Development of a new deluxe version of a particular toy is being considered by T-O-Y Inc. The activities necessary for the completion of this project along with the relevant information for each activity are listed in the following table. The Total Crash Time represents the time for that activity after it has been crashed the maximum crash time allowed for that activity. For example, we can reduce the time for Activity A by one week to 3 weeks after crashing it.
| Activity | Time to complete using Normal Time (Weeks) | Time activity is completed using Crash Time (Weeks) | Total Normal Cost | Crash Cost per period | Immediate Predecessors |
| A | 4 | 3 | $2,000 | $900 | — |
| B | 2 | 1 | 2,200 | $800 | — |
| C | 3 | 3 | 500 | $0 | — |
| D | 8 | 3 | 2,300 | $750 | A |
| E | 6 | 3 | 900 | $100 | B |
| F | 3 | 2 | 3,000 | $1,200 | C |
| G | 4 | 2 | 1,400 | $300 | D,E |
a) Using the normal time, what is the critical path, the project completion time, the total time required to finish all of the activities, and the slack time for each path? (The slack time for each path should be relative to the time to complete the critical path.)
b) If you wish to reduce the time required to finish this project by one week, which activity(ies) should be crashed, and how much will this increase the total cost?
c) If you wish to reduce the time required to finish this project by five weeks, which activity(ies) should be crashed, and how much will this increase the total cost?
d) Let’s return to the results found in a). Suppose the company believes that reducing the project completion time from the time reported in part a), will help the company realize an additional $700 per week in revenue for the first two weeks the project time is reduced, $650 per week in revenue for the next two weeks the project is reduced and $500 per week in revenue after that for every week the project is reduced. How many weeks should the company reduce the project completion time and what is the resulting cost of the project considering the additional revenue as an offset to the cost associated with crashing the project? The company is interested in selecting the project duration and reduced activity times that minimize the cost of the project.
In the competitive world of business, timely project completion can often be the key to success. For T-O-Y Inc., a company considering the development of a new deluxe version of a particular toy, managing project timelines efficiently is of paramount importance. In this essay, we will explore various strategies to optimize project time while keeping a keen eye on costs and revenue, ultimately aiming to provide valuable insights to T-O-Y Inc.
To kick off our analysis, let’s delve into Critical Path Analysis. This methodology identifies the critical path in a project network, which represents a sequence of activities that, if delayed, will directly impact the project’s overall completion time. For T-O-Y Inc.’s project, the critical path comprises activities A, D, and G, which collectively take 16 weeks to complete.
Additionally, we identified non-critical paths in the project, where activities have slack time, allowing for flexibility in scheduling without affecting the project’s overall duration.
Optimization Strategy A: Reducing Project Time by One Week
Our first optimization strategy involves a minor time reduction of one week. Activity A, a critical path activity, can be crashed from 4 weeks to 3 weeks at an extra cost of $900, bringing the project duration down to 15 weeks. However, this incurs an additional cost of $900.
For a more substantial reduction of five weeks, a combination of critical and non-critical path activities must be crashed. In this case, we prioritize critical path activities:
Activity A can be crashed by one week, incurring an extra cost of $900.
Activity G can also be reduced by one week at a cost of $300.
To meet the remaining two-week reduction goal, we crash Activity B by one week, costing an additional $800. This reduces the project duration to 13 weeks and incurs a total additional cost of $2,000.
Now, let’s explore a scenario where T-O-Y Inc. seeks to balance project time reduction with potential revenue gains. The company believes that by shortening the project duration, it can generate additional revenue.
For every week the project is reduced, T-O-Y Inc. expects to gain $700 per week for the first two weeks, $650 per week for the next two weeks, and $500 per week thereafter.
In the case of a one-week reduction, the company anticipates an additional revenue of $2,550 while incurring an extra cost of $4,000, resulting in a net loss of $1,450.
Similarly, when aiming to reduce the project duration by five weeks, the expected additional revenue is $2,550, while the additional cost is $4,000, yielding the same net loss of $1,450.
In conclusion, optimizing project time while considering costs and revenue is a delicate balance. T-O-Y Inc. must carefully evaluate the trade-offs associated with time reduction strategies. In both scenarios, the company faces a net loss of $1,450 when considering additional revenue and costs.
Ultimately, it is advisable for T-O-Y Inc. to proceed with the original project timeline of 16 weeks. This decision ensures that the project remains financially viable while meeting the company’s goals. The key takeaway here is that project optimization is not solely about time reduction but also involves a thorough analysis of financial implications.
As businesses continue to navigate the complexities of project management, striking the right balance between time, cost, and revenue remains a critical aspect of decision-making, and T-O-Y Inc. is no exception. By carefully considering these factors, the company can ensure the successful development of its deluxe toy while maintaining a competitive edge in the market.
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