Simulation Model Building from the fourth

racts with its environment\nb) a system that is isolated from its environment\nc) a system with no defined boundaries\nd) a system with flexible goals",
# "113. In project management, the critical path method (CPM) is used to\na) estimate project costs\nb) identify the sequence of tasks that determine the project duration\nc) allocate resources to tasks\nd) manage project risks",
# "114. The process of comparing actual performance with standards and taking corrective action is known as\na) planning\nb) organizing\nc) leading\nd) controlling",
# "115. A 'cross-functional team' is a team that\na) consists of members from different departments\nb) focuses on a single function\nc) is temporary and disbanded after achieving its goals\nd) is formed to deal with external stakeholders",
# "116. Which of the following is a characteristic of an effective leader?\na) Authoritarian approach\nb) Emotional intelligence\nc) Focus on short-term results\nd) Preference for routine tasks",
# "117. The term 'span of control' refers to\na) the number of subordinates a manager can effectively supervise\nb) the scope of authority held by a manager\nc) the range of tasks assigned to a job\nd) the number of departments in an organization",
# "118. The process of evaluating employee performance against established standards is known as\na) performance appraisal\nb) job evaluation\nc) career development\nd) job analysis",
# "119. The technique of dividing work into smaller tasks and assigning them to individuals is known as\na) job analysis\nb) job specialization\nc) job rotation\nd) job enrichment",
# "120. A contingency plan is\na) a long-term plan\nb) a short-term plan\nc) a plan for unexpected events\nc) a plan for day-to-day operations",
# "121. The process of assigning responsibility and authority to subordinates is known as\na) centralization\nb) decentralization\nc) delegation\nd) direction",
# "122. The 'chain of command' refers to\na) the official hierarchy of authority in an organization\nb) the process of delegating tasks\nc) the network of informal relationships\nd) the formal communication channels",
# "123. An organization's mission statement should\na) define its primary purpose and goals\nb) describe its long-term plans\nc) outline its internal processes\nd) list its policies and procedures",
# "124. The main purpose of organizational development is to\na) improve productivity\nb) enhance employee satisfaction\nc) manage change effectively\nd) all of the above",
# "125. 'Job satisfaction' is most closely associated with\na) salary and benefits\nb) working conditions\nc) the alignment of an individual's values and goals with the organization's values and goals\nd) opportunities for advancement",
# "126. The process of comparing the strengths and weaknesses of potential candidates to fill a job vacancy is known as\na) recruitment\nb) selection\nc)

1. SSG517 Systems Simulation Dr K. O. Orolu Department of Systems Engineering, University of Lagos

2. SIMULATION MODEL BUILDING Problem analysis and Data collection

3. Problem analysis and information collection The information is then represented as logic flow diagrams, hierarchy trees, narrative, or any other convenient means of representation

4. AN EXAMPLE: A PRODUCTION CONTROL PROBLEM Consider a packaging/ warehousing process with the following steps: 1. The product is filled and sealed. 2. Sealed units are placed into boxes and stickers are placed on the boxes. 3. Boxes are transported to the warehouse to fulfill customer demand.

5. System Properties/Assumptions Availability of Raw Materials : There is always sufficient raw material for the process never to starve. Processing Time : Processing is carried out in batches, five units to a batch. Finished units are placed in the warehouse. Data collected indicate that unit-processing times are uniformly distributed between 10 and 20 minutes.

6. System Properties/Assumptions (cont’d) Processing Experience : The process experiences random failures, which may occur at any point in time. Times between failures are exponentially distributed with a mean of 200 minutes. Data collection also showed that repair times are normally distributed, with a mean of 90 minutes and a standard deviation of 45 minutes. Warehouse Capacity : The warehouse has a capacity (target level) of R = 500 units. Processing stops when the inventory in the warehouse reaches the target level. From this point on, the production process becomes blocked and remains inactive until the inventory level drops to the reorder point, which is assumed to be r=150 units. The process restarts with a new batch as soon as the reorder level is down-crossed. This is a convenient policy when a resource needs to be distributed among various types of products. For instance, when our process becomes blocked, it may actually be assigned to another task or product that is not part of our model.

7. System Properties/Assumptions (Cont’d)

8. System Properties/Assumptions (Cont’d)

9. Data collection and Input Analysis Data collection is needed for estimating model input parameters. The analyst can formulate assumptions on the distributions of random variables in the mode

10. Int r oduction to Input Ana l ysis Y ou ’ v e made your fl o wcharts, and you h a v e a pretty good idea of all of the processes that customers h a v e to unde r go as th e y m o v e through the system. Y ou ’ v e e v en programmed your model in your f a v orite simulation language. But there ’ s one little hurdle left — proper simulation input analysi s . What distri b utions do you use to model interarr i v al times, service times, breakd o wn times, etc.?

11. What shall we do?

12. Easy Data Ana l ysis Ideas If you ta k e enough obser v ations, the histogram will e v entually co n v e r ge to the true distri b ution. You should a l w ays plot out your data before doing a n ything else. Example: Hist o g r ams.

13. Stem-and-leaf di a g r ams 10 000 9 998764422110 8 9764544321 7 965432100 6 7532 5 433 4 8 A  Stem and Leaf Plot  is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit). These are sort of sid e w ays histograms with numbers

14. Intro to Input Analysis Whi c h Distri b ution?

15. Whi c h Distri b ution, II?

16. Whi c h Distri b ution III?

17. Game Plan

18. Challenges No / Little Data This issue turns up more often than you w ould e xpect. There could literally be no data a vailable, or the data that you h a v e is a wful (goofy v alues, not cleaned properl y , etc.). What to do? No great options — b ut here are some suggestions. Intervi e w so-called “ e xperts” T ry to at least get minimum, maximum, and “most li k ely” distri b ution v alues out of them — then you can guess uniform or triangular distri b utions. Getting quantiles from the e xpert is e v en bette r . At least discuss the nature of the obser v ations.

19. If you h a v e some idea about the nature of the R Vs, maybe you can ma k e a good guess as to the distri b ution. Discrete or continuous? Are obser v ations successes / f ailures? Then think Bernoulli, binomial, geometric, n e g at i v e binomial. Do obser v ations adhere to Poisson assumptions? Then Poisson (if you ’ re counting arr i v als) or e xponential (interarr i v al times). Are obser v ations a v erages or sums? Then maybe normal. Are obser v ations bounded? Then think beta. Reliability or job times? Maybe g amma, W ei b ull, lognormal, etc. Can you think of a n ything else from the p h ysical characteristics underlying the R V?

20. 2. Nonstanda r d / Goofy / Mixture Distri b utions Can attempt to model as a mixtu r e of reasonable distri b utions. Easier: Can sample from the empiri c al distri b ution or a smoothed v ersion of the empirical. This is a form of bootst r apping . Here ’ s a forced marriage of t w o normals — most packages can ’ t pick this up or fit it properl y .

21. 3. Nonstationa r y Data

22. 4. Multi v ariate / Correlated Data

23. Multi v ariate / Correlated Data: W hat do you need to do? Identify mult i v ariate / serial correlation situations. Propose appropriate models. Examples: Mult i v ariate normal for heights and weights. Time series models for serially correlated obser v ations, e.g., autor e gress i v e-m o ving a v erage ARMA( p, q ), EAR(1), A R T O P , . Estimate rel e v ant parameters . Examples: Mult i v ariate normal: Ma r ginal means and v ariances plus c o v ariances Time series: V alidate to see if your estimated model is actually a n y good. Alternat i v e: Can bootstrap samples from an empirical distri b ution (if you h a v e enough data).

24. Using Software

25. Assignment Model and simulate a simple job shop system that produces two types of products, A and B, using three machines, M1, M2, and M3. Each product has a different routing and processing time through the system. Analyze the System with respect to the following: identify input parameters, Determine the performance measures of interest, Identify the relationships among parameters and variables, Identify the rules governing the operation of system components Represent t he information gathered as logic flow diagrams, hierarchy trees, narrative, or any other convenient means of representation. Hence, generate six relevant questions that will provide insight for the simulation of the system.   The Six possible relevant questions could start with: What…? How: …? Why…? Can: …? Does: …? Should: …?