an holistic approach to product selection

7/30/2019 An Holistic approach to product selection

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ABSTRACT:

The purpose of this paper is to develop and demonstrate an outsourcing modelin which constraint resource prevents the throughput of the organization. Thepaper proposes an integrated model by combining the productivity criterion, the

theory-of-constraints (TOC) and linear programming (LP) into a single evaluationmodel in a multi-product constraint resource environment. A case study ispresented to demonstrate the effectiveness of this model. The decision modelcompares three alternatives: standard cost accounting, standard TOC and ourown solution, which is an approach that combines TOC, LP, and the productivitycriterion. The numerical results show that this model is superior and morerealistically optimizes resource allocation and measures the performance of themodel.This research is limited to the production processes that do not havemultiple constraints. This is the first time that the integrated model comprising ofProductivity -TOC-LP model has been used to maximize the product throughput.Instead of calculating $ return per constraint minute, this method decides thepriority of product and resource centre that maximizes the product throughput in

the constraint resource environment. It makes a significant contribution to themanufacturing organization where one can compare the financial performance ofthe organization by selecting the right decision model.

INTRODUCTION:

The decision to outsource production is the outcome of constraint resourceanalysis. Such situations are characterized by market demand in excess of acompanys production capacity. This article analyzes a scenario in which marketdemand exceeds a companys capacity to manufacture. The decision makerneeds to decide how much is to be manufactured and how much is to be bought

from external contractors. This section presents a brief review of the modelling inthe cost accounting literature. Since different models provide radically differentanswers to the outsourcing problem, we compare four alternatives: standardcost accounting, standard theory-of-constraints (TOC) (Goldratt, 1988; Fox, 1988;Ronen and Starr, 1990), linear programming and our Productivity-TOC-LP model.

The present study outlines an integrated model combining the Productivitycriterion, TOC, and the LP technique. The Productivity criterion is best suited forgiving priorities to each product of the product-mix problem for manufacturingcost analysis. The degree of relative importance for technical requirements iscomputed with the Productivity criterion. Integrating Productivity criterion with

TOC determines the optimum profit. Literature survey of the various methodsreveals the following drawbacks:

i) Standard cost accounting does not consider constraint resources.ii) Standard TOCs considers constraint resources but it does not provide

optimal solution.

This study analyzes the case in which demand exceeds a companyscapacity to manufacture and applies the Productivity procedure to the analysis ofconstraint resources. This evaluation technique requires input parameters, likeraw material cost, hourly rate, selling price, demand, working time, and so on.

The following section presents, the proposed methodology, the modelformulation and a case study that uses a combined Productivity -TOC-LP model.

The last section compares between three alternatives: standard cost accounting,standard TOC (Goldratt, 1988; Fox, 1988 and our integrated Productivity -TOC-LP


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model. The result obtained clearly shows that our integrated model gives thebest result.

LITERATURE REVIEW:Many researchers explained the difficulties of standard accounting

procedure (Johnson, 1991; Mehra et al., 2005). One research stream stressedthroughput accounting (Goldratt, 1988; Dugdale and Jones, 1996; Srikant andRobertson, 1995; Srikant and Umble, 1997). Another research stream worked on

TOC with traditional cost accounting and activity-based cost management (Kee,1995; Baxendale and Gupta, 1998). Another group of researchers (Spencer andCox, 1995) focused on software optimized production technology. Luebbe andFinch (1992) conclude that a TOC-based approach is superior to the LP approach.On the other hand, Balkrishnan and Cheng (2000), using a small modification tothe data of Luebbe and Finch (1992) explain that the LP approach is superior to a

TOC-based approach when dealing with several binding constraints. Lee andPlenert (1993) analyze a slightly modified form of product mix decision, in whichthe launch of a product under one binding constraint is analyzed. Plenert (1992)found that when multiple constraint resources exist, LP is a better planning toolthan TOC. Posnack (1994) criticized Lee and Plenert. He argued that withouthaving integer solution, TOC heuristics solution would be optimal. Among thenew management philosophies established in recent decades, the TOC,developed by Goldratt at the beginning of 1980s, plays a vital role. Its mainpurpose is to identify, analyze, and eliminate those constraints that restrict afirms value adding process (Goldratt and Fox, 1986). As a tool for product mixdecision, the approach based on TOC (Lockmy and Cox, 1994) is often used

alternatively (or parallel) to optimiza-tion tools, such as the contribution margin(CM) per constraint unit method or LP approaches. The present work explainshow the authors were able to determine the product throughput of amanufacturing firm using a combined Productivity- TOC-LP model and discussesthe justification of the proposed model. Much research has been done on outsourcing problems. But no researcherhas studied the performance aspect of the Productivity -TOC-LP model. Whileanalyzing constraint resources, researchers mostly considered three decisionmodels: standard cost accounting, standard TOCs, and LP as base model. Ray etal. (2007a, b) compared these three models with LP enhancement of goalprogramming technique and AHP-TOC-LP model. They have described the latteras the optimum model for outsourcing. Soren et al. (2005) assessed quality of

the TOC-based approach which generates good or even optimal solutions withdifferent results particularly when compared with other product mix decisiontools. Low (1992), Luebbe and Finch (1992), Patterson (1992), Boyd and Cox(2002), and Mabin and Davies (2003) show by means of numerical results fromsituations with one constraint that the TOC-based approach leads to an optimalsolution. Umble et al. (2006) criticized the traditional cost accounting andstressed the throughput accounting. Sarkar et al. (1998, 2001) suggestedcombining LP with the TOC concept. A.Ray et al. (2008) compared Standardaccounting, standard TOC, LP and there proposed Hurwicz-TOC-LP model. Theyhave described the latter as the optimum model for outsourcing.

NOTATIONS:


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Let us introduce the following items:

i Product Index

j Resource Index

aij number of minutes required by resource j to process product i

bj resource js capacity (in min)

Ri raw material cost

Di demand

Pi market price

Ci contractors price

OE operating expenses

i productivity of product i

PROPOSED METHODOLOGY:

The following methodology has been developed-

Step1: The priority of each product is calculated using Productivity

Analysis.

Step1.1: Here first the input cost (in terms of $) and output (profit in $)

received are evaluated for each product.

Step1.2: Productivity of each product is calculated which is the ratio of

output (profit) to input cost for each product.

Step1.3: The product which gives the highest value for productivity is of

top priority.

Step1.4: The priorities of other products are according to the decreasing

order of productivity.

Step2: According to priority we allocate the resource centres to the raw

materials.

Step3: According to TOC we will check whether bottlenecks capacity is

exhausted or there is insufficient capacity remaining to produce another

unit of product.


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Step4: If answer to the step 3 is Yes then satisfy the following LP

function-

i(Pi-Ri ) + (Di-Xi)(Pi-Ci )

ijXi bj , i= 1,....,N, j=1,.....,M

Xi Di

And compare the results with other models.

MODEL FORMULATION:

Management aims to maximize its product throughput from manufacturedquantity and from outsourced quantity. The product throughput frommanufacturing one unit of product i is defined as the difference between market

price and the cost of raw materials, or Pi Ri. Production of Xi units of product igenerates a total product throughput ofXi(Pi Ri). To satisfy market demandthe company orders a quantity of(Di Xi) from outside contractors, generating

a product throughput of(Pi Ci) per contracted unit, accounting for a totalproduct throughput of(Di Xi)(Pi Ci) for product i, units contracted outside.

Thus total profit from product i is equal to Xi (Pi-Ri) + (Di-Xi) (Pi-Ci).

Profits from all M products equal to i(Pi-Ri) +(Di-Xi)(Pi-Ci)]- O.E

Where OE denotes the companys operating expenses.

The product mix problem should satisfy the following standard LP format:

Max i(Pi-Ri)+(Di-Xi)(Pi-Ci)] - O.E

Subject to Xi Di, i {1,..., N} product demand constraint

ij bj ,j {1,....,M} manufacturing resource constraint.

A CASE STUDY:

A south-east Asia-based manufacturing firm produces three products P, Q, and R

using three resources R1, R2, R3 (Table I). Due to its limited resources the

company wants to outsource some production to a subcontractor. The available

facility is five days a week for one shift consisting of eight hours per day. So the

total working minutes available are 5 x 8 x 60 = 2400 min. The flow layout

(Figure 1) of the product processing describes each of the three products


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incorporating two of four raw materials 1, 2, 3, and 4. The cost of each raw

material is $20. The market price of the products P, Q, and R are $130, $150,

and $190, respectively. The customer demand is 100 units of each one of the

three products. Contractors selling price to the company for P, Q, and R are $66,

$68, and $98, respectively. These prices include the cost of raw materials.

Resources P Q R Min/Weeks UtilizationRatio,Demand/2400

R1 2 4 13 1900 79.16%R2 12 12 17 4100 170.83%R3 4 10 10 2400 100%

18 26 40

Table 1: Resources per product in minute

Figure1: Resource time per product in minutes


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STANDARD ACCOUNTING:

Standard accounting procedure decides those products that are moreprofitable per production time unit. To calculate the cost of each product thecompanys operating expenses $6,000 are divided by the number of resourcesand the maximum time limit per week. Thus the cost per minute of work for anyresource is equal to $6,000/3/2,400=$0.83.The cost of each product is the sumof its raw material cost and total minutes of work for all three resources

multiplied by the companys cost per minute ($0.83). The CM per product is thedifference between the selling price and the cost. Product profit per minute isdetermined by dividing the product profit by total minutes of work as follows :$4.17 for P, $3.40 for Q and $2.92 for R. P is the most preferred product tomanufacture since its contribution per work minute is the highest, followed by Q,making R the least preferred to manufacture. Hence the constraint resource Bwill manufacture 100 units of product P and 100 units of product Q, but due tounavailability of time, will not manufacture any units of product R. Thethroughput of each manufactured product is the difference between productselling price and raw material cost. The calculated throughput is multiplied bythe number of units manufactured. The throughput of each contracted unit iscalculated as its selling price less the price paid to the contractor. Finally, total

product throughput (Table II) is the sum of manufactured throughput andcontracted throughput.

Product P Q R

Total work min/product 18 26 40Product cost: time + rawmaterial

$54.94 $61.58 $73.2

Product selling price $130 $150 $190Product profit $75.06 $88.42 $116.8Product profit/ min $4.17 $3.4 $2.92

Demand 100 100 100Units to manufacture 100 100 0


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Units to contractor 0 0 100Throughput/manufactured unit $90 $110 $150Throughput/ contracted unit $64 $82 $92Total product throughput $9000 $11000 $9200Total facility throughput $29200

Operating expenses $6000Net profit $23200

Table II: Standard accounting analysis.

STANDARD TOCTOC decides product throughput per unit of working time at the bottleneck. Wedivide the throughput by the bottleneck resource R2s time. Product Q has thehighest throughput per constraint minutes, that is, $9.16 per constraint minute,and is therefore the first preference to manufacture. Hence, we manufacture 100units. Product R with a throughput per constraint minute ratio of $8.82 per

constraint minute is next (Table III). Due to R2s constrained capacity we onlymanufacture 70 units and outsource 30 units. Product Ps throughput perconstraint minute ratio is the lowest, i.e. $7.50 per constraint minute, and sinceno more manufacturing capacity is available we outsource the full 100 units.

Components P Q RSelling priceper units

$130 $150 $190

Raw material costper unit

$40 $40 $40

ProductThroughput

$90 $110 $150

Constraint resourceR2 min

12 12 17

Throughput/constraintR2 min

$90/12= $7.5/min

$110/12= $9.16/min

$150/17= $8.82/min

Demandsin units

100 100 100

Units toManufacture

0 100 70

Units toContractor 100 0 30


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Throughput /manufactured units

$90 $110 $150

Throughput /Contracted units

$64 $82 $92

Product throughput

for manufacturedunits

0 $11000 $10500

Throughput forcontracted units

$6400 0 $2760

Total productThroughput

$6400 $11000 $13260

Total facilityThroughput

$30660

OperatingExpenses

$6000

NetProfit $24660

Table III: Standard TOCs.

PROPOSED METHODOLOGY VALIDATION:

Step1: The priority of each product is calculated using Productivity Analysis.

Step1.1: Here first the input cost and output received are evaluated for each

product.

Step 1.11: The input cost for each product will include cost of raw materials usedand operating expenses (which will depend on the operating time of eachproduct). To calculate the operating cost of each product the companysoperating expenses $6,000 are divided by the number of resources and themaximum time limit per week. Thus the cost per minute of work for any resourceis equal to $6,000/3/2,400=$0.83.

The input cost of each product is the sum of its raw material cost and totalminutes of work for all three resources multiplied by the companys cost perminute ($0.83).Step 1.12: The net output from each product is the difference of the selling price

and the input cost (which will include the raw material cost and operationalexpenses as discussed in the earlier step).Step1.2: Productivity of each product is calculated which is the ratio of output

value to input value for each product. Productivity of a product is given by the

formula:

The productivity for P, Q and R after calculation is found to be1.36, 1.43 and 1.59

respectively.


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Step1.3: As the productivity of R is largest so product R is of top priority followed

by Q and P respectively.

Step2: According to priority we allocate the resource centres to the raw materials

based on bottleneck capacity of the resource centres. As in Table 1 we can see

that resource R2 consumes maximum time out of the three resources, thereforeconsidering R2 as the bottleneck resources we have allocated the products for

manufacturing as shown in Table III.

Productaccording topriority

MarketDemand

Timerequired perunitproductfor

resource centreR2

ProducedQuantity

Usedtime inbottleneckresource centre

R2(inminutes)

Left timeinbottleneckResourcecentre,R

2 (inminutes)

R 100 17 100 1700 700Q 100 12 58 696 4P 100 12 0 0 4

Table III: Used and Left time for bottleneck resource R2

Step3: According to TOC we will check whether bottlenecks capacity is

exhausted or there is insufficient capacity remaining to produce another unit of

product.

There are 2400 minutes available for resource R2. Producing 100 R will

leave 700 minutes for rest of the units as shown in Table III. Producing 58 units

of Q will consume 696 minutes leaving 4 minutes. Now 4 minutes is not enough

for producing any units of Q or P, so the remaining units will be outsourced.

This method calculates the net profit to be of $25224, which is better than

standard accounting and traditional TOCs. Net profit is calculated by subtracting

operating expenses from the sum of the facility throughput, which is shown in

Table IV.

Products P Q R

Selling price per unit $130 $150 $190Raw material cost per product $40 $40 $40Operating expenses per unitproduct

$0.83X18=14.94

$0.83X26=21.58

$0.83X40 =33.2

Total input cost per unit product $54.94 $61.58 $73.2Total profit(output) per unit

product

$75.06 $88.42 $116.8

Productivity, P 1.36 1.43 1.59


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Demand, Di 100 100 100Units to manufacture 0 0 100Units to contractor 0 58 100

Throughput/Manufactured units $90 $110 $150Throughput/ Contracted units $64 $82 $92

Total facility throughput $6400 $9824 $15000Operating expenses $6000Net profit $25224

Table IV: Productivity TOC LP analysis.

Step 4: The solution satisfies the following LP function:

max z = 90 X 0 + 64 X 100 + 110 X 58 + 82 X 42 + 150x100 + 92 X 0 - 6000

s.t.

4 X 0 + 2 X 58 + 13 X 100 2400

12 X 0 + 12 X 58 + 17 X 100 2400

4 X 0 + 10 X 58 + 10 X 100 2400

0 + 100 100

58 + 42 100

100 + 0 100

0, 58, 100, 100, 42, 0 0

The net profit is obtained by subtracting the plants operating expenses fromthe total throughput. In house throughput for product R= 100 X $150 = $15,000.

The throughput for product Q (in house)= 58 X$110=$6,380 and P=0,respectively. Contracted throughput for product Q=42X$82=$3,444, R=0, andP=100X$64 = $6,400. The plants operating expenses = $6,000. Therefore, thetotal net profit=$25,224.

CONCLUSION AND DISCUSION:

Various methods have been proposed to deal with outsourcing problems. Anefficient assessment system is essential for selecting the appropriate model. This

paper started by describing the cause of the outsourcing problem, formulated itas a LP problem, developed a satisfying function, and offered a simplifiedcriterion for the ordering products in terms of preference to manufacturing andpreference to outsourcing. A real life production outsourcing problem is solvedby combined Productivity-TOC-LP analysis. The result is compared (Table VI) withstandard accounting, TOC, and LP model. Out of these four models, standardaccounting is inferior as it does not consider constraint resource separately;rather it considers all resources as equal. TOC considers constraints resource,but, this model does not provide the optimal solution. On the other hand, theproposed model,

Components Standard

Accounting

TOC Our Model

P- manufactured 100 0 0


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Q-manufactured 100 100 58R- Manufactured 0 70 100P-outsourcedquantity

0 100 100

Q-outsourced

quantity

0 0 42

R-outsourcedquantity

100 30 0

Net profit $23200 $24660 $25224

Table VI: Summary of three methodologies.Considers priority of each product in terms of throughput to input cost ratio.

Therefore, priority of product and resource centre is important as it justifies theproduct throughput of the organization and measures the performance of thesystem by optimizing in-house quantity with maximum throughput. TheProductivity criterion is used to assess the performance of each product, and the

result shows that constraint resource centre R2 has the maximum processingtime (as shown in Table I). In spite of its similarity to the outcome of the LPsolution, the proposed model is better than the LP model. The proposedmethodology described here has been analyzed and indicates severaladvantages:(1) The Productivity criterion decides the priority of each product based onOutput to input ratio.(2) This integrated model is well suited to deal with the throughput analysis thatinvolves quantitative factors.(3) The degree of importance for each of the products determines the profitobtained from the product mix.

(4) Rigorous and mathematical expressions of LP problems can be eliminated toa large extent.Some weakness of our proposed method might be:

(1) It is difficult to change the traditional cost accounting system.(2) It would take time to implement the approach.

It is very clear that the integrated model can be widely applied in industryand will be of immense practical value. In comparison with standard costaccounting and standard TOCs this integrated model is applicable and moreeffective.

an holistic approach to product selection

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