advances in apo optimization

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Optimizing mid-term and long-term supply chain planningpromises tremendous benefits. SAP now has the technology tohelp master supply chain planning, and SAP APO deliversvarious optimization tools. This article covers those tools, andthe advances SAP has made in optimization process for supplychain planning.Optimizing mid-term and long-term planning - including supply network planning anddetailed scheduling - promises tremendous benefits, including:

Lower inventories

Reduced production and transportation costs

Increased manufacturing throughput

Higher levels of service

The results are improved product margins and a better return on assets. The tasksand obstacles that line the path to this payoff are listed in Figure 1.

When performing supply chain planning (SCP), the IT staff or the supply chainplanner is pressed to find the most accurate and fastest view of the supply chain withoutoverwhelming IT resources. Relief comes in the form of SAP's Advanced Planner andOptimizer (SAP APO), which is at the heart of SAP's Supply Chain Management (SCM)solutions. The APO has always included modules that are integrated to enhanceoptimization, but the most recent advances in Release 3.0 - developments such asliveCache and new optimization libraries - offer your users an even bigger payoff in theirsupply chain planning, scheduling, and analysis.

This article takes you through the benefits of supply chain planning with SAP APO,and then goes in-depth into the ways that supply chain planners, IT departments, andeven the operations research (OR) community generally can make the most of the R/3supply chain process and the new open structure of SAP APO.

With these specific needs in mind, this article discusses the developments in SAP'soptimization solution, SAP APO.

Tasks ChallengesAutomatically update costs and pricingAny supply chain optimizer

should consider in itsobjective the followingfunctions: storage costs,production costs,transportation costs, andsales profits. These factorsshould be derived fromactual business pricingdata, so that changes in the

New Advances in SAP APO to Optimize the Supply Chainby Dr. Heinrich Braun | SAPinsider

October 1, 2000

by Dr. Heinrich Braun, SAP AG, and Claus Gruenewald, SAP AG SAPinsider - 2000 (Volume 1), October (Issue 2)

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Page 1 of 9New Advances in SAP APO to Optimize the Supply Chain

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supplier's actual price listare automatically reflected.

Accurately model the supply chain Modeling the supply chainon a reasonable level ofdetail may generate verylarge optimization problems.You need to be able toavoid these problems withthe right solution, forexample: globaloptimization on a rough-cutmodel for mid-termplanning, versus localoptimization on a detailedmodel for short-termplanning.

Offer a generic solution The optimizer should meetthe needs of your particularindustry. At the same time,it should also provide astandard software approachthat can be configured tohelp you solve the supplychain scenarios for variousbusiness areas (e.g., high-tech, process industry, etc.),rather than individuallydeveloped optimizerstailored only to a specificarea.

Provide seamless integration The system must be able tointegrate differentoptimization methods ondifferent planning levels -operational, tactical, andstrategic - eachautomatically updated fromthe execution systems. (Fordescriptions of theseplanning levels, see thesidebar on the followingpage.)

Allow for scalability You need solutions of acompetitive quality that cansuccessfully consider variousproblem sizes and allowedruntimes. There is an inevitabletradeoff between the quality of thesolution and the used runtime.Scalability means that you achievea balance, allowing for "gracefuldegradation" of the quality of thesolution in exchange for:

Lowering the runtime given afixed problem

Increasing the problem sizegiven a fixed runtime (forexample, the 5 CPU hoursduring the night break)

Alternatively, you may expectsignificant improvements in thesolution quality by scaling up theruntime or the number ofprocessors.

Figure 1Tasks and Challenges of Supply Chain OptimizationSAP's Advances in OptimizationWith the increases in processing that have made possible initiatives such asmySAP.com industry solutions, SAP now has the technology to help master thenecessary basic ingredients for truly optimizing supply chain planning.

For example:



SAP APO now enables transactional ERP systems in the supply chain to beinterconnected, in order to accurately and easily reflect costs and pricing.

SAP APO now has several gigabytes of main memory, which allows you toadequately model the supply chain much faster.

SAP APO now has advanced optimization libraries - e.g., fast linear programming(LP) solvers with polynomial time complexity using interior point methods andefficient constraint propagation for scheduling problems. They can be used as basicbuilding blocks for tackling the need for a generic solution.

SAP APO delivers different optimization tools for different SCP problems. Thesetools include:

Genetic Algorithms - e.g., in the Product Planning/Detailed Scheduling (PP/DS)modules

Constraint Programming - e.g., in the Product Planning/Detailed Scheduling (PP/DS)modules

Mixed Integer Linear Programming - e.g., in the SNP module

Tabu Search - e.g., in the Transportation Planning/Vehicle Scheduling (TP/VS)module, as of APO 3.0

Because the optimizer server can now use several gigaflops of CPU power in amultiprocessor architecture, the server can enable computation of sophisticatedoptimization strategies. In the following sections, we cover how SAP APO is meeting thechallenges of accuracy, generic solutions, seamless integration, and scalability for SCPproblems.

Dual Server for Accurate Supply Chain ModelingOf course, accurately modeling the complete supply chain often requires a huge amountof information. SAP is now capitalizing on technologies, such as 64-bit generationprocessors, that already make it possible to maintain almost unlimited amounts of datausing several gigabytes of main memory.

With this technology in mind, SAP created liveCache - a newly developed objectdatabase in main memory, designed by SAP especially for planning problems thatrepresent vast amounts of relevant data: demand, supply, capacity profiles, andactivities and their time constraints, among others.

For example, take the data involved in planning the actual week for a reschedulingrun on the operational level. The optimizer reads the planning problem out of liveCacheand solves this problem on a separate server.

SAP liveCache technology is already at work in modules such as the SNP, PP/DS,ATP, and TP/VS modules. Customers who implemented these modules are now usingliveCache, and include Fischerwerke and Wacker Siltronic AG of Germany.

This separation has two benefits:

SAP APO performs better. The performance of the liveCache server is not reducedduring the CPU time that is consumed in the optimization run.

SAP APO is more flexible. You, as the supply chain planner, have some choices asto which optimization model you use. SAP APO's internal model can use theliveCache model or it can use another optimization algorithm.

One difficulty for many ERP systems is data transfer. In most standard ERPsystems, you need fast access to a portion of a complex network for successful datatransfer. liveCache technology solves this problem, since it comprises object-orienteddata structures in main memory that are especially tailored for planning problems.

Figure 2 depicts the architecture of the optimizer in SAP APO. The Core Model, orinternal data model, is the central component. The task of the model generator is totransfer a selected planning problem from liveCache into the Core Model of theoptimizer.



Figure 2SAP APO Optimizer Model

Supply Chain Planning: Three LevelsIn this article, we discuss three levels of supply chain planning. SAP has differentmodules and solutions that address each specifically, all incorporated in the SAP APO.The levels are:

Operational Level. APO Module: Detailed Scheduling (DS). At this level, youmonitor the short-term, day-to-day operations, focusing especially on exceptions insupply chain operations. The optimizer schedules orders according to manufacturingconstraints that handle complex manufacturing environments with alternativeroutings and resources, secondary resources, and multistage production.

Tactical Level. APO Modules: SNP, Capable to Match (CTM). At this level, youmonitor mid-term planning scenarios for the global supply chain, from distributioncenters to plants and suppliers. The optimizer automatically processes bills ofmaterials while taking capacities into account, and optimizes transportation costs,production costs, storage costs, and revenues for demand. The sheer complexity ofthis global view is mastered by a rough-cut model that aggregates the time inbuckets (e.g., day or week) and products and resources in families.

Strategic Level. APO Module: Network Design. This stage involves long-termplanning for the supply chain. It is at this level that you graphically construct andmaintain a model of the entire supply chain. You also analyze the optimal use ofdifferent resources in your supply chain based on a long-term view (for example,closing or creating distribution centers or plants).

Dual Modeling for Optimization Across Supply ChainLevels

SAP APO provides a suite of special tools tailored for all blocks of the SCP cubeillustrated in Figure 3. SAP APO's modeling approach consists of two types of planning:aggregated planning based on LP solvers for a more global view of the supply chain (forlong- and mid-term planning), and detailed planning based on scheduling algorithms toensure accuracy at a finer level of analysis (for short-term planning).

Figure 3Classification of Planning ProblemsAggregation As a Strategy for Long-Term and Mid-Term Planning



On the strategic and tactical levels (where mid- and long-term planning occurs), SAPAPO performs aggregated planning to provide a more global view of the entire supplychain. For mid-term planning, this aggregation provides an adequate level of detail,depending on the degree of uncertainty in the planning data. Factors to consider whenanalyzing the level of uncertainty in planning data include new orders, ordercancellation, forecast errors, and market changes. Mid-term and long-term planningproblems may include various constraints - for example, linear constraints such as:

Due-date deadlines

Maximum delay

Shelf life (maximal range of coverage)

Storage and handling capacity

Capacity calendar for resourcesM

Break calendar, including work stoppage, holidays, etc.

More difficult constraints are discrete constraints such as:

Minimal/discrete lot sizes

Full truck load

Discount rates (piecewise linear cost functions)

Supply chain planning problems that involve only linear constraints can be reliablysolved to optimality using the LP solver of ILOG CPLEX. However, SCP problems thatinclude the additional constraints of the second group (discrete constraints) are muchharder to solve. Problems with discrete constraints are modeled as mixed integer linearproblems (MILP) and solved via ILOG CPLEX's branch-and-bound. In order to achievebest solution quality in the given runtime, SAP has developed heuristics that take theeconomical semantic of the decision variables into account.

Scheduling for Detailed, Short-Term Planning

On the operational level, SAP APO performs detailed supply chain planning. All theactivities in the supply chain (e.g., transportation, production lots, etc.) are scheduledprecisely at a particular time on specific individual resources, such as productionresources, transportation resources, or even warehouse capacity. With SAP APO,several supply chain planners can work simultaneously on one plan, each focusing on asmall section of the larger supply chain.

Scheduling problems are modeled in the most generic way possible through what iscalled Multi-mode Resource Constraint Project Scheduling Problems with maximum andminimum time lags (MRCPSP/max). Maximum time constraints include:

Deadlines, shelf life, and expiration dates

Storage capacities

Sequence-dependent setup times

Processing interruptions by breaks

Objectives, such as minimizing setup times, setup costs, resource costs, earliness,and due-date delays

APO Scheduling Approaches

The suite of algorithms in the current SAP APO uses the following three approaches:

Constraint Programming (CP). The CP scheduler is the most generic scheduler. Itis based on the ILOG libraries and uses dynamic constraint propagation at everyoptimization step.

Genetic Algorithm (GA). The GA scheduler is based on an evolutionary approach.The genetic representation of the supply chain comprises control information, whichis used by a fast scheduler for generating a new supply chain solution.

Repair Algorithm (RA). This scheduler is based on solving a resource relaxation(i.e., respecting only time constraints and assuming infinite resource capacity), whichcan be done in polynomial time. The resource capacity constraint violation is solvedby adding precedence constraints between the conflicting resource requirements to



dynamically solve over-capacity conflicts and then, again, calling the solver for theresource relaxation until no capacity overload remains.

However, the relative performance of these alternative optimizers for detailedscheduling may depend on the individual planning scenario. Therefore the supply chainplanner, along with the manager, may select the most appropriate algorithm after someexperimental studies. In SAP APO, supply chain planners can construct their ownobjective function by combining the previous objectives with priorities (linear weights).

Seamless IntegrationTo seamlessly integrate the different levels of the supply chain, the aggregated planmust be disaggregated for short-term planning on the operational level.

Scheduling algorithms determine the resource allocation out of a set of alternativeresources (disaggregation of resource families) and precise time scheduling(disaggregation of time buckets). SAP APO provides a generic framework, which allowsit to integrate several scheduling algorithms based on CP, GA, or RA approaches. Theplanner may select the most appropriate scheduler or may even combine them using ascript (e.g., first optimize the bottleneck resources with the GA scheduler and thencomplete this schedule using the CP scheduler). Moreover, this architecture is open,which allows us to integrate other optimizers for detailed scheduling.

Decomposition TechniquesTime Decomposition: This method breaks the large-scale scheduling problem into aseries of smaller-scale planning problems consisting of smaller overlapping time frames.Imagine a moving planning window, which slowly "glides" over your Gantt chart. In thisway, SAP APO solves smaller problems one by one, instead of solving the complete,large-scale planning problem all at once, as shown in Figure 4.

Resource Decomposition: The idea behind resource decomposition is that it involvesconsidering a planning window not defined by a time frame but by a set of resources. Asin time decomposition, the set of activities outside the window is fixed. The challenge ofthis decomposition technique is to define the set of resources for each planning windowin a sensible way. The objective is a decomposition in loosely connected parts.

Product Decomposition: The idea behind product decomposition is to define theplanning window by the material flow: consider all resources (e.g., production andtransportation), intermediate materials, and activities that could be used to produce agiven product. The challenge is to combine material flows with many commonresources. In this sense, it is similar to resource decomposition. However, in productdecomposition, activities using the same resources but belonging to different materialflows may not be rescheduled at the same optimization step.

Priority Decomposition: The idea behind priority decomposition is to decompose theproblem into the set of activities that belong to different priorities for the customerdemands. Planners may use this technique for optimizing first the activities of thehighest priority and then fixing them before optimizing the next priority class.

Bottleneck Relaxation: This technique is used for business scenarios with a large-scale scheduling problem. The most important (or expensive) resources create thebottleneck of the scheduling problem. Therefore it may be a good strategy to first find ahigh-quality schedule for the bottlenecked resources, and then relax the capacityconstraints on the non-bottleneck resources (i.e., plan them with infinite capacity). In asecond step, this schedule may be enhanced to complete the schedule while fixing theoptimized sequence of the activities on the bottleneck resources. With SAP APO, thistechnique is used for campaign optimization and block scheduling (see Figure 5). Theblocks (e.g., production lot size for a certain product) or campaigns (e.g., sequence oflot sizes) are built by focusing on the bottleneck production stage.

Figure 4Time Decomposition Model



Figure 5Bottleneck RelaxationScalabilityComplete optimizing procedures guarantee that the global optimum is found withexponential time complexity. Because it will lead to unacceptable runtime, however,such a guarantee is obviously useless for practical purposes. Even reducing the qualitygrade requirement to 5 percent below the optimum generally cannot be guaranteed.Here are some factors to consider, depending on the kind of scaling needs you have,and how SAP APO addresses these factors:

Scaling in quality - runtime versus optimization quality. If more time is used foroptimizing, then a higher-quality grade can be expected. SAP APO's decompositionstrategies give you flexibility when adjusting procedures to fit the needs of the user.

Scaling in problem size - runtime versus problem size. Time expenditure generallyincreases in proportion to the problem size. In the case of large optimizing problems,even algorithms with quadratic time complexity can be too time consuming. Thedecomposition strategies in SAP APO have a time complexity of O (n log n) using aconstant window size, and can thus solve large planning problems.

SAP APO provides a generic framework combining several decompositiontechniques (including time, resource, product, and priority) and several basic optimizers(LP solver, CP scheduler, GA scheduler, and RA scheduler). Decomposition focusesthe optimization activities on smaller problems within the larger planning problem.However, you must be aware of the level of optimization and the size of the problem:fine decomposition in small subproblems (such as local optimization) requires lowruntime, but runs the danger of a lower-quality local optimization. On the other hand,coarse decomposition in large subproblems may cause unacceptable runtime. By usingthe appropriate decomposition technique, SAP APO can make it possible to seamlesslyclose the gap between local improvement heuristics and global optimization.

When trying to improve on the current solution, local improvement heuristicsconsider only the direct local neighborhood (i.e., the valid solutions for a specificoptimization problem). This search may be trapped by local optima. Decompositiontechniques can scale up the neighborhood (i.e., increase the decomposition width). SAPAPO enables tuning of the optimal decomposition width. The methods of decomposition(see the sidebar on the facing page) illustrate the various ways SAP APO achieves aseamless transition from heuristics to global optimization.

Using Decomposition to Reduce Supply ChainComplexityEven with SAP APO, there are limits to what a supply chain optimization can do; one isthe complexity of the supply chain. A supply chain that is unnecessarily complex willextend the calculation time, or will never find a feasible solution and lead to theproblems discussed earlier in this article. However, through decomposition, you canreduce the complexity to match your resources.

The Two-Step Process of Decomposition

There are two stages to solving an optimization problem through decomposition. First,generate a feasible solution by combining various decomposition techniques withdifferent optimizers in SAP APO. The architecture even makes it possible to startseveral optimizers per planning window and to use the best result in each case. Then,take further steps to improve the solution.

For mastering both cases, SAP's generic architecture makes it possible to combinedifferent decomposition strategies with different optimizers. For example, we could firstgenerate a solution by choosing bottleneck relaxation as the decomposition method,and then using the genetic algorithm as the optimizer. Then, at the second stage, toimprove on this solution, you could select time decomposition, using constraintprogramming as the optimizer.

Taking Decomposition Further

You could even take this a step further and divide the second stage into two phases:first optimize the customer service level (to minimize due date violations), then minimize



earliness (storage), for a result that produces goods as late as possible without anincrease in due date violations.

SAP's architecture offers parallelization that is seamlessly integrated into thedecomposition strategies, so that it is possible to start several optimizers, each withdifferent objectives per planning window, and run them in parallel using the computingpower of a multi-processor system.

Planning Your IT Resources for Maximum Supply ChainBenefitWith all the benefits that SAP APO has to offer, supply chain optimization can still belimited by the available computing power. Less computing power is often compensatedfor by more severe decomposition, which may decrease the quality of the generatedsolutions. There may be a number of reasons for limited computing power, and SAPAPO offers you the flexibility to address some of these causes at the source.

The problem may be due to multiple users working in parallel. This problem issolved in SAP APO by a three-tier client/server architecture configurable formultiprocessor servers.

Separating the application servers also can alleviate this problem. liveCache andSAP APO may run on separate application servers. This architecture is recommendedfor modeling a large SCP problem, since both require high-level computing power andhigh main-memory capacity. It is even possible to configure the system with severaloptimizer servers or with multiprocessor architectures. On the other hand, smallercompanies can also use just one application server for both liveCache and SAP APO.

Both the optimization algorithms and the decomposition techniques offer a lot ofpotential in parallelization. With the multiuser capability of SAP APO, the supply chainplanner may parallelize the optimization manually by using decomposition techniques.Optimizing in a parallel session will separate parts of the supply chain, and thus reducethe load on the computing resources.

In SAP APO Release 3.0, the inherent parallelization of multiple agents may beused on a multiprocessor server. This approach is integrated in the decompositiontechniques. For each decomposed planning problem, different agents may run inparallel. These agents may differ in which basic optimizer (GA, CP, and RA) or objectivefunction is used, each doubling the focus on one single criterion of the given multicriteriaobjective defined by the user (e.g., one function doubles the setup costs, the otherdoubles the delay costs). After each optimization run, the user may select one solutionchosen from a set of solutions that have similar overall quality but differ in the singlecriterion.

Conclusion - And An InvitationSAP APO is a generic solution for optimizing the supply chain configurable to masterspecific business scenarios. Because of its open architecture, it is open to futureenhancements concerning model functionality, improved optimization algorithms(libraries), and higher degrees of parallelization. The only limits of this algorithmicapproach are the available computing power and the complexity of the supply chain.

In order to benefit from the potential of parallelization, SAP APO is designed formultiprocessor architectures. However the user should not expect this to be the "silverbullet" that solves all problems. Supply chain planners must still work carefully to avoidtoo complex a supply chain calculation - which would unavoidably result in pooroptimization performance. This overview provides the groundwork to better plan yourown supply chain and take advantage of the new features in SAP APO.

One additional note on what you can expect of SAP APO in the future: because it hasan open architecture, we also offer an invitation to the OR community to contribute totruly optimizing the supply chain to meet your optimization needs. In the future, you canlook for announcements regarding the APO Extension Workbench (APX). This tool willallow the OR community to create and use customer-specific optimization algorithmsthat may be integrated with SAP APO.

The first customer shipment of SAP APO 3.0 was May 2000, with general availability at the end of September

2000.

For example, planners may want to set priorities to meet different objectives. If you must meet all due dates,

the supply chain must factor in smaller lot sizes, which, of course, will lead to higher production costs.

For example, in SNP you will have a kind of rough planning phase, such as simply matching supply and

demand. This is basically the dispatching of demand to different plants, which is the aggregated plan. To

effectively detail scheduling of each of these various plants, this plan then has to be disaggregated for supply

chain optimization.



Dr. Heinrich Braun has a degree in computer science and a doctoral degree from theUniversity of Karlsruhe. Dr. Braun joined SAP AG in 1996, and in 1997 became projectlead of the development team for SAP APO's optimization algorithms. Since January2000, he has worked as the development manager for optimization algorithms in SAPAPO.

Claus Grunewald has worked with SAP since 1996 in logistics development. Mr.Grunewald is a product manager for SAP APO and is currently involved with strategicbusiness development for supply chain management.

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