lecture 6 : hard or
• classifications of problem situations
• functionalist, interpretive and
emancipatory systems approaches
• hard OR, hard ST
– formulation
– modelling
– implementation
• example : the LOD project
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Jackson & Keys’ classification of problem situations:
divergence of values and interests
unitary
weak
strong
systemicity
hard OR
hard OR/ST
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pluralistic
conflicting
soft ST
soft OR/ST
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(emancipatory st
critical ST etc.)
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it is useful to distinguish between ways that complexity
acts in, the three dimensions of complexity:
1. technical complexity
e.g. in pickup and delivery vehicle scheduling there is a huge
number of courses of action
2.probabilistic complexity ie. uncertainty
e.g. in the same problem situation demands and traffic
congestion are not known in advance
3. purposive complexity ie. diversity of interests
and values
e.g. in screening for breast cancer there will be conflicting
objectives among stakeholders
another example:
greenhouse gases causing global warming: high degree of
complexity in all three dimensions
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• Figure 1 shows the 3-dimensional space of
problem situations
• three zones Z1, Z2 and Z3 are shown, enclosed
by thick-gray boundary lines
• the relative size of these zones do not indicate
the level of complexity of the problem situation,
• for example a situation that falls into Z3 can
involve a degree of probabilistic complexity as
high as that of a situation that falls into Z1
• the size of each zone indicates the type of
systems thinking that is more suitable for the
problem situation of interest
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probabilistic
complexity
Z2
Z1
Z3
purposive
complexity
technical
complexity
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• functionalist ST can deal with technical
and probabilistic complexity much more
effectively than it can deal with
purposive complexity
• hence the boundaries of Z1 extend
further along the technical and
probabilistic axes, implying that we have
the possibility of using quantitative
techniques and mathematical models
when inquiring into situations that can be
addressed by functionalist ST
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• functionalist ST can deal with technical
and probabilistic complexity much more
effectively than it can deal with
purposive complexity
• hence the boundaries of Z1 extend
further along the technical and
probabilistic axes, implying that we have
the possibility of using quantitative
techniques and mathematical models
when inquiring into situations that can be
addressed by functionalist ST
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• interpretive ST can deal with
– technical and probabilistic complexity to a
lesser extent,
– whereas it can deal with purposive
complexity to a greater extent
than functionalist ST can
• hence the boundaries of Z2
– extend further along the purposive axis
– but not along the technical and probabilistic
axes
compared to the case of functionalist ST
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• emancipatory ST is suitable for problem
situations lying far out on the purposive axis;
these are situations involving irreconcilable
conflict (emancipation means freedom from legal,
social, or political restrictions)
• such situations can also involve
– high levels of uncertainty and
– a certain level of technical complexity
– but purposive complexity is so dominant that the
priority in emancipatory ST is on conflict, rather
than on technical and probabilistic aspects; that is
why Z3 is drawn smaller
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probabilistic
complexity
Z2
Z1
Z3
purposive
complexity
technical
complexity
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functionalist systems approaches
• subject-object duality assumed to hold in general
• systems regarded more as out-there, ontological
constructs
• different points of view about the system are allowed
• there can be multiple objectives but they are
reconcilable; therefore there is a common goal
• the question is not what to do, it is how to do it
• widespread applicability in situations involving
– high technical complexity, and
– managable uncertainty (eg. when probability distributions are
available)
• hard OR, systems engineering, systems
analysis, cybernetics
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interpretive systems approaches
• systems regarded more as epistemological
constructs
• there are multiple objectives that are not
necessarily irreconcilable
• hence the question is more about what to do, and
less about how to do it
• so technical complexity and uncertainty are less
relevant and are not handled routinely
• the goal is to learn about the system so that
shared commitment to action becomes possible;
even though values may not be shared
• soft OR
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emancipatory systems approaches
• systems regarded as epistemological constructs
• essentially different system conceptualisations by
stakeholders
• so boundaries are subject to disagreement
• there are multiple, irreconcilable objectives
• the question is all about what to do
• full emancipation is often not possible since positions
of power will not be given up willingly
• coercion may leave no possibility except conflict,
passive resistance and disobedience
• technical complexity and uncertainty are much less
relevant than conflict
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• hard OR and hard systems thinking in general
are functionalist approaches
• the traditional applications of IE are often
based on the hard, functionalist approaches
• soft OR and soft systems thinking in general
use interpretive and in some cases,
emancipatory approaches (only a few
emancipatory methodologies have been developed,
applicability is limited since such situations are very
complex)
• soft approaches are mostly experiential, they
can only be developed and learned through
practice
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the hard OR paradigm assumes that:
1. the problem has been clearly defined, implying that
– the objectives of the decision maker are known and there
exist criteria to see when they have been achieved,
– even if there are conflicting objectives, tradeoffs can be
defined,
– the alternative courses of action are known, as a list of
options or a set of decision variables,
– the constraints on the decision choices are known, and
– the input data needed is available;
2. the problem is relatively well structured, meaning that
– the relationships between the variables are known
– system behaviour can be captured in mathematical models,
– the computational effort for determining solutions is
economically feasible;
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3. the problem can be sufficiently well insulated from
its wider system, ie. boundary setting is relatively
straightforward
4. optimisation of the objectives, whenever possible,
is the ideal
5. the problem is of a technical nature, free of
politics; people are mainly seen as passive objects
6. if there are multiple stakeholders, a consensus
can be reached about how objectives can be
achieved
7. the decision maker has the power to implement or
enforce the implementation of the solution
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• the figure implies that hard-OR is not all hard:
• the formulation phase (involving issue and
problem structuring) and the implementation
phase (involving human considerations) relate
to ontological aspects, that are qualitative
and messy
• the modelling phase relates to epistemological
aspects that accepts quantification
• this means that the hard/soft, or the
functionalist/interpretive distinction is not as
distinct as black/white; both will be relevant in
the same problem situation
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formulation
• this phase either involves formulation directly (for
example if the problem owner is doing the inquiry
herself), or it may involve some preliminary problem
scoping first
• problem scoping may produce a project proposal
• formulation requires full definitions of the narrow
and the wider systems, often aided by influence
diagrams
• such a proposal should discuss whether:
– a quantitative approach is feasible
– data is available
– the project is cost-effective
as openly and honestly as possible
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modelling
• this phase involves the hard aspects of OR
• if the situation fits a well-known structure, a
structural approach can be followed in modelling; eg.
using a known LP model for production planning, or a
known DP model for equipment replacement
• otherwise a process approach will be needed,
building the model from scratch; this is the more
usual case
• an influence diagram can be constructed to help
modelling:
– if technical complexity is not very high, a low scale,
– otherwise a high scale diagram can be used at the start
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•the model should have as many of the
desirable properties of “good” models as
possible
•most importantly the model must have:
–internal validity; meaning that the model is
logically and mathematically correct and complete;
internal validity should be tested logically and
numerically and as early as possible
– and external validity or generalisability meaning
that the model must be representative of reality,
that its findings must make sense in respect of
applications;
ensuring external validity is problematic; but showing
that the model is not externally valid is possible
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• concepts such as validity and reliability are
fundamental also to research design, and to
measurement in all sciences
• validity is about measuring what we want to
measure and not something else
• in experimental sciences the internal validity of
an experimental design ensures that an
observed effect (ie. ∆y) is indeed the result of
a certain cause (ie. ∆x) and not that of some
other cause; ie. if y = f(x,w,z, ...), then we must
make sure that
∆y = f(x+∆x,w,z, ...)-f(x,w,z, ...)
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• (note that we do not know how many variables
x,w,z, .. there are that affect y)
• validity would be assured if we could exercise
complete control over measurement
• control means that all other possible causes are
kept unchanged (∆w = ∆z = ... 0)
• this may be possible in a laboratory
• if there is no laboratory, what we can do is to
apply the stimulus ∆x > 0 to an experimental
group and the stimulus ∆x = 0 to a control
group that are two random samples selected
from the same population
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• in this way the effects of ∆w > 0, ∆z > 0 etc...
will cancel out between the groups as we test
the difference ∆ye -∆yc, where:
∆ye= f(x+∆x, w+∆w, z+∆z, ...)-f(x,w,z, ...),
∆yc= f(x, w+∆w, z+∆z, ...)-f(x,w,z, ...)
since the groups are members of the same
population and will be affected in the same way
• the relationship established between x and y in
this way will be nonspurious
• experiments conducted with control groups are
said to have strong designs, ie. their internal
validity is assured
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• hence the controlled experiment is the most
powerful research instrument in science
• experimental designs will be weaker if there is
no control group)
• in some disciplines experimentation is normally
not possible with or without control groups;
hence disciplines such as economics have to
rely on much weaker research designs with
limited validity
• the internal validity of models that are used in
economics, in OR or IE is restricted to logical
and mathematical correctness
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• external validity is about the
generalisability of research findings
• even when a nonspurious relationship is
established between x and y under
laboratory conditions, the relation can fail
to hold under real world conditions where
all the other variables w, z, ... are
simultaneously changing
• outside a laboratory, the concern is about
the representativeness of samples; (samples
may not be truly random or of sufficient
size)
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• the presence of reactive arrangements
such as the Hawthorne effect is another
concern for external validity
• in general there is no definite way to
ensure the external validity of research
designs or of mathematical models
• hence generalising research findings to
real world situations is always
problematic and requires caution, (if we
do not want to end up in bullshit)
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• reliability is another key attribute of research
design and of measurement
• reliability is about stability, or about the absence
of random errors in measurement
• a reliable measurement may not be valid
• the reliability of mathematical models is usually
not a problem since a model will produce exactly
the same output when the same input data set is
used
• however we should know how sensitive model
results are to input data
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• sensitivity analysis is a very important step in
hard OR, helping to question,
– model robustness and vulnerability to errors,
as well as
– the external validity of the model
• modelling should end with the submission of a
project report complete with findings,
recommendations, an account of the strong and
weak parts of the inquiry and all supporting
evidence that is necessary
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implementation would involve
steps such as:
– planning the implementation
– establishing control over the solution
(ie. when is it necessary to update the
current solution and why?)
– implementing
– auditing (ie. monitoring and
evaluation)
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the LOD case study
• this is a simple application of hard OR that illustrates
the first seven steps of Figure 6-1
• LOD manufactures and sells 400 types of lubricants in
containers to over 1000 customers made from refinery
products
• auditors report that LOD stock turnover averages 12 per
year, well below the company target of 24
• the vice-president for finance brings this to the
attention of the VP for production, who then asks the
LOD manager to deal with this issue
• the manager of the LOD then seeks advice from the OR
team at company headquarters and a preliminary
(scoping) study is initiated
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• the rich picture indicates a number of issues:
– batch size and cut-off levels can be adjusted for better
turnover
– current service level can also be adjusted for better turnover
• VP-Finance & LOD Manager share the common W:
– make efficient use of LOD resources, ie. minimise costs
• VP-Finance thinks:
– speed-up stock turnover --ie. reduce inventories -- save from
capital costs
• LOD Manager thinks:
– consider also the set-up costs
– maintain current service quality
• the narrow system is defined as the LOD productioninventory system, the wider system is the LOD
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the six elements of the problem are:
• immediate decision maker: the LOD manager.
• objective: achieving low operating cost for the LOD's
operation subject to maintaining the same level of
customer service
• performance measure: the total operating costs of the
LOD.
• decision criterion: minimising total costs
• alternative courses of action: (i) adjusting stock
replenishment batch size and (ii) adjusting the cutoff
point separating big and small orders
• wider system of interest: the LOD operation and the
Sandpoint refinery
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• problem scoping -- rather than a full
formulation -- was the first step
• boundary judgements:
– orders and facilities lie outside the wider system
• sharing equipment and depot capacity by different products
assumed independent at the beginning
• investing in equipment and depot capacity is not an option
• demand management is not an option
– these are not strictly true but permissible, as long as
reconsideration of boundaries remains an option
– in fact any solution produced by the LOD study is likely to
affect facilities and customers
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• a project proposal is submitted
– to justify a prelimiary work on a
sample of products,
– because data collection for a full scale
study is costly and therefore needs to
be justified,
– and since it would be easy to extend
the preliminary work into a full scale
study
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PROJECT PROPOSAL
PRODUCTION INVENTORY CONTROL STUDY LUBRICATION OIL
DIVISION, SANDPOINT REFINERY
Table of Contents
1. Introductory statement
2. Executive summary ofrecommendations
3. Statement of the problem situation
4. Brief description of proposed analysis
5. Resources required and time-table
1. INTRODUCTORY STATEMENT
In the middle of March, Mr Black, Manager of the LOD, approached the Management
Science Group at the Company's Headquarters with a request to study the LOD
production/inventory operations of packaged goods and make recommendations concerning
appropriate stock levels. It is my understanding that this request is a follow-up on remarks
in the Company's internal auditors' report about the current level of investments in stocks
at the LOD. In particular, the auditors pointed out that the LOO's stock turnover of
packaged goods was well below the Company's target of24 times per year, resulting in a
level offunds tied up in packaged goods judged as excessive.
I arranged for a visit to the LOO's production and warehousing facilities at Sandpoint on
March 27 and 28, during which 1 had extensive discussions with Mr Black, Mary C1arke, the
stock control clerk, Bill Quick, the data processing supervisor, and all four operations
supervisors. I also consulted with the Cost Control Department at Headquarters. The
following report outlines my recommendations for a preliminary study, briefly motivates
and describes the proposed analysis, and lists the resources required and a time-table for
undertaking the study.
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2. EXECUTIVE SUMMARY OF RECOMMENDATIONS
It is recommended that the Company's Management Science
Group undertakes a preliminary study of the production/inventory
operations. The study would develop a model for finding optimal
stock replenishment sizes as well as the minimum size when it
becomes more economical to meet individual customer orders by
a separate mixing and filling run. Based on this model. reliable
estimates of the potential savings in operating costs can be
computed with the aim of establishing whether a full-scale
investigation can be justified. The results of the study would be
available within 4 weeks and the internal charge to the LOD
would amount to $6,400.
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3. STATEMENT OF THE PROBLEM SITUATION
The auditors' report states that the LOO's stock turnover rate over the last
two years averaged 12 times per year and hence is well below the
company's target rate of 24. As a result, they conclude that the amount of
funds tied up in stocks is about twice as high as it should be.
What are the cost implications of a given stock turnover rate? For the
current customer deliwry policy and production lead time, the average
amount of funds tied up in stocks and hence the cost of carrying this
investment for any given product, is proportional to the size of its stock
replenishment batches. On the other hand, the annual production setup
cost is inversely proportional to the size of replenishment batches. Any
reduction in average stock levels and the annual cost of carrying the
corresponding investment can therefore only be achieved by increasing
the annual production setup cost. It can easily be shown that there is a
best size for each replenishment batch for which the sum ofthese two
costs is at its lowest possible level. This also implies a best turnover rate
for each product, which is likely to be different from product to product.
Only by coincidence will the average turnover rate over all products be
equal to the target rate of 24. A target turnover rate of24 may thus not
achieve the lowest total cost for the LOD operations.
¨¨
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4. BRIEF DESCRIPTION OF PROPOSED ANALYSIS
The preliminary analysis will be done for a random sample of products. Its results will be
extrapolated to all products carried by the LaD. The following major steps are involved:
(a) Development of model: After further on-site study, a model for the total annual relevant cost.
suitable for use on all products carried by the LOO, will be developed. It will be used for
detennining the best combination of stock replenishments and cutoff point for special production
runs for each product. The objective is to minimize the total annual operating costs. The model
will be in the form of a computer spreadsheet.
(b) Sample selection and data collection: With a view to increasing the accuracy of potential
sayings estimates for the new policy, products will be grouped according to annual sales and a
representative sample selected from each, making up about 5% of all products. Demand and cost
data will be estimated for all products in the sample using readily avaiJable data from the LOO
data base of customer orders and costing data from the Cost Control Department.
(c) Estimation of total saving: The total annual operating cost for the best policy will be
determined individually for each product in the sample. These costs will be extrapolated for each
product group and finally to the entire product line. This extrapolation is an estimate of the total
annual cost of using the best policy for all products. This estimate will be compared with the
annual costs incurred for the current policy. The difference represents the potentia] annual
savings. No change in the expected office costs of running the new policy is expected.
(d) Estimation offurther expenses for a full-scale study: The expense in terms of internal employee
charge-out rates, materials, and computer running costs for undertaking a fullscale study will be
estimated.
(e) Forming of recommendations and preparation of project report: The recommendation will state
whether a full-sca]e study should be undertaken, based on the norma] company criterion that all
expenses for such a study must be recovered by the savings generated within one year of
implementation of the recommendations. If appropriate, the project report "'ill also present a
detailed budget of resources needed and a timetable for undertaking the full-scale study.
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5. RESOURCES REQUIRED AND TIMETABLE
Task
Analyst time
Other staff time
Elapse time
Model dewlopment
2 days
I day (LOO staff)
2 days
Sampling design
1 days
2 days (LOO staff)
4 days
Data collection
4 days
3 days (cost control)
8 days
3 days (LOO staff)
Savings estimates
2 days
1 day (cost contra])
4 days
2 days (LOO staff)
Writing recommendations 3 days
Totals
12 days
4 days
4 days (cost control)
22 days
8 days (LOO staff)
Chargeable costs: 12 days at $400/day
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the LOD model:
consider first the batch-size problem, assuming the cutoff point L is held constant :
min T(Q) = 0.5Qvr + (sD1/Q) + h1D1 + vD1
therefore the EOQ is : Q* = (2sD1/vr)½
D1 is that part of the total annual demand D = 7132 to be
met from stock; (for example if the cut-off point is
L=12 drums, then D1= 7132 - 2992 = 4140)
s=$18 is the set-up cost
r=%18 is the cost of capital
v=$320 is the price of one drum of oil
h1=$1.10 is the handling charge for drums stored
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• the total relevant cost will be:
T(L,Q) = sN + h2D2 + 0.5Qvr + sD1/Q + h1D1
where N is the annual number of big orders; D2 = 7132 –
4140 = 2992 is the total number of drums to be shipped
directly to big customers and h2= $0.45 is the handling
charge per drum
• eg. since the number of all orders = 1266, when L = 12,
N = 1266 – 1079 = 187, and Q* = EOQ = 50.9, in which
case the total minimal cost for L =12 will be:
T(12,50.9) = (18)(187) + (0.45)(2992) + (0.5)(50.9)(320)(0.18) +
(18)(4140)/50.9 + (1.10)(4140) = 12 196.37
• the optimal solution can be determined by
enumeration, ie. by trying out different values for L;
so: L* = 20, Q* = 61.8 (see the Excel chart)
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• extending the project from scoping to full
analysis would include steps such as:
– repeating the solution for all the remaining 803
products
– determining whether equipment and capacity
constraints are satisfied
– combining same-day big orders
– combining small orders with big orders
– combining all orders and then deciding a special run
if these exceed the cut-off level
– combining special runs with replenishments etc.
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• testing the LOD model
– internal validity assessed by hand; external validity assured by
theory
– performance evaluation possible by sampling after an A-B-C
analysis
• sensitivity analysis
– the LOD model is fairly robust. EOQ model is not very sensitive
to parameters.
– capacity or equipment resources may reflect high marginal
values (ie. the shadow price of resources)
– further investigation of uncertain data may or may not be
called for
• error analysis
– sensitivity analysis to establish all parameter intervals for
optimality
– to see how far past data can be relied on to predict the future
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PROJECT REPORT
PRODUCTION/INVENTORY CONTROL FOR PACKAGED GOODS AT THE
LUBRICATION OIL DIVISION, SANDPOINT REFINERY
Table of Contents
Introductory statement
Executive summary of findings and recommendations
Statement of the problem
Major steps of analysis
Major findings
Recommendations for implementation
Appendices: Spreadsheet for finding optimal policy for product Y
Computations performed
Detailed description of model
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