Interactive Decision Support:

Advantages of an Incomplete Utility Model

Richard Goodwin John RachlinSesh Murthy Rama Akkiraju

IBM T. J. Watson Research Center

Yorktown Heights, NY{rgoodwin,rachlin,murthy, akkiraj u } @watson.ibm.corn

Effective production scheduling is at the heart of anyefficient manufacturing process and is the key toprofitability. Because scheduling is complex, manufacturesuse computers to generate near optimal schedules.However, using a computer to find a single near optimalschedule requires a precise definition of optimality whichmust tradeoff the competing interests of productionefficiemy, customer satisfaction, profitability and productquality. Performing these tradeoffs automatically is beyondthe fidelity of any utility model that could be constructedwith reasonable effort. Scheduling systems work best asassistants to human schedulers, keeping track of complexconstraints and presenting the a set of alternatives thathighlight the tradeoffs. The system must allow the humanscheduler to examine and manipulate the schedules inorder for the human to arrive at the best schedule. Theutility model must capture the high level factors thatcontribute to a good schedule, but it does not need tocapture all the subtlety needed to select the best schedule.For manufacturing interests, scheduling objectives fallalong four broad dimensions: Time, factors that relate toon time delivery, Quality, factors related to product quality,Money, factors related to profitability and Disruptions,factors related to the ease of manufacture. Thesedimensions map to the interests of the customer servicerepresentatives, quality engineers, accountants andmanufacturing supervisors respectively. The humanscheduler is presented with a set of schedules that representthe Pareto-Optimal frontier and negotiates a selectionbetween these competing points of view. In this paper, weelaborate on our approach to interactive decision-supportand illustrate it with examples from the IBM Load PlanningSystem, which uses an asynchronous team of agents tocreate schedules for shipping manufactured goods tocustomers.

IntroductionAny utility function used to model preferences over real-world outcomes is necessarily incomplete, given limitedresources to create the utility function. Such is the case inscheduling for manufacturing processes where the numberof schedules is exponential in the size of the problem and

determining the preferred schedule involves subtle tradeoffsbetween competing objectives. A complete utility functionfor this domain would specify a partial order over allpossible schedules and outcomes. If there are n possibleoutcomes, then there are nl complete orderings, and farmore partial orderings, each of which is a possible utilitymodel. In some cases, where the objective is to minimize asingle, easily calculated value, such as cost, the utilitymodel is relatively easy to elicitation and can berepresented compactly. However, most problems involvetradeoffs between competing objectives to minimize cost,maximize on time delivery, minimize productiondisruptions and maximize customer satisfaction. The utilityfunction can be arbitrarily complex and may not have acompact representation. Furthermore, the effort needed toelicit a complete utility model may not be justified by theexpected benefit, even assuming that people representingcompeting interests could eventually agree on a preferenceordering over outcomes.

In our approach to computer aided decision making, werecognize that utility models are incomplete and rely onhuman operators to make the subtle distinctions necessaryto resolve tradeoffs. We see decision making inorganizations as a process of negotiation that computers cansupport by supplying relevant information and suggestinggood alternative solutions. The purpose of the utilityfunction is to guide search and to identify potentially goodsolutions for presentation to the human decision-maker.The partial utility model must capture the high level factorsthat contribute to a good schedule, but it does not have tocompare dissimilar measures of utility that representtradeoffs between competing interests. We use a multi-valued utility function that evaluates a schedule along a setof dimensions. For manufacturing interests, we have foundthat objectives can be evaluated along four broaddimensions: Time, factors that relate to on time delivery,Quality, factors related to product quality, Money, factorsrelated to profitability and Disruptions, factors related tothe ease of manufacture. Not incidentally, these fourmeasures map to the interests of the customer servicerepresentatives, quality engineers, accountants andmanufacturing supervisors respectively. The utility modelis used to aggregate factors that contribute to each category,

55

From: AAAI Technical Report SS-98-03. Compilation copyright © 1998, AAAI (www.aaai.org). All rights reserved.

but comparisons between categories are left to the humanscheduler who is presented with a set of schedules thatrepresent the Pareto-optimal frontier. The scheduler canuse these solutions as a basis for evaluating the tradeoffs,negotiating with other people in the company and comingto a final decision.

In the rest of this paper, we elaborate on our approach tointeractive decision-support and illustrate it with examplesfrom the IBM Load Planning System. We begin byintroducing the load planning problem, motivating itsimportance and describing the competing interests of theparties involved. We then describe our planning system,which uses an asynchronous team of agents (A-Teams) create schedules for shipping manufactured goods tocustomers. The A-Team architecture provides a robust,scaleable framework that allows the human expertscheduler to guide search, inject partial solutions and posewhat if scenarios. These features are essential because theyallow the scheduler to conduct negotiations with otherpeople responsible for parts of the manufacturing processand with the manufacture’s customers. Through examples,we show how the scheduler can negotiate to change thedefinition of the scheduling problem and allow for efficientsolutions.

Load PlanningManufactures in the process industries, such as steel andpaper producers, need to ship their goods from the mill totheir customers. Load planning is the process of creating aplan that assigns each item to be shipped to a particularkind of vehicle, selects a carrier and route for the vehicleand schedules the vehicle’s departure from the mill. Themanifest for each vehicle must satisfy constraints onweight, volume, the mixing of product types and the mixingof orders from customers that are competitors. Each carriermakes some number of vehicles, of particular types,available to the mill each day and each carrier chargesdifferent rates for delivery. The plan must only use thevehicles that are available, while respecting contractualobligations to give a certain volume of loads to each carrierin order to receive volume discounts. In addition, loadingdocks at the mill and at customers’ sites have capacitylimits on the number of vehicles, the types of vehicles andthe amount of material that can be handled in a given shift.In addition, vehicles may be packed with items going tomultiple locations, with some items dropped off on the wayto the final destination. The routing of vehicles betweendestinations for these drop shipments affects both thearrival time and the cost. Load planning in this context ismore than simple bin packing, but does include bin packingas a sub-problem.

The main objectives of load planning are to ensure on timedelivery while minimizing cost. Load planning is of greatconcern to manufacturers since distribution costs representa significant percentage of their revenue, with ten percentnot being unusual. Reductions of a fraction of one percentin distribution costs translate into millions of dollars ofprofit over the course of a year. Manufactures alsocompete for customers primarily on the basis of cost andservice, since their goods are commodity items with almostuniform quality across the industry. Failure to meetdelivery dates can cost a manufacture future business and isparticularly important for customers that operate in a just-in-time fashion. However, secondary concerns aboutproduct quality and disruptions at the mill are stillimportant. Product quality can be affected by the amountof time an item remains in inventory, the suitability of aparticular kind of vehicle for transporting it and by the carethat a carrier takes when transporting the material. Theefficiency of the loading dock is also affected by theschedule. Each switch between loading trucks and loadingrail cars disrupts the operations of the loading dock andadds delays, reducing capacity. Excess inventory at thedock reduces efficiency by making it hard to maneuveritems into the vehicles.

Problem DefinitionIn general, the load planning system is given as input thefollowing information:

¯ An Orderbook, which defines, attributes of eachincluding destination, earliest and latest due date, physicaldimensions and quantity.

¯ A list of available vehicles and carriers which defines theoptions for shipping and gives any contractual volumerequirements.

¯ Freight rates which define the cost for shipping goods asa function of the weight and distance, the type of product,the type of vehicle and the carrier.

¯ Loading rules which determine whether a given set ofitems can legally be loaded into a given vehicle. Theserules include constraints on stacking, weight and productmixing.

¯ Distances and transit times, defined by mode, are used todetermine arrival dates, given a ship date and todetermine cost, given a freight rate in $ per mile.A production schedule defines when items in productionwill be available to ship.An inventory list gives items that are waiting to beshipped.

¯ Dock shipping and receiving constraints give limits onthe number and type of vehicles and on the amount ofmaterial that can be handled at the mill and at eachcustomer’s receiving dock in a given shift.

56

t/)O

O

CyAy

By

C is dominated by A

~4~~ O NO sOlutiOn dominates A

O No solution dominates BA and B are therefore "non-dominated"

©

............................... ( OJ ©"’\ 0

O

........................................o

’rAx Cx Bx

TardinessFigure 1: Non-dominated solutions form the Pareto-Optimal frontier.

The current loadplan which lists loads that were plannedfor shipment. Load planning is an incremental processwith a scheduling horizon that may cover a week. Eachday the load plan is updated to reflect new orders andchanging production schedules. The five-day scheduleservers as a basis for predicting vehicle need and orderingvehicles from carriers. Substantial changes to the currentplan can create problems if vehicles have already beenordered and customers notified to expect delivery on aspecific day.

The goal is to produce a set of vehicle manifests, each oneassigned to a particular carrier and scheduled for aparticular shift at the loading dock. Sequencing of vehicleswithin a shift is not included because it is easier to do as thevehicles arrive at the dock and the exact location of eachitem in the staging area is known.

ObjectivesGiven the problem definition and the definition of asolution, the quality of the solution is determined by howwell it satisfies the objectives of the company. We nowfocus on the problem of determining the objectives of thecompany and formulating these objectives in a way that canbe used by the computer to guide search. In this section, weexplain our approach to creating partial utility functions.

For load planning and related manufacturing processscheduling problems, the objectives of the manufacturer fallalong four broad dimensions: Time, factors that relate to ontime delivery, Quality, factors related to product quality,Money, factors related to profitability and Disruptions,factors related to the ease of manufacture. These fourcategories map to the interests of the customer servicerepresentatives, quality engineers, accountants andmanufacturing supervisors respectively. Our utility modelaggregates factors that contribute to each category, butcomparisons between categories are left to the humanscheduler who is presented with a set of schedules that

represent the Pareto-Optimal frontier, represented by blocksin figure 1.

Aggregating utility factors within each category to create acombined utility for each category is easier than aggregatingacross categories. Within each category, the utility functioncompares like measures that reflect the same basic objectiveand tend to be expressed in comparable units. Eachcategory also maps to the direct interests of a small numberof people who have similar personal objectives. Customerservice representatives are evaluated on how well customersare satisfied and can give the relative importance of eachmeasure of timeliness. Product quality engineers can assessthe relative impact that inventory delays and the use ofspecific vehicles have on product quality. Accountants cangive the formula for calculating inventory holding costs andcarrier rate structures give transportation costs, both indollars. Finally, loading dock supervisors are evaluated onthe throughput of the loading dock and can give the relativecost of each type of disruption.

Within each category, there are multiple measures of utility.Some measures are standard across the industry, whileothers are used because a particular company finds themeasy to measure or believes that they better reflect the trueobjective. For example, tardiness can be measured as thenumber of orders that are late. Given the total number oforders, this measure can be translated into the percentage oforders that are late, a typical measure used in the industry.However, this measure does not indicate how late the ordersare and using it to optimize schedules would create apreference for making an order one month late rather thanmaking two orders one day late each. It also ignores the sizeof the order and the importance of the customer. Given theoption, it is probably better to make a 5-ton order late ratherthan a 50-ton order. Some mills also rank customers, withhigh volume customers getting higher priority for gettinggoods there on time. To account for these preferences,companies may weight the number of tardy orders by thenumber of days late, the size of the order and the

57

importance of the customer. But an individual measuretends not to capture the desired objective. For example, itmight be better to have one 50-ton order 1 day late than tohave two 25-ton orders one day late. Both have the samenumber of ton-days late, but the second one disappoints twocustomers while the first one disappoints only one. Thebest utility function may use a combination of tardinessmeasures.

In creating scheduling systems, we have included industrystandard measures of utility. These measures haveaugmented with measures used by the mills that we havevisited and with measures that complete patterns. Forexample, we have encountered mills that use the number ofhigh priority orders late, the number of ton-days late and thenumber of late orders. To this we have added the fullcomplement of measures that weight late orders by thenumber of days, the weight, and the priority of thecustomer, in any combination. The full set of measures foreach category is given in below. Within each category, theIBM Load Planning System allows the customer toaggregate these measures using a linear weighted sum. Thissimple utility representation has the advantage that it is easyto understand and tune. Give the formula, schedulers canunderstand the reasons that one schedule was ranked higherthan another. This improves their understanding of how thesystem works and, consequently, their confidence in itsoperation. Finally, we recognize that even non-linear utilityfunctions can be approximated by linear functions, over asmall range of values that one sees in normal operations.¯ Time:

0 Number of orders early or late.Weighted by the number of days late or early.Weighted by the weight of the order,Weighted by the priority of the customer

0 Number of orders after the drop-dead date, the last datethe customer will accept delivery.

Weighted by the number of days late or early.0 Weighted by the weight of the order.

Weighted by the priority of the customer¯ Quality:. Quality is a measure of product quality and

perceived product quality.Number of loads shipped by a mode other than thatpreferred by the customerNumber of loads shipped by a carrier other than thatpreferred by the customerNumber of loads shipped in a vehicle other than thatpreferred by the customerExcess loads arriving at the customer dock per day.

0 Excess weight arriving at the customer dock per day.Number of items in inventory for more than X days.

0 Weight of items in inventory for more than × days.0 Number of loads that mix products0 Number of loads that mix orders.

¯ Money: Factors which impact costs and revenues areincluded in this category, including:o Transportation cost.

Average transportation cost per tonTotal drop-off chargesInventory carrying costs

Disruptions: This category addresses operational concernson the manufacturing floor, or at the loading docks, or whilethe goods are in transit such as:0 Number of drop shipments0 Number of transitions between the loading of different

modes (i.e. Truck and train)0 Number of loading dock capacity violations

Planning ApproachRather than going directly from inputs to solutions, the IBMload planning system divides the problem up into threesteps: group formation, load formation and load sequencing.

Group formation: Items are partitioned into groups of itemsthat are going to the same or similar destination, at about thesame time and that can legally be loaded together into thesame types of vehicles. This is the divide step of a divideand conquer approach. It reduces the problem size andeliminates attempts to create loads with items that can notbe loaded together in any vehicle. The rules for partitioningare not rigid and improvement algorithms can move itemsbetween groups, coalesce groups and split groups whenlooking for better solutions.

Load formation: Items are assigned to vehicles in ways thatcreate legal manifests. A complete solution loads all itemsonto vehicles. One of the principle heuristics for achievingefficiency is to maximize vehicle utilization in order toreduce the number of vehicles needed, there by reducingcosts, reducing the demand on loading dock capacity andmaking best use of the available vehicles. All of these helpto achieve on time delivery as well. However, increasingvehicle utilization by combining orders going to similardestinations can lead to longer transit times and increaseddrop off charges that negatively impact both cost andtimeliness. Combining orders also means that the vehiclecan not leave until the last order is ready for shipment.Finally, there is a basic tradeoff between speed and cost.Shipping by rail tends to be less expensive, but slower.Trucks are faster and can go directly to more destinations,but tend to be more expensive. Delaying an order tocombine it with another to achieve good vehicle utilizationmay require a change from rail to truck in order to meetdelivery dates and result in a net increase in cost.

Load sequencing: Given a set of legal loads, loadsequencing assigns these loads to specific docks and shifts,taking into account the dock capacity and vehicleavailability. Each load is available to ship when the lastitem in the load has been produced. A simple heuristic forcreating initial solutions is to assign each vehicle to the shiftwhen it is first available for shipment. This may violatevehicle availability constraints and dock capacityconstraints, which force the load’s ship date to be pushed

58

Improvers~ modify existing

load plans

Destroyersdiscard badload plans

Constructorscreate new load plans

Figure 2. An A-Team is a software agent architecture that encapsulates different problem solvingapproaches as autonomous intelligent agents.

out. Delaying a shipment for want of a vehicle or dockspace may make the load late and require a change fromtrain to truck in order to deliver the shipment on time.

Asynchronous TeamsAn Asynchronous Team or A-Team [TSM94], [Souza93], isan agent-based architecture well suited to multi-objectivedesign problems. In this architecture, independent agentsevolve a population of solutions towards the Pareto-Optimalfrontier. As shown in Figure 1, agents (shown as blocks)communicate only through a population of candidatesolutions. There are three basic roles played by agents:

1. Constructors create new solutions and add them to apopulation.

2. Improvers take a copy of one or more existingsolutions, and modify them to produce a new solution,which is then added to the population.

3. Destroyers keep the size of the design population incheck by removing bad or redundant solutions.

The collection of agents runs as an anytime algorithm, witheach agent embodying a different approach to improving thepopulation of solutions. Often the approaches are heuristic.For example, constructors often use greedy algorithms thatfocus on a single objective. Using a set of greedyconstructors, each of which focuses on a different objective,tends to seed the population with a diverse variety ofsolutions. From this beginning, improver agents can lookfor opportunities to hill climb solutions, along one or moredimensions, towards the Pareto-Optimal frontier. Addingdomain specific heuristics, such as moving late orders totrucks from rail cars to reduce tardiness, allows the systemto take advantage of knowledge to guide the search forbetter solutions. However, agents are not limited to runningsimple heuristic algorithms. In the load planning system,for example, we use linear and mixed-integer programming

algorithms to generate initial solutions and to improveexisting solutions.

The A-Team architecture does not define the content of theagents, but only their possible roles and the fact that theycommunicate solely through a shared population ofsolutions. This allows us to make use of the research inoptimization and search which has focused on developingalgorithms for solving particular problems. An A-Team canembody many such algorithms simultaneously. However,agents are more than simply function calls to iterativeimprovement algorithms. They decide for themselves whatto work on, when to work, how often to work, and in aparallel distributed environment, even where to work. Theintelligence for controlling their individual behavior liessolely within the agent itself rather than some centralcontroller

In addition to load planning, A-Teams have been used tosolve nonlinear algebraic equations [TPM83], solvetraveling salesman problems [TS92], configure task-specificrobots [Murthy92], designing high-rise buildings[Quadrel91 ], control electric networks in real-time [TR93],and diagnosing faults in power systems [CT93]. A moredetailed account of how A-Teams support cooperativeapproaches to scheduling may be found in [MRAW97].[HLH97] demonstrates how combining multiple algorithmstogether produces solutions which are preferable to thesolutions generated by individual algorithms operatingalone.

Interactive SchedulingTo illustrate the interactive nature of the IBM load planningsystem, we include two brief scenarios that give typicalinteractions between the scheduler and the system. In thefirst scenario, the scheduler uses the system to create aschedule. We show how the scheduler can inject extra

59

knowledge to guide search and how the scheduler canmodify the problem to allow for good solutions. In thesecond scenario, we show how the scheduling system can beused to answer what if questions and support negotiations.

Typically, schedulers begin each day by updating the load-planning schedule to reflect changes in the productionschedule, in orders, in loading dock capacity and in vehicleavailability. The scheduler starts the load planning systemand it loads the new information from the mill’s logisticssystem. The existing schedule is automatically updated toremove orders that no longer exist and is re-evaluated toshow how well it solves the revised load-planning problem.The scheduler can then have the system generate a set ofalternative solutions. The existing solution is used to seedthe A-Team population and the A-Team agents are run togenerate a new set of solutions. The scheduler is presentedwith the set of non-dominated solutions along the Pareto-Optimal frontier. Suppose the scheduler decides to focus ontwo low cost solutions, and notices that one reducestardiness by placing three small high priority orders intrucks. In order to reduce cost and increase vehicleutilization, the solution also fills each truck with part ofanother low priority order going to the same location. Thescheduler notices that the destination for one of the highpriority orders is on the way to the destination for another.He combines these two orders into one truck to form a dropshipment and discards the loading for the items that wereused to fill the rest of the two trucks. He then re-runs theoptimizer and it packs the unloaded items into partiallyfilled rail cars. The third truck was scheduled to get anorder to a customer by Friday. From the items in the order,the scheduler suspects that it is inventory replenishmentorder used to maintain supply safety levels but notscheduled for immediate use. The priority is high onlybecause it is going to a major customer. Sending the orderby rail will get it there by Monday, three days later, but thenext business day. The scheduler knows that the customerruns the plant 7 days a week, but only logs items intoinventory on weekdays. The scheduler decides to call thecustomer to confirm this suspicion and ask if a delay isacceptable. The customer agrees and the scheduler changesthe due date to Monday. Rerunning the optimizer producesa solution that efficiently packs all the items into rail cars.

In the above scenario, the scheduler has interjectedknowledge to improve the solution and to change theproblem. In many cases, the schedulers have years ofexperience and can recognize opportunities for improving asolution that our heuristic search methods might havemissed. Sometimes these opportunities represent newheuristics that are applicable to a particular mill or customerbut are not appropriate for inclusion in a generic load-planning product. The interactive nature of the schedulingsystem allows the schedulers to make use of theirknowledge without requiring changes to the schedulingsoftware. This interaction also provides opportunities forthe scheduling system to learn from the scheduler.

Unfortunately, we have not had the time to take advantageof this opportunity yet. In addition, buy highlighting thetradeoff between the two low cost solutions, the schedulingsoftware identified a situation where the scheduler couldnegotiate with a customer to change the problem and reducecosts.

In the second scenario, the scheduler receives a call from acustomer service representative who wants to know why acustomer’s order will arrive two days late and why it wasnot put on a truck to get it there sooner. Using the loadplanning system, the scheduler can add a constraint thatforces the order to go by truck and re-run the optimizer.Simply moving the items to a truck would not give theimpacts of the change on other parts of the schedule andwould not allows for optimizations, like adding extra itemsto the truck in order to reduce overall cost. Suppose that theload planning system returns two solutions. The firstsolution gets the order there on time by shipping it today ina truck that is not well suited to the type of product. Thistruck was used because no trucks of the right type areavailable today. Using this type of truck risks damage tothe product. The second solution ships the order tomorrowin a truck of the appropriate type and gets it there one daylate. Sending the order by truck costs an extra $1000. Thescheduler can then use these solutions as a basis forinforming and negotiating with the customer servicerepresentative. If the representative insists on shipping theproduct tomorrow to save a day, the customer servicerepresentative’s name is recorded as authorizing the $ I000expenditure. Providing facilities for track and authorizingdecisions helps improve accountability.

ConclusionsIn this paper, we have presented our approach to computeraided decision making, which recognises that utility modelsare incomplete and relies on human operators to make thesubtle distinctions necessary to resolve tradeoffs. We seedecision making in organizations as a process ofnegotiation that computers can support by supplyingrelevant information and by suggesting good altemativesolutions. Partial utility functions that evaluate a solutionalong a number of incomparable dimensions provide theinformation needed for guiding computer automated searchwhile giving solutions that high light tradeoff for humanschedulers. The use of a standard set of dimensions: time,quality, money and disruptions, and aggregating utilitymeasures within each dimension using a linear weightedsum simplifies the elicitation procedure for deployment inreal systems. Combining our incomplete utility model witha an interactive A-Team based optimizer has resulted inrobust scheduling systems that improve the efficiency andoperating profits of our customers.

60

References[Biermann93] Biermann, C.; 1993. Essentials of Pulping

and Papermaking, San Diego: Academic Press.

[HLH97] Huberman, B., Lukose R., Hogg T.; 1997.An Economics Approach to Hard ComputationalProblems. Science 275 (pp 51-54).

[Murthy92] Murthy S.; 1992. Synergy inCooperating Agents: Designing Manipulatorsfrom Task Specifications, Ph.D. Dissertation,Carnegie Mellon University.

[MRAW97] Murthy S., Rachlin J., Akkiraju R., andWu F.; 1997. Agent-based cooperative scheduling,1997 Workshop on Constraints and Agents (TechnicalReport WS-97-05). Menlo Park : AAAI Press.

[Quadrel91] Quadrel R.; 1991. Asynchronous DesignEnvironment." Architecture and Behavior, Ph.D.Dissertation, Carnegie Mellon University.

[Souza93] Souza P de.; 1993. AsynchronousOrganizations for Multi-Algorithm Problems,

Ph.D. Dissertation, Carnegie MellonUniversity.

[TPM83] Talukdar S.N., Pyo S.S., MehrotraR.; 1983. Distributed Processors forNumerically Intense Problems, (Final Reportfor EPRI Project, RP 1764-3).

[TR93] Talukdar S.N., Ramesh V.C.;1993. Cooperative Methods for SecurityPlanning, 4th International Conference onExpert Systems Application to PowerSystems, Melbourne, Australia, Jan 4-8.

[TS92] Talukdar S.N., Souza P.S. de;1992. Scale Efficient Organizations,Proceedings of the 1992 IEEE InternationalConference on Systems, Man, andCybernetics, Chicago, Illinois, Oct. 18-21.

[TSM94] Talukdar S.N., Souza P. de, Murthy S.;1993. Organizations for Computer-Based Agents,Engineering Intelligent Systems, (1:2).

61