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Chapter 13

Resource Allocation and

Negotiation Problems

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Resource allocation models

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the central purpose of resource allocation models in decision analysis is to resolve what is known as the commons dilemma.

decentralize its decision making centralize decision making The dilemma can be resolved by the

managers meeting as a group, possibly in a decision conference, and examining the effect of trading off resources between their areas of responsibility.

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Variables are areas to which resources might be directed

–e.g. products, projects, regions or departments

A package is a combination of strategies

–containing one strategy for each variable

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An illustrative problem

Consider the following problem which relates to a hypothetical English furniture company.

Four sales regions: North, West, East and South, and a manager had been made responsible for each.

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The North sales region, with nine outlets, had accounted for about 30% of national sales in the previous year, but the region had been economically depressed for some time and the immediate prospects for an improvement in the position were bleak.

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The West region had only three outlets and the company had been facing particularly stiff competition in this region from a rival firm.

In the East region there was an even smaller operation with only two outlets, but this was known to be a potential growth area, particularly in the light of the recent electrification of the main railway line to London.

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To date, the most successful sales area, accounting for 50% of national Sales, had been the South.

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The management of the company were planning their strategy for the next five years and the main problem they faced was that of deciding how the available resources should be allocated between the sales regions.

It was resolved that the key managers involved should meet as a group with a facilitator available to structure a decision analysis model of the problem.

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Stages in building a resource allocation model

1. Identify variables, resources to be allocated

and objectives2. Identify possible strategies available for

each variable3. For each variable assess costs and

benefits of each strategy(continued...

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Stages in building a resource allocation model (contd)

4. Assess within-criterion weights so that each benefit can be measured on a common scale

5. Assess across-criteria weights to compare ‘importance’ of different benefits

6. Propose a package that appears to achieve objectives

(continued...

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Stages in building a resource allocation model (contd)

7. Use a computer to identify costs and benefits of all packages and the efficient frontier

8. Use the computer to find if there are more efficient packages than the proposed package

9. Perform sensitivity analysis

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English Furniture Company

Region No. of outlets

Comments

North 9 30% of national sales here, but economically depressed

West 3 Stiff competition

East 2 Potential growth area

South 14 Planning restrictions on new outlets

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Planning strategy for next 5 years Variables = 4 regions Resource to be assigned = money Objectives:

1. Sustain profitability in short term (PROFIT)

2. Increase market share (MKT SHARE)3. Minimize risk (RISK)

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Identifying the possible strategies for each region

The group of managers considered the strategies which were available in each region and these are summarized in Figure 13.1.

The strategies for each region are organized in the order of the level of resources which would be required, with level 1 representing the lowest level of expenditure.

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Each combination of strategies is referred to as a package.

The number of packages that were available was 2x3x3x3, which equals 54.

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Identifying strategies for each region

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Costs and benefits of strategies in individual regions

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Measuring each benefit on a common scale

Because the values were assessed separately for each region, a movement from 0 to 100 for a particular benefit in one region might be more or less preferable than the same movement in another region.

Measure these changes in benefit on a common scale.

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Figure 13.2 shows the two value scales for market share side by side.

Normally, the longest scale is used as the common scale.

The different lengths of the scales are measured by the within-criterion weights.

For short-term profit the weights were calculated directly from the group's original monetary estimates.

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Comparison of East & West’s scales for market share

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Within-criterion weights: Profit

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Within-criterion weights: Market share

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Within-criterion weights: Risk

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Value of strategies with benefits measured on common scale

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Comparing the relative importance of the benefits

The managers wanted to be able to assess the overall benefit of using a particular package by combining the values for all three benefits.

a better method is to compare the importance of a change (or swing) from the worst position to the best position on one benefit scale with a similar swing on each of the other benefit scales.

The resulting weights are known as the across-criteria weights.

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Across-criteria weights

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Identifying the costs and benefits of the packages

The group were asked to propose a package which they felt would lead to the best use of the company's funds.

The package that they suggested was a fairly cautious one.

It simply involved maintaining the status quo in every region except the East, where an expansion of operations to four outlets would take place.

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Value of benefits= 0.167 x (value for profit) + 0.556 x

(value for market share)+ 0.278 x (value for risk)

= (0.167 x 203.2) + (0.556 x 110) + (0.278 x 112)

=126.2

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For the least beneficial package, the value of benefits would be found to be 87.49. The corresponding figure for the most beneficial package is 159.9.

The values are rescaled, so that the worst and best packages have values of 0 and 100, respectively. Since 126.2 is about 53.4% of the way between 87.49 and 159.8, the benefits of this package would achieve a value of 53.4 on the 0-100 scale.

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All the other packages can be displayed on a graph such as Figure 13.5.

On this graph the efficient frontier links those packages which offer the highest value of benefits for a given cost.

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Identifying the efficient frontier

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Package B In the North: Maintain the status quo In the West: Expand to six outlets In the East: Maintain the status quo In the South: Expand to 16 outlets This package would cost $71 million,

which was less than the proposed package but would lead to benefits which had a value of 84.7.

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The group were surprised that the package did not involve any expansion in the promising East region.

The explanation for this was partly provided by the EQUITY program which enabled the costs and benefits of each strategy to be compared for individual regions.

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Investigating costs and benefits in the West region

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Investigating costs and benefits in the East region

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Figures 13.6(a) or (b), the ‘middle’ strategy will never be recommended by the computer.

This means that in the East the choice is between the status quo and a major expansion to 10 outlets. The problem is that this major expansion would cost an extra $38 million, and the model suggests that this expenditure is not worthwhile given the limited funds which are available.

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Investigating costs and benefits in the South region

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Sensitivity analysis

Because there was some uncertainty about how much money would actually be available, the group felt that it might be worth identifying the best packages if the company had more funds at its disposal.

Clearly, if more money is available then this will involve a move along the curve to the right.

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This would lead to the maximum possible value of benefits of 100, but would involve expenditure of $109 million. The group agreed that this level of expenditure would not be feasible.

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The group also investigated the effect of reducing the money which was available to be invested.

One of the group next suggested that not enough attention had been paid in the model to risk.

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Negotiation models

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Characteristics of negotiation problems

No. of parties: two or more than two? Monolithic or non-monolithic parties? No. of issues: one or more than one? Time constraints? Final agreement binding? Third party intervention possible?

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We consider negotiations involving -two parties -several issues

Objective: To find deals which are beneficial

to both parties

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Illustrative problem Management v. Union negotiations

Union demand:* 15% pay rise* 3 extra days’ holiday per year

* reinstatement of workers sacked after breach of regulations

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Efficient frontier

If a deal is on the efficient frontier any improvement for one party can only be achieved at the expense of the other party. This is known as Pareto optimality.

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Values and weights for pay rise

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Values and weights for holidays

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Values and weights for reinstatement

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Value of tentative deal to management and union

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Identifying the efficient frontier

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Reported advantages of applying decision analysis to negotiations

Creative attitude in negotiations Negotiators could prepare in advance and

anticipate position of other party Clearer understanding of problem and

increased flexibility Improved communication within

negotiation team