Chapter 5 Modeling Detailed Operations

MIS 463-Asli Sencer An Automative Maintenance and Repair Shop Current location is in downtown. Additional three-bay facility is to be built in suburb. Appointments for both locations will be from downtown. In the suburb, appointments can be made upto 3 working days in advance. If a customer is unable to schedule an appointment during this period, they call back the next day or may schedule the work to be performed in downtown. Customer arrivals follows a stationary poisson process with mean rate 29 calls/day.

MIS 463-Asli Sencer 55% callers asks an appointment for the next day, 30% for two days after 15% for three days after If an appointment can not be scheduled in the chosen day, 90% will ask to schedule for the following day. 80% customers leave their car the entire day 20% wait with car and they are given an approximate waiting time=book time(i.e., approx. Serv. Time)+1hr. Book time distr. is (44+90*BETA(2,3)) Actual Service time distr. is GAMM( Book time/1.05,1.05) No more than 5 appointments for waiting customers/day! The number of appointments/day is limited by max. book time hours scheduled/day=8 hrs/day/bay max. actual service time scheduled/day=24 hrs/day

MIS 463-Asli Sencer ● Assume 5 workdays/week/bay and 8 hrs/day Capital and labor Cost =$45/hr for each bay Customer charge=$78/hr * book time ● To compensate for the service time variability, each service bay can stay open at most 3 extra hrs/day. The overtime cost=$120/hr for each bay If an already-started service can not be completed in that day, it will be completed the next day and customer will be provided a loaner vehicle. Loaner vehicle cost=$35/day If the service can not be even started for a vehicle on its scheduled day, the customer takes his car and brings it the next day. No loaner vehicle is given in this case. ● Every day, the first hr is used to allocate future appointments, so resources are not available!! Cost Issues

MIS 463-Asli Sencer Required Statistics Daily profit Daily Book Time Daily Actual Service Time Daily Overtime Daily number of wait appointments not completed on time.

MIS 463-Asli Sencer SETS ●Group similar objects (resources, sequences, pictures, other) together under a single name ●Define: Sets module from Basic Processes ●Refer to objects in a Set by their original name and by an index Ex: Operators{Lynn, John, Sue}, In Arena, Operators(2)=John ●An object can be a member of more than one Set (or not be in any Sets) Ex: Setup{Lynn, Fred}, Lynn is common in both sets ●There can be sets of sets

MIS 463-Asli Sencer Sets (cont.’d) ●Perhaps the most common Sets: Resources Allows dissimilar resources to be grouped — more general than multi-Capacity single Resources, where they all have to be identical Entities can choose among members of a Resource Set according to preferences, rules Can animate individual Resources in Set (state, picture) — unlike multi-Capacity single Resources ●Also group entity pictures into sets for ease of access (via part-type number) ●In our model: Define resource set:Bays {Bay1, Bay2, Bay3} Define entity picture set: Customers{Picture.red entity, Picture.blue entity} Define vehicle picture set: Vehicle {Picture.red car, Picture.blue car}

MIS 463-Asli Sencer Variables 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: Transfer time in model 4.2 can be a variable ● 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. ● In our model: Define “Day” variable to keep track of the current day of the week.

MIS 463-Asli Sencer Expressions 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 Similar motivation to Variables — re-use the same “thing” 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 In our model: Define expressions to generate the Book time, the actual service times, type of appointment request (wait or leave)

MIS 463-Asli Sencer Submodels Large models can be partitioned into smaller models by submodels, which may or may not interact. In our model: Generate appointment calls, Make appointment Service activity Update performance variables Control logic

MIS 463-Asli Sencer Batching and Seperating Entities Use Batch and Seperate in basic process panel to create dublicate entities ● Often used as control enities that can perform variety of functions. ● Batch of entities, then split the batch ● In our model: Dublicate entities to represent the incoming calls requesting appointments.

MIS 463-Asli Sencer Holding Entities ●Hold entities at some place until a specified condition is satisfied. Two different methods: ●Hold and signal modules ●Hold the entity until a signal to proceed is sent by another activity. ●Hold entities until some condition exists ●In our model: entities will be held until the day of scheduled service.

MIS 463-Asli Sencer Simulation Replication Data Project replication parameters Run/Setup dialog – Replication Parameters tab 10 Replications of 20 days each Four options for Initialization Between Replications: Initialize system (yes), initialize statistics (yes)  10 independent and identical replications – no calls carried over  Reports for each day separately Initialize system (yes), initialize statistics (no)  10 independent replications – no calls carried over  Cumulative summary reports (day 1, days 1-2, days 1-3, …, days 1-10) Initialize system (no), initialize statistics (yes): Selected  200 continuous days – calls carried over  Reports are by replication (after each 20 day) Initialize system (no), initialize statistics (no)  200 continuous days – calls carried over  Cumulative summary reports