Posted by Jim Duggan <jim.duggan@nuigalway.ie>
Hi,
I'd be interested in opinions on how best to formulate an equation for Desired Resources in a capacity constrained system. For example, consider a simple two stock system. One of the stocks is ""Backlog"", the other is ""Resources"".
[This could model a service industry such as inland revenue (tax filing) or any labour intensive supply/demand scenario. The backlog is the amount of work remaining, the resources are the amount of available labour, and the productivity is the completion rate for a single resource).]
The resources determine how quickly the Backlog is dealt with, and the size of the backlog determines how many resources are needed (assuming a goal seeking system).
The main equations are:
Backlog = INTEG(Demand - Orders Completed, Init Value)
Demand = Exogenous variable
Orders completed = MIN(Backlog, Capacity)
Capacity = Productivity * Number of Resources
Resources = INTEG (Hire Rate, Init Value)
Hire Rate = (Desired Resources - Resources)/ Adjustment Time + Expected Loss Rate (Stock management structure)
My question is: is the following formulation for Desired Resources adequate...
Desired Resources = Backlog / Productivity
(So for example, if we have a backlog of 1,000 and
the productivity of one resource is 100, then our desired resource value is 1000/100 = 10).
best regards,
Jim.
_________________________________
Dr. Jim Duggan, Chartered Engineer,
Department of Information Technology,
National University of Ireland, Galway,
IRELAND.
Email: jim.duggan@nuigalway.ie
Web: http://corrib.it.nuigalway.ie
Phone: 353-91-493336Posted by Jim Duggan <jim.duggan@nuigalway.ie>
posting date Wed, 02 Nov 2005 16:26:32 +0000
Desired Resource Formulation
-
Jim Duggan jim.duggan nuigalway.
- Junior Member
- Posts: 6
- Joined: Fri Mar 29, 2002 3:39 am
-
Martin Kunc MKunc london.edu
- Junior Member
- Posts: 2
- Joined: Fri Mar 29, 2002 3:39 am
Desired Resource Formulation
Posted by Martin Kunc <MKunc@london.edu>
Jim,
> (So for example, if we have a backlog of 1,000 and
> the productivity of one resource is 100, then our
> desired resource value is 1000/100 = 10).
Not exactly, the value of the resource depends not only on
the actual backlog but also on the demand (the inflow) and
the time you need to clear the backlog. You may hire 10 units to clear your backlog in one month and fire them next month if the demand is zero, or hire 2 units (200 units of capacity) and clear the backlog in 10 months if the demand is 100 units per month (net flow to backlog = -100).
Best regards,
Martin
Martin Kunc
Ph.D. in Decision Science
London Business School
Posted by Martin Kunc <MKunc@london.edu>
posting date Thu, 03 Nov 2005 21:23:25 GMT
Jim,
> (So for example, if we have a backlog of 1,000 and
> the productivity of one resource is 100, then our
> desired resource value is 1000/100 = 10).
Not exactly, the value of the resource depends not only on
the actual backlog but also on the demand (the inflow) and
the time you need to clear the backlog. You may hire 10 units to clear your backlog in one month and fire them next month if the demand is zero, or hire 2 units (200 units of capacity) and clear the backlog in 10 months if the demand is 100 units per month (net flow to backlog = -100).
Best regards,
Martin
Martin Kunc
Ph.D. in Decision Science
London Business School
Posted by Martin Kunc <MKunc@london.edu>
posting date Thu, 03 Nov 2005 21:23:25 GMT
-
Ford David dford civil.tamu.edu
- Newbie
- Posts: 1
- Joined: Fri Mar 29, 2002 3:39 am
Desired Resource Formulation
Posted by ""Ford, David"" <dford@civil.tamu.edu>
Concerning Jim Duggan's question about modeling desired resources...
I have done some modeling of resource demand (desired resources) based on backlog. My work has been in a development project context in which the backlogs change endogenously, but it appears relevant.
Conceptually, I initially note that resources do not get work done. Resources only get work done by being applied over some period of time. We would expect that a single person would work off more backlog in a week than in a day. This points to one potentially confusing issue, the difference between (definitions of) resources and labor, which seem to be equated in Jim's work. I find a need to distinguish between the resource that provides the effort and the amount of effort provided. To facilitate this I often expand ""labor"" into ""labor effort"". Resources has units [fte] or [persons] or perhaps [crews] and labor (effort) has the units [person-days] or [fte-days], etc. and represents the amount of effort that a single resource unit provides in a time unit.
Likewise, resources are only productive over a period of time, and the units are [units/(person-day)], NOT [units/person]. I think that including the application of resources over time is critical to modeling the demand for resources. This raises the question ""How fast do you want the resources to work off the backlog?"" Assuming that resources are the only constraint (which they are not, contact me if you want more about
that...) and that the current backlog sets desired resources (which it probably does not, but contact me if you want more about that one, too!)...we would desire more resources if the target time to work off the backlog (time to some deadline or time available) is shorter. This suggests a desired rate at which the backlog is being worked off. Using work packages [wp] as the product unit, full time equivalent persons [fte] as the resource, and days...
Desired Resource Rate [wp/day] = Backlog [wp] / Time to Deadline [days]
Desired Resource Rate [wp/day] = Desired Resources [fte] / Resource productivity [wp/(fte-day]
This MAY be consistent with Jim's equations, especially if there is a built-in assumption that the backlog wants to be worked off in the next time unit (but is that realistic?)...but I find it difficult to keep this clear without doing the units algebra, even after having modeled this for several years.
Dave Ford
davidford@tamu.edu
Posted by ""Ford, David"" <dford@civil.tamu.edu>
posting date Thu, 3 Nov 2005 09:02:16 -0600
Concerning Jim Duggan's question about modeling desired resources...
I have done some modeling of resource demand (desired resources) based on backlog. My work has been in a development project context in which the backlogs change endogenously, but it appears relevant.
Conceptually, I initially note that resources do not get work done. Resources only get work done by being applied over some period of time. We would expect that a single person would work off more backlog in a week than in a day. This points to one potentially confusing issue, the difference between (definitions of) resources and labor, which seem to be equated in Jim's work. I find a need to distinguish between the resource that provides the effort and the amount of effort provided. To facilitate this I often expand ""labor"" into ""labor effort"". Resources has units [fte] or [persons] or perhaps [crews] and labor (effort) has the units [person-days] or [fte-days], etc. and represents the amount of effort that a single resource unit provides in a time unit.
Likewise, resources are only productive over a period of time, and the units are [units/(person-day)], NOT [units/person]. I think that including the application of resources over time is critical to modeling the demand for resources. This raises the question ""How fast do you want the resources to work off the backlog?"" Assuming that resources are the only constraint (which they are not, contact me if you want more about
that...) and that the current backlog sets desired resources (which it probably does not, but contact me if you want more about that one, too!)...we would desire more resources if the target time to work off the backlog (time to some deadline or time available) is shorter. This suggests a desired rate at which the backlog is being worked off. Using work packages [wp] as the product unit, full time equivalent persons [fte] as the resource, and days...
Desired Resource Rate [wp/day] = Backlog [wp] / Time to Deadline [days]
Desired Resource Rate [wp/day] = Desired Resources [fte] / Resource productivity [wp/(fte-day]
This MAY be consistent with Jim's equations, especially if there is a built-in assumption that the backlog wants to be worked off in the next time unit (but is that realistic?)...but I find it difficult to keep this clear without doing the units algebra, even after having modeled this for several years.
Dave Ford
davidford@tamu.edu
Posted by ""Ford, David"" <dford@civil.tamu.edu>
posting date Thu, 3 Nov 2005 09:02:16 -0600
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Paul Newton plnwtn gmail.com
- Junior Member
- Posts: 3
- Joined: Fri Mar 29, 2002 3:39 am
Desired Resource Formulation
Posted by Paul Newton <plnwtn@gmail.com>
Hi Jim,
First, let me say that I really enjoyed working on the formulation problem you posed! It seems we are getting more and more of these types of questions on the SDList which I think is a good thing.
I think the implausibility of the formulation
Desired Resources = Backlog / Productivity
is first revealed from a units check.
Units for the equation:
runit = bunit / ( ( bunit / month ) / runit )
yields
runit = runit / month
which is not true. (Note: runit = resource unit, bunit = backlog unit)
In real modeling practice, to paraphrase John Sterman from his Business Dynamics book, it seems to me that we should ask the people who establish desired resources what information cues they use to determine desired resources and how they use them to do so, and then we should convert their natural language description into algebra. However, since your question is really asking for plausible formulations, here is one suggestion that passes a units check:
(1) desired resources = desired steady state order completion resources + desired backlog adjustment resources
Units:
runit = runit + runit
(2) desired steady state order completion resources = Expected Demand Rate / resource productivity
Units:
runit = ( bunit / Month ) / ( ( bunit / Month) / runit )
Comment: By ""desired steady state order completion resources"" I mean the desired number of resoures required to process the expected steady state incoming order rate.
(3) Expected Demand Rate = SMOOTH(demand rate, demand rate expectation
delay)
Units:
bunit / Month = bunit / Month
(4) desired backlog adjustment resources = - desired backlog adjustment rate / resource productivity
Units:
runit = bunit / Month / ( ( bunit / Month ) / runit )
Comment: A negative sign is required here because, for example, if the Backlog is greater than the desired backlog, the desired backlog adjustment rate is negative, thus requiring more (positive) resources to reduce the Backlog to the desired backlog level.
(5) desired backlog adjustment rate = ( desired backlog - Backlog ) / desired time to adjust to desired backlog
Units:
bunit / Month = ( bunit - bunit ) / month
Not related to your specific question, there is also a units mismatch in the following equation from your email:
Orders completed = MIN(Backlog, Capacity)
Units:
The unit of <orders completed> is <backlog units / time unit> The unit of <Backlog> is, well, <backlog units> (say, bunits, as above) The unit of <Capacity> is <( backlog units / time ) / capacity unit>
A better formulation can be found in Sterman's Business Dynamics text in Section 13.3.1, an example of which is something like the following:
(6) order completion rate =MIN ( capacity , maximum order completion rate )
Units:
bunit / Month = MIN ( bunit / month , bunit / month )
(7) maximum order completion rate = Backlog / minimum time to complete one unit of backlog
Units:
bunit / Month = bunit / month
Criticisms welcome!
Paul Newton
Ithaca, NY
plnwtn@gmail.com
Posted by Paul Newton <plnwtn@gmail.com>
posting date Thu, 3 Nov 2005 10:44:48 -0500
Hi Jim,
First, let me say that I really enjoyed working on the formulation problem you posed! It seems we are getting more and more of these types of questions on the SDList which I think is a good thing.
I think the implausibility of the formulation
Desired Resources = Backlog / Productivity
is first revealed from a units check.
Units for the equation:
runit = bunit / ( ( bunit / month ) / runit )
yields
runit = runit / month
which is not true. (Note: runit = resource unit, bunit = backlog unit)
In real modeling practice, to paraphrase John Sterman from his Business Dynamics book, it seems to me that we should ask the people who establish desired resources what information cues they use to determine desired resources and how they use them to do so, and then we should convert their natural language description into algebra. However, since your question is really asking for plausible formulations, here is one suggestion that passes a units check:
(1) desired resources = desired steady state order completion resources + desired backlog adjustment resources
Units:
runit = runit + runit
(2) desired steady state order completion resources = Expected Demand Rate / resource productivity
Units:
runit = ( bunit / Month ) / ( ( bunit / Month) / runit )
Comment: By ""desired steady state order completion resources"" I mean the desired number of resoures required to process the expected steady state incoming order rate.
(3) Expected Demand Rate = SMOOTH(demand rate, demand rate expectation
delay)
Units:
bunit / Month = bunit / Month
(4) desired backlog adjustment resources = - desired backlog adjustment rate / resource productivity
Units:
runit = bunit / Month / ( ( bunit / Month ) / runit )
Comment: A negative sign is required here because, for example, if the Backlog is greater than the desired backlog, the desired backlog adjustment rate is negative, thus requiring more (positive) resources to reduce the Backlog to the desired backlog level.
(5) desired backlog adjustment rate = ( desired backlog - Backlog ) / desired time to adjust to desired backlog
Units:
bunit / Month = ( bunit - bunit ) / month
Not related to your specific question, there is also a units mismatch in the following equation from your email:
Orders completed = MIN(Backlog, Capacity)
Units:
The unit of <orders completed> is <backlog units / time unit> The unit of <Backlog> is, well, <backlog units> (say, bunits, as above) The unit of <Capacity> is <( backlog units / time ) / capacity unit>
A better formulation can be found in Sterman's Business Dynamics text in Section 13.3.1, an example of which is something like the following:
(6) order completion rate =MIN ( capacity , maximum order completion rate )
Units:
bunit / Month = MIN ( bunit / month , bunit / month )
(7) maximum order completion rate = Backlog / minimum time to complete one unit of backlog
Units:
bunit / Month = bunit / month
Criticisms welcome!
Paul Newton
Ithaca, NY
plnwtn@gmail.com
Posted by Paul Newton <plnwtn@gmail.com>
posting date Thu, 3 Nov 2005 10:44:48 -0500