Chapter 5
Modeling Detailed Operations
A Simple Call Center System
With lower
priority than the
sales calls
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Balking
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 test
NR(TrunkLine)<MR(TrunkLine)
NR(TrunkLine): Number of busy resources of TrunkLine
MR(TrunkLine): Capacity of resource TrunkLine
Aside recall: NQ(Rework Process.Queue): Number in queue
of the Process Module named Rework Process.
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Arrival Cutoff Logic
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.
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Priority Queues
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
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Priority Queues
2) 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 Duration
Stop 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
(Hint: Use Expression builder by right clicking on the cell.)
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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 Capacity
1) 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
Dynamic capacity resources have identical skills, schedules!
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Personal Working Schedules
2) 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 Resources
The 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.
Save attribute=Tech Agent Index, attribute holds the index of
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the selected resource.
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
• There can be sets of 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 Costs
Model 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 12:0016:00.
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
+ 12,820
Type 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
counter.
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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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