When is the Objective Function more important than the Constraints, and vice versa?

Let’s start by identifying the two parts to this question, as explained by Heizer & Render (2009):

1)     Objective Function:  “A mathematical expression in linear programming that maximizes or minimizes some quantity (often profit or cost, but any goal may be used)”

2)     Constraints: “Restrictions that limit the degree to which a manager can pursue an objective”

Circumstances where the objective function is more important than the constraints:

A scenario where the objective function is more important can be where the objective is critical to the success of the project in the development phase. Heizer & Render’s (2009, p.591) example of “OM in Action” for Homart Development company illustrates such a situation (book not required, continue reading). For Homart to develop their new mall their objective of attaining 3 “anchor” stores is an important factor in the success of the mall. The anchor stores are the largest stores that will no doubt attract the most customers. It is based on these anchor stores that many other stores will decide to rent in the mall and where they will position themselves in relation to the types/positions of the anchor stores. If the objective function is to get 3 anchor stores as tenants and the constraints are the required square meters floor size and required monthly rental income then if a highly popular anchor store offers to be a tenant with a higher required floor size and a lower required rental, Homart may very well consider taking the offer due to the popularity/benefits of having that anchor store in their new mall.

To state this rule in general terms I would say that where the benefit of the objective outweighs the constraints, or the future success of the project relies upon the objective being met then the constraints may be overlooked.

Circumstances where the constraints are more important than the objective function:

A situation where I would consider the constraints being more important than the objective function would be where the constraints are a valuable commodity that has a limitation that can be considered not-optional. Referring to Heizer & Render (2009, p.599) in their example of Cohen Chemicals (book not required, continue reading) where the organisation had an inventory of highly perishable raw materials that had to be used within the next 30 days to avoid wastage. While there may be situations where wastage of inventory is not an option it should be made high priority to use the raw materials the organisation has already purchased; more so than achieving the objective. In this situation, I am assuming that the outstanding orders have a certain leeway in which production is able to extend beyond the deadline; whereas the deadline for the raw materials to perish is non-negotiable.

The above example can be generally explained as; where the project has constraints that constitute to a greater loss than if the objective is not fully met (eg: needing to get rid of existing stock/inventories).

 

References

Heizer, J. & Render, B. (2009) Operations Management. Ninth Edition. Prentice Hall: New Jersey.

 

Using network diagrams to define your critical path in Project Management and Project Planning

Firstly I would like to introduce the two methods that use the network diagrams to give us a critical path in project management/planning.

1)     Critical path method (CPM)

2)     Program evaluation and review technique (PERT)

The network diagrams are constructed by generally following the steps in project plan. These steps can be considered as:

1)     Breaking the tasks of a project down into a Work Breakdown Structure (WBS), which involves breaking down the project into “its major subcomponents (or tasks)” (Heizer & Render, 2009), followed by breaking down the major components into sub-components and further into activities in which detailed task lists can be defined.

2)     Drawing up a Gantt Chart which represents the tasks on a chart that represents the time each task will take along a timeline, also showing overlaps where tasks may be done simultaneously. This chart will give a good overview of the timeline of activities to complete the project (Heizer & Render, 2009). The Gantt chart is actually one of the 3 alternative options after step 1, but if time permits it may be useful to prepare a Gantt chart as well. The PERT and CPM charts have an advantage over the Gantt charts as they offer a view of the relationships between activities and resources (Heizer & Render, 2009).

3)     The second of the 3 options mentioned in point (2) is to draw up a CPM network. CPM was developed in 1957 by DuPont to address the challenges in shutting down and restarting chemical plants (NetMBA, n.d.). CPM represents tasks in a project as different nodes in a network and links them together based on the beginning and ending of a task (linking the ending of one task to the beginning of another) (NetMBA, n.d.).

4)     The third of the 3 options is the PERT chart. It was developed in the late 1950s for the U.S Navy (NetMBA, n.d.) and tackles the major downfall of the CPM. The PERT chart follows the same steps of the CPM above and is represented in the same graphical method (a network); but takes into consideration the effect of time variations on a projects tasks (NetMBA, n.d.).

The major difference between PERT and CPM is that CPM gives each task (node) only one time estimate and PERT gives each task (node) 3 different time estimates when drawing up the network diagram (optimistic time, most likely time, pessimistic time).

To construct these charts there are 6 main steps involved (NetMBA, 2009):

1)     Identify activities and milestones (i.e. point 1 above)

2)     Identify the proper sequence of each activity (which follows which, etc. could use a Gantt chart of this).

3)     Construct the network diagram.

4)     Mark the time estimates for each activity on the network nodes of the diagram

5)     Determine the critical path

6)     Update the charts as the project progresses..

The critical path can be explained as determining the longest activity path in the project diagram by adding together the amount of time it takes to complete the tasks which rely on each other’s start and finish dates (NetMBA, n.d.). The critical  path measures the full calendar length of a project from start to finish, if tasks outside of the critical path change their timelines (within limits) it should not affect the critical path (NetMBA, n.d). By identifying the critical path we can also identify the amount of time that other paths on the project network can be delayed by without affecting the timeline of the project, this is called the “slack time” (NetMBA, n.d.).

I think it is safe to say that the reason why it’s called the “critical” path is because of the fact that that specific path defines the length that the project is going to take, therefore it is the most important path to monitor.

References

Heizer, J. & Render, B. (2009) Operations Management. Ninth Edition. Prentice Hall: New Jersey.

NetMBA (n.d.) CPM – Critical Path Method [Online]. Available from: http://www.netmba.com/operations/project/cpm/ (Accessed: 14 May 2011).

NetMBA (n.d.) PERT [Online]. Available from: http://www.netmba.com/operations/project/pert/ (Accessed: 14 May 2011).