Port-statescan also represent utilities (steam, power), utensils (operators, tools) as well as signals such asdata, time, tasks, etc. Each of the two products D and E have tanks available for storage and isa requirement when balancing the production-side supply with the transportation-side demandof the value-chain. Finally, the lines or arcs between the unit-operations and port-states andacross an upstream unit-operation-port-state to a downstream unit-operation-port-statecorrespond to flows as one would except given that the superstructure is ultimately composed ofa network or graph of nodes/vertices and arcs/edges (directed).We now feature the capital investment or facilities location details of the problem where theobjective function of the problem is to maximize the net-present-value6 (NPV) of the profit(revenue minus feed costs and capital costs) over time. The time-horizon is usually modelledover several years where the time-periods are in years or sub-years such as quarters. Thesetime-periods can also be non-uniform in the sense that their durations can be variable butexogenously defined (known a priori). These types of problems may have different aggregatedor disaggregated formulations such as lot-sizing reformulations (Liu and Sahinidis, 1996) whichare not applied explicitly in this model7.The unit BATCH is existing but its capacity can also be expanded at a cost. This cost is wellknown to have essentially two parts, a fixed and a variable cost where the fixed cost is appliedto the binary or logic variable determining the existence of the expansion (i.e., its setup orstartup logic) and the variable cost is applied to its throughput or batch-size. When knownpower-law relationships of capital cost versus throughput are available such as found in Garyand Handwerk (1994), Johnson (1996) and Kaiser and Gary (2007), simple linear regressioncan be applied to convert these to approximated fixed+variable coefficients (Liu et. al. 1996 andKelly 2004a) that can be easily used inside MILP formulations such as that presented here. 6 NPV simply discounts the objective function coefficients according to an inflation or deflation rate parameterwhich can also be time-varying or time-dependent. 7 These types of reformulations can be generated automatically for each unit or unit-operation that isidentified as having a lot-sizing structure for example.
Each of the expansion and installation unit-operations shown i.e., EXPANSION1, etc. have aCAPITAL port-state which carries the NPV cash-flow to the unit-operation named BUDGET(diamond shaped). The inlet port-state of this unit-operation will have a time-varying NPV cash-flow lower and upper bound to constrain the expansions and/or installations according to theexpected cash-flow profiles in the future. An additional restriction required, sometimes referredto as a side-constraint, is the fact that if an expansion/installation unit-operation is selected insome future time-period then it must be setup for the rest of the time-horizon. This can bemodeled using our up-time8 logic constraint where a lower or minimum up-time is configured asthe time-horizon length of the problem (Wolsey, 1998, Kelly and Zyngier, 2007 and Zyngier andKelly, 2009).The unit CONTINUOUS is non-existing and requires a completely grass-roots or green-fieldinstallation or construction. If selected, based on its economic viability with respect to itsexpected installed cost and projected revenue of E, it will use D and either A or B as its co-feedsand will produce final product E which also requires its own newly installed storage vessel. Thisunit is also strictly conditional on either of the BATCH units expansion operations beingselected. That is, the CONTINUOUS unit will not be installed unless either EXPANSION1 orEXPANSION2 operation is chosen. This is known as an implication or sequence-dependencytype of constraint and is managed by the fact that if there is no flow of D from the BATCH unit tothe CONTINUOUS unit then the CONTINUOUS unit cannot be installed or constructed giventhat an infeasibility will occur during the branch-and-bound search of the MILP solution.CIFL-IMF Solving DetailsOnce the flowsheet has been configured as in Figure 1, a *.UPS file (short for UOPSS) isconstructed using the UOPSS object names via a Python 2.3 macro (IALconstructer.py)embedded in the Dia drawing package and is shown in Appendix A. This file can then beincluded into the IML file or the IPL code and will define the necessary named keys or index-sets for the various capacity data necessary to create the mathematical model. A useful facet ofthe UPS file is the application of "aliases". Aliases allow the capacity configuration of manyUOPSS objects simultaneously - see ALLPARTS, ALLINPORTS, ALLOUTPORTS andALLPATHS.TBDReferencesSahinidis, N.V., Grossmann, I.E., Fornari, R.E., Chathrathi, M., "Optimization model for longrange planning in the chemical industry", Computers & Chemical Engineering, 13, 1049, (1989).Williams, H.P., "Modeling building in mathematical programming", 3rd Edition, John Wiley &Sons, (1993).Gary, J.H., Handwerk, G.E., "Petroleum refining technology and economics", 3rd Edition, MarcelDekker, New York, (1994).Winston, W.L., "Operations research: applications and algorithms", Wadsworth PublishingCompany for Duxbury Press, Belmont, California, (1994). 8 Up-time is also known as a run or campaign-length and essentially restricts a shutdown of the unit-operationfor a specified number of time-periods in the future.
Liu, M-L., Sahinidis, N.V., “Computational trends and effects of approximations in an MILPmodel for process planning”, Industrial & Chemistry Engineering Research, 34, 1662, (1995).Liu, M-L., Sahinidis, N.V., “Long range planning in the process industries: a projectionapproach”, Computers & Operations Research, 23, 237, (1996).Liu, M-L., Sahinidis, N.V., Shectman, J.P., "Global optimization in engineering design",Grossmann, I.E. (editor), Kluwer Academic Publishers, Boston, (1996).Johnston, D., "Complexity index indicates refinery capability, value", Oil & Gas Journal, 94, 12,(1996).Wolsey, L.A., "Integer programming", Wiley-Interscience, New York, (1998).Kelly, J.D., "Formulating production planning models", Chemical Engineering Progress,January, 43, (2004a).Kelly, J.D., "Production modeling for multimodal operations", Chemical Engineering Progress,February, 44, (2004b).Kelly, J.D., "The unit-operation-stock superstructure (UOSS) and the quantity-logic-qualityparadigm (QLQP) for production scheduling in the process industries", In: MISTA 2005Conference Proceedings, 327, (2005).Kaiser, M.J., Gary, J.H., "Study updates refinery investment cost curves", Oil & Gas Journal,105, 82, (2007)Kelly, J.D., Zyngier, D., "An improved MILP modeling of sequence-dependent switchovers fordiscrete-time scheduling problems", Industrial & Engineering Chemistry Research, 46, 4964,(2007).Zyngier, D., Kelly, J.D., "Multi-product inventory logistics modeling in the process industries", In:W. Chaovalitwonse, K.C. Furman and P.M. Pardalos, Eds., Optimization and LogisticsChallenges in the Enterprise", Springer, 61-95, (2009).Maravelias, C.T., "On the combinatorial structure of discrete-time MIP formulations for chemicalproduction scheduling", Computers and Chemical Engineering, 38, 204, (2012).Appendix A - CIFL-IMF.UPS (UOPSS) Filei n d u s t r I A L g o r i t h m sAll Rights Reserved (c)checksum,184!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Unit-Operation-Port-State-Superstructure (UOPSS) *.UPS File.! (This file is automatically generated from the Python program IAConstructer.py)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!&sUnit,&sOperation,@sType,@sSubtype,@sUseA,,perimeter,,A,,pool,,B,,perimeter,,B,,pool,,BATCH,EXISTING,processb,,BATCH,EXPANSION1,processb,,BATCH,EXPANSION2,processb,,BUDGET,EXPENDITURE,perimeter,,