Supply Chain Planning and Control
Q1. Learning Curve
Benson Racing is training a new pit crew for its racing team. For its first practise run, the pit crew is able to complete all the tasks in exactly 30 seconds. On its second attempt the crew improve by 4.5 seconds.
a) Determine the learning rate based on the above timings.
b) It has been determined that the crew should complete all tasks in 15 seconds to be competitive. How many times will the crew need to practise to reach this target?
c) Is it realistic to expect the crew to improve indefinitely?
Q2. Capacity Decisions
Consider the two capacity options for Arktec Manufacturing shown below:
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Annual Fixed Costs
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Variable Cost per Unit
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Option 1
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€500,000
|
€2
|
|
Option 2
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€100,000
|
€10
|
The following are three scenarios identified by Arktec:
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Annual Demand
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Probability
|
|
25,000
|
30%
|
|
60,000
|
40%
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|
100,000
|
30%
|
a) What is the expected value of each option? Which option should be chosen based on these values?
b) If the lowest and highest estimates are updated to 40,000 and 110,000 respectively, what would be the updated expected values? Explain what has happened.
c) Draw the decision tree for Arktec Manufacturing using initial data. You are to assume that a capacity option is chosen before demand levels are known.
d) Calculate the expected value for each branch. Which option would you choose and why?
Q3. Sales & Operational Planning
Flynn Commercial Freezer Ltd. (FCF Ltd), makes commercial and industrial freezers (the kind hotels and restaurants use, and has the aggregate demand requirements for the next six months as given in the table below as are the costs and other necessary data. The firm has regular capacity for 820 units, and overtime capacity for 40 more. Currently, subcontracting can supply up to 100 units per month and this is unlikely to change in the near future.
Month
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Demand
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Costs and other data
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1
|
440
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Previous output level
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460 units
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2
|
480
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Beginning inventory
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0 units
|
|
3
|
520
|
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Stockout cost
|
€800 per unit
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|
4
|
500
|
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Inventory holding cost
|
€400 per unit at end of month
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|
5
|
420
|
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Unit Cost, regular time
|
€1,500 per unit
|
|
6
|
400
|
|
Subcontracting
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€2,100 per unit
|
|
|
|
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Unit Cost, overtime
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€1,800 per unit
|
|
|
|
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Hiring workers
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€200 per unit
|
|
|
|
|
Firing workers
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€500 per unit
|
FCF Ltd is considering one of the following three aggregate plans:
Plan A is to produce level quantity, incurring back orders and inventory charges,
Plan B is to produce a base quantity of 800, using first, overtime, then subcontracting, to meet demand and Plan C, a chase plan, using overtime and then subcontracting if regular capacity is insufficient to cover monthly demand.
The company wishes to minimise costs.
Note: there is no need to start and end on the same output level.
FCF Ltd has asked you to recommend one of the plans. Prepare each of the plans, calculate the costs associated with each plan and make a recommendation.
Q4. Scheduling
(a) A particular operation uses a two-step sequence that all jobs in a certain category follow. For the group of jobs listed below;
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Processing time (minutes)
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Jobs
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a
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b
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c
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d
|
e
|
|
Workstation A
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27
|
18
|
70
|
26
|
15
|
|
Workstation B
|
45
|
33
|
30
|
24
|
10
|
(i) Find the sequence that will minimise the total completion time.
(ii) Construct a progress chart for the sequence of jobs. Clearly identify the amount of idle time at workstation B and the makespan of the batch of jobs.
(iii) What jobs are candidate for splitting? Why? If they were split, how much would idle time and makespan time be reduced? (Assume splitting the jobs in half)
(b) The table below contains information concerning four jobs that are awaiting processing at a work centre.
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Job
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Processing Time (days)
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due date (days)
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|
A
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15
|
28
|
|
B
|
12
|
20
|
|
C
|
8
|
30
|
|
D
|
10
|
26
|
(i) Sequence the jobs using the SPT, EDD and Critical Ratio priority rules.
(ii) For each of the job sequences from part (i) calculate the mean flow time, the mean number of jobs at the work centre, the mean tardiness, the maximum lateness and the number of late jobs.
(iii) Which sequence performs best for this batch of jobs?
Harvard referencing system.