Chapter 5

Modeling Detailed Operations

A Simple Call Center System

With lower priority than the sales calls

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A call is balked, i.e., gets a busy line sound on the phone and rejected from the call center system, if all trunk lines are busy.1)After creation of a call, use a Queue and Seize blocks where the trunk line resource capacity =26 and queue capacity=0. 2)After creation of a call, use a Decide module to testNR(TrunkLine)<MR(TrunkLine)NR(TrunkLine): Number of busy resources of TrunkLineMR(TrunkLine): Capacity of resource TrunkLine

Aside recall: NQ(Rework Process.Queue): Number in queue of the Process Module named Rework Process.

Balking

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No more calls are allowed to enter the call center after 6 p.m., say after 600 min. of the simulation time. Thus no more calls should be created after 600 min.

Arrival Cutoff Logic

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Sales Calls are processed by Sales Resource. Order Status calls may ask to be processed by Sales Resource as well. Then they enter a ‘shared queue’ with Sales calls, where they have lower priority than the Sales Calls.

1)

Use Process Sales Call.Queue

Priority Queues

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Priority Queues2) Default queue ranking rule= FIFO. Others are LIFO, Lowest attribute value, Highest attribute value.

Generate attribute: Sales Call Priority (Default value=0)

=0, if it is a Sales Call;

=1, if it is an Order Status Call that seizes a Sales Resource.

Data Module Queue: Process Sales Call.Queue

Type= Lowest Attribute value

Attribute=Sales Call Priority

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Undefined Simulation DurationStop call arrivals at 18:00 by using Arrival Cutoff Logic;

And continue simulation until all the existing calls at 18:00 are processes

Use Assign to generate a counter WIP: Work in Process

WIP:=WIP+1 when a call can seize a Trunk Line

WIP:=WIP-1 When a call departs from the system

Use Run Set up:

Replication Length=Infinite

Termination Condition = TNOW>=600 &&Total WIP= =0

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Nonstationary Call Rates Model 5.2

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Nonstationary Call Rates Model 5.2

Average call rates differ during the day due to a nonstationary Poisson Process.

Schedule Data Module::

Define average call rates in each hour of a day, name it Arrival Schedule.

Create Call Arrivals:

Time between arrivals: Type=Schedule

Schedule Name=Arrival Schedule

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Dynamic Resource Capacity1) Sales Resource has dynamic capacity.

Schedule Data Module:

Define dynamic resource capacities and name it Sales Schedule.

Resource Data Module:

Resource name= Sales resource

Type=Based on Schedule

Schedule Name= Sales Schedule

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Personal Working Schedules2) Each Tech. Support Resource has his/her working schedule.

Use Schedule and Resource Data modules similar to part (1)

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Multi Skilled ResourcesThe members of the Technical Support resource have multiple skills.

Use Set Data Module to define these resource sets.

Product 1={Charity, Noah, Anna, Sammy, Molly}

Product 2={Tierry, Adrian, Emma, Anna, Sammy}

Product 3={Shelly, Jenny, Christie, Anna, Sammy, Molly}

Use Process Product Type 1 Tech. Call

Resource type=Set, Set name=Product 1

Selection Rule=Preferred Order, i.e., their order in the set defines their preference in getting seized.

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Sets• Group similar objects (resources, sequences,

pictures, etc.) together under a single name• Define: SETS data module from Basic Processes• Refer to objects in a Set by their original name and

by a set index Product 1={Charity, Noah, Anna, Sammy, Molly}

In Arena, Product 1 (2) = Noah.

• An object can be a member of more than one Set (or not be in any Sets) Ex: Anna and Sammy are common in all resource sets

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Sets• Resource Sets

– Allows dissimilar resources to be grouped– Entities can choose among members of a Resource

Set according to preference rules.– Can animate individual Resources in a Set (state,

picture) — unlike Dynamic-Capacity Resources• Sets of entity pictures (can access via part-type number)• In our model: Resource sets: Product 1, Product 2, Product 3 Counter set: Rejected Calls with ten members indicating

the number of rejected calls in each hour

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Trace the number of rejected calls in each hour

• Statistic data module:

Generate 10 counters: Period i Rejected Calls, i=1,2,…,10

• Set data module:

Generate Counter set Rejected Calls with ten members

• Record module

Type=count, Value=1, Record into Set=Check

Counter set name=Rejected Calls

Set Index=AINT((TNOW/60)+1)

Ex: TNOW=90min., 90/60+1=2.5, AINT(2.5)=2

So, Rejected Calls(2)=Period 2 Rejected Calls will be incremented by 1.

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Selecting a Specific Resource

Some technical calls require back office research and return call. A call is processed by the same resource member the next time it is processed again.

Seize Block: Seize Tech Agent Type 1

Selection Rule=Specific Member

Attribute=Tech Agent Index, is created in Process Product Type 1 Tech. Call to keep the index of the previous agent used.

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Adding Staffing and Resource CostsModel 5.3

Current staff costs

Sales staff altogether=45 hr/day x $20/hr x 5days/wk=4,500/wk

Tech Support staff

8 people x 8hr/day/person x $18/hr x 5days/wk=$5,760/wk

1 person x 8hr/day/person x $20/hr x 5days/wk=$800/wk

2 people x 8hr/day/person x $22/hr x 5days/wk=$1,760/wk

Total Cost=$12,820/wk (Model 5.2)

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Adding variable number of staff

Add both sales and technical support during 12:00-16:00.

Variable: New Sales, might be any value

Schedule: Sales schedule

Since New Sales variable will be used in the dynamic capacity, Graphical editor can not be used!

Value (Capacity), Duration=1,2

Value (Capacity), Duration=5+New Sales,1

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Costs of the new resources• New Sales staff cost=

$17/hr x 20hrs/wk = $340/wk/sales-staff

• New Type 1 techs (Larry) cost=

New Type 2 techs (Moe) cost=

New Type 3 techs (Curly) cost=

$16/wk/tech-staff x20 hrs/wk = $320/wk/tech-staff

• New Type all (Hermann) cost=$18/wk/tech-all-staff (capable of all types)

$18/wk/tech-all-staff x20 hrs/wk = $360/wk/tech-all-staff

• Trunk Line cost=$98/wk/trunk line

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Expressions of Model 5.3

• Use Expressions Data Module New Resource Cost = New Sales x 340

+ (New Tech 1+New Tech 2+New Tech 3) x 320

+ New Tech All x 360 + 98 x MR(Trunk Line)

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Variables Data Module• A data module in the Basic Process panel.

• Some parameters of the model can be set as a global variable so that if they has to be modified in the future it will be easier.

Ex: New Sales, New Tech1,2,3,All are variables

• Can be a scalar, vector, or 2-dim. matrix, but any entity can change the value of a variable during simulation.

• Allow re-use of the same number(s) in different places

• Cannot involve arithmetic expressions, entity attributes, other Variables, or distributions.

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Expressions Data Module• A data module in the Advanced Process panel.

• Can be a scalar, vector, or 2-dim. Matrix., but the form of the expression cannot be changed during the simulation

• Aim is to use the same expression in several places in the model

• A fixed “formula” or function that can involve arithmetic, entity attributes, other Variables, and distributions — very general

• Expressions do not store values, name of the expression corresponds to a mathematical expression and its value is returned

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Adding Costs due to Poor Customer Service

• People have limits for waiting on the line 1 min. for Sales calls; 2 min. for Order Status calls

3 min. for Technical calls; • Beyond these limits, system incurs a cost

81.8 cent/min. for Sales calls; 34.6 cent/min. for Order Status calls

36.8cent/min. for Technical calls;

Note: Simulation is run for a day. To estimate the weekly total costs, daily costs are multiplied by 5! So we have $4.09, $1.73, $1.84 as weekly costs per min. excess waiting.

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Expressions of Model 5.3

• Use Assign Module Excess Technical Wait Time= Excess Technical Wait Time + MAX(ENTITY.WAITTIME-3,0)• Entity.Waittime: Built in Arena attribute that holds the total

waiting times of an entity (also the delays in Wait state) Check Costing box in Run>Set up>Project parameters

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Statistic Data Module• New Resource Cost= Excess Sales Wait Time x 4.09 + Excess Status Wait Time x 1.73 + Excess Technical Wait Time x 1.84

+ 12,820Type of statistic=Output Output statistics are computed only at the end of the

simulation and shown in the reports under User Specified. • Percent Rejected= 100 x NC(Total Rejected Calls) /

NC(Attempted Calls) NC is a bult in Arena function that returns the value of the

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Simulation Replication Data

• Project replication parameters– Run/Setup dialog – Replication Parameters tab– 5 Replications of 660 min. each (No stopping condition)– Four options for Initialization Between Replications:

• Initialize system (yes), initialize statistics (yes)– 5 independent and identical replications – no calls carried over– Reports for each day separately

• Initialize system (yes), initialize statistics (no)– 5 independent replications – no calls carried over– Cumulative summary reports (repl. 1, repl. 1-2, repl. 1-3, …, repl. 1-5)

• Initialize system (no), initialize statistics (yes): Selected– 5 continuous days (660 x 5 min.) – calls carried over– Reports are by replication (after each day)

• Initialize system (no), initialize statistics (no) – 5 continuous days (660 x 5 min.) – calls carried over– Cumulative summary reports (repl. 1, repl. 1-2, repl. 1-3, …, repl. 1-5)

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