5.1
Chapter 5: Systems models and diagrams Exercise solutions for Management Science, ISBN 1-4039-4174-2 © H.G. Daellenbach and D.C. McNickle, 2005. Palgrave Publishers Ltd. Note that in this, as well as chapters 2, 3, 4, 7, 8, 9 and 15, some of the exercises have no simple, clearcut answers. There are legitimate alternative view and resolution levels. 1.
Process approach (as for instance needed for analysing the problem by simulation): Before starting, we need to place the problem in its context and make tentative boundary judgements. In this case the emphasis is on the telephone system, not the entire operation of the emergency service centre, hence all processes of dealing with emergencies once a call has been answered are assumed given. Since loss of life, etc., is also affected by things beyond the control of the centre, we shall use the average waiting time of caller as the measure of performance. We answer the four questions in Table 5-1 on page 86 for each aspect/item. Number of operators on duty for each (small) time interval: control input. Number of lines available to be put on hold: (infinite) irrelevant. Incoming calls: system components. Character of incoming calls: (ignored) irrelevant. Incidence/arrival rate of incoming calls over time: uncontrollable input. Total number of calls over a given time interval: system component. Time to service each call: system component. Service time distribution to deal with an incoming call: uncontrollable input. Waiting time of each incoming call: system component. Average waiting time for incoming calls over time interval: output. Waiting time distribution: output. Const/wages of operators and all other cost factors: uncontrollable inputs. All other equipment: (not constraining) irrelevant. Number of calls lost over a given time interval: output. Total idle time of operators over a given time interval: output. Total time on duty of operators: system component. Total relevant operating cost: output. Statistics on loss of life, injury, damage: (ignored) irrelevant. For waiting time situations, a structured approach using well-known queueing models is usually simpler and often adequate.
2.
The viewpoint taken is the one of the Government. Mortality rate from breast cancer: by (2) an output. Total cost of policy/year: by (2) an output. Number of women in each age group: by (1) an input. Rate of breast cancer for each age group: by (1) an input. Rate of progression of cancers from benign to malign: by (1) an input (may be age dependent). Mortality rate for malign cancers: by (1) an input (may be age dependent). Decision on number of machines: by (1) an input, i.e., a control input. Decision on frequency of screening: by (1) an input, i.e., a control input. Decision on age range of screening: by (1) an input, i.e., a control input. Average number of cancers diagnosed by screening program, grouped as benign and as malign (by age of diagnoses): by (3) a component. Average number of women dying from cancers (by age of diagnoses): by (3) a component. Average cost per instance of treating benign/malign cancers: by (1) an input. Average cost of screening: by (1) an input. Average cost of machine, including installation and initial training: by (1) an input. Total investment in equipment and initial training: by (3) a component. Total cost of screening operation/year: by (3) a component. A more extensive analysis might also include the potential loss of earnings of women dying. Hence additional inputs and outputs would be relevant.
5.2
3.
Causal-loop diagram of blood bank operation.
4.
Causal loop diagram for breast cancer screening problem (entries in italics assume background in discounting, hence optional).
5.3
5.
Causal loop diagram for NuWave Shoes.
Main difference with cognitive map: causal loop diagrams are concerned with how controllable and uncontrollable system inputs and the structure and processes of a system affect system outputs/outcomes, by tracing all effects through system components and variables, or what aspects/events cause a change in the system. For NuWave Shoes it traces mainly financial consequences. On the other hand, Elly’s cognitive map also expresses her personal preferences and perceptions, i.e., how she views various aspects. 6.
Causal loop diagram for unemployment, poverty, and public health interactions.
Note there are four feedback loops, several of which are positive or reinforcing.
5.4
7.
Influence diagram for Lim’s problem.
8.
Influence diagram for breast cancer screening problem, as seen from a public service point of view.
5.5
Boundary judgements: 1. Mass screening of population outside age range chosen considered ineffective (or economic concerns about financial equipment and operating costs take precedence over mortality). 2. A high majority of women are willing to participate in scheme. 3. Medical side-effects (increased incidence of cancer) of screening non-existent or ignored. 9.
Influence diagram for blood bank operation.
One day later feedbach loop
10. Material flow chart for electric toothbrush manufacture.
5.6
11. Material flow chart for commercial bread making.
12. Precedence chart for kite kits making.
One-person time: (sum of all task times) 23 Two-person time: (first: A, B, F, G, H; second: C, D, E) 16 However, if many kites are produced, then person 1 repeats A, B, F, G (total 12), while person 2 repeats C, D, E, H (total 11). If they alternate doing G, then both have 1 minute idle every second kite. Note that the repetitive time cycle is shorter than the critical path A-B-F-G-H.
5.7
13. Decision flow chart for buying a second-hand car.
14. Spray diagram for small pleasure boat fatality.
