An improved theory of constraints
The Authors
Amitava Ray, Department of Mechanical Engineering, Sikkim Manipal Institute of Technology, Majitar, East-Sikkim, India
Bijan Sarkar, Department of Production Engineering, Jadavpur University, Kolkata, India
Subir Kumar Sanyal, Department of Mechanical Engineering, Sikkim Manipal Institute of Technology, Majitar, East-Sikkim, India
Acknowledgements
The authors are very appreciative for the thoughtful and constructive comments made by the anonymous reviewers of this paper.
Abstract
Purpose – The primary aim in this paper is to develop and demonstrate a theory of constraints (TOC) model in which constraint resource prevents the throughput of the organization.
Design/methodology/approach – In this paper, the authors propose an integrated model by combining Laplace criterion and TOC into a single evaluation model in a multiproduct constraint resource environment. A case study is illustrated to demonstrate the effectiveness of this model. The outsourcing decision model compares three alternatives: standard cost accounting, standard theory-of-constraints, and our own solution.
Findings – The numerical results show that the new approach is superior to Standard cost accounting and Theory of Constraints and presents a more realistic state of optimum allocation of resources and measures the performance of the model.
Research limitations/implications – This research is limited to the production processes that do not have multiple constraints.
Originality/value – This is the first time that the integrated model comprising of Laplace-TOC model has been used to maximize the product throughput. Instead of calculating $return per constraint minute, this method decides the priority of product that maximizes the product throughput in the constraint resource environment. It makes a significant contribution to the manufacturing Organization where one can compare the financial performance of the Organization by selecting the right decision model.
Article Type:
Case study
Keyword(s):
Standard costs; Outsourcing.
Journal:
International Journal of Accounting and Information Management
Volume:
16
Number:
2
Year:
2008
pp:
155-165
Copyright ©
Emerald Group Publishing Limited
ISSN:
1834-7649
Introduction
The constraint resources are characterized by market demand in excess of the organization's production capacity. The decision to outsource is a major strategy base for most companies, since it involves cost savings against the consequences of loss in control over the product or service. This study investigates the case where market demand exceeds the company's capacity to manufacture.
Since different models provide radically different answers to the outsourcing problem we compare three alternatives: standard cost accounting, standard theory-of-constraints (TOC; Goldratt, 1988, Fox, 1988, Ronen and Starr, 1990) and our own model.
This paper proposes a model for evaluating the appropriateness of adopting new approach. The proposed model is based on Laplace criterion which contributes to the evaluation of the proposed model before its implementation. In recent years, many authors have written about the shortcomings of Standard accounting procedure (Johnson, 1991, Mehra et al., 2005). Many authors stressed on throughput accounting (Goldratt, 1988, Dugdale and Jones, 1996, Srikant and Robertson, 1995, Srikant and Umble, 1997). Kee (1995) and Baxendale and Gupta (1998) worked on TOC with traditional cost accounting and activity based cost management. Spencer and Cox (1995) focused on software optimized production technology (OPT). Of the new management philosophies established in recent decades, the Theory of Constraints (TOC), which was developed by Goldratt at the beginning of 1980 s, plays a vital role. Its main purpose is to identify, analyze and eliminate those constraints that restrict a firm's value adding process (Goldratt and Fox, 1986). As a tool for product mix decisions, the TOC (Lockmy and Cox, 1994) based approach is often used alternatively (or parallel) to optimization tools, such as the contribution margin per constraint unit method or linear programming (LP) approaches. It is the aim of this paper to compare a new approach with the other existing model and provide more insight into the constraint resources.
There are several works by researcher on outsourcing problems. But no researchers studied the performance aspect of Laplace criterion in analyzing constraint resources. While analyzing constraint resources many researchers considered three decision models: Standard cost accounting, standard TOC and LP as base model. Ray et al. (2007) compares these three models with the following models: LP enhancement of goal programming technique and AHP-TOC-LP model and identify the optimum model for outsourcing. Soren et al. (2005) assessed quality of the TOC based approach which generate good or even optimal solutions with different results particularly when compared with other product mix decision tools. Low (1992), Luebbe and Finch (1992), Patterson (1992), Boyd and Cox (2002), and Mabin and Davies (2003) show by means of numerical results of situations with one constraint that the TOC-based approach leads to an optimal solution. Lee and Plenert (1993) analyze a slightly modified form of product mix decision, in which the launch of product under one binding constraint is analyzed. With regard to Lee and Plenert (1993), and Posnack (1994) claims that their TOC based approach was incorrect. He concludes that TOC based approach is preferable to the integer LP approach. Luebbe and Finch (1992) come to the conclusion that TOC based approach is superior to LP approach. Contrarily, Balkrishnan and Cheng (2000) explain with a small modification to the example data of Luebbe and Finch (1992) that the LP approach is superior to TOC based approach when dealing with several binding constraints. Umble et al. (2006) criticized the traditional cost accounting and stressed the throughput accounting. Coman and Ronen (2000), Chakrabarty et al. (2006), Campbell (1995), Salafatinos (1995), Gupta et al. (1997), and Gupta (2001) studied the performance measurement aspect of TOC with standard cost accounting and activity based cost management. Plenert (1992) found that when multiple constrained resources exist, LP is an optimum-planning tool than TOC.
The present study outlines Laplace criterion (Taha, 2006) representing a compromise between the optimistic and the pessimistic approach to decision making under uncertainty and rank the order of the product for manufacturing cost analysis. Computation of the degree of relative importance for technical requirements is made through Laplace criterion.
This study analyzes the case where demand exceeds company's capacity to manufacture and application of Laplace criterion in the constraint resources. This evaluation technique requires raw material cost, hourly rate, selling price, demand, workflow, working time, etc.
The following section presents, a brief review of Laplace criterion, the proposed methodology and the case study using the proposed model. The last section compares three alternatives: standard cost accounting, standard TOC (Goldratt, 1988, Fox, 1988), and our model and scope of further work.
Notation
Let us introduce the following items:
i – product index;
j – resource index;
P i – market price;
R i – raw material cost;
D i – demand;
DM – decision matrix;
C i – contractor's price;
OE – operating expenses;
X i – units of product i produced;
P j – maximum available time; and
CM i – contribution margin of product i.
Laplace criterion
Decision making under uncertainty, as under risk, involves alternative decisions whose payoffs depends on the states of nature. The Laplace criterion is based on the principle of insufficient reason (Taha, 2006). The alternative decision are evaluated using the optimistic assumption that all states are equally likely to occur, that is, P{s 1}=P{s 2}=ċ=P{s n }=1/n. The payoff of a decision problem with m alternative actions and n states of nature can be represented as follows:
The elements a k represents action k, and the elements s l represents state of nature l. The payoff or outcome associated with action a k and state s l is ν(a k ,s l ).
The best alternative is the one that yields: Equation 1
Proposed methodology
The following methodology has been developed:
- The in house contribution margin (CM) of each product is calculated by subtracting raw material cost from selling price. Contribution margin, CM i =P i −R i , i=1…n.
- The contractor's contribution margin of each product i is calculated by subtracting supplier's price from selling price of the product, i.e. CM i =P i −C i .
- Develop the decision matrix as follows: Equation 2 where a i1 and a i2 are the in house throughput and contractor's throughput.
- Calculate the priorities for each of the products by taking average of each row (Laplace criterion).
- Identify the constraint resource.
- Rank the products using the normalized weights of each product.
- Calculate the time left on the bottleneck as follows: Equation 3
- Whether dominant bottleneck's capacity is exhausted or there is insufficient capacity remaining to produce another unit of product.
- If answer to the step 8 is ‘yes’ then determinations of profit and comparisons of said profit to that with other model.
A case study
A south-east Asia based manufacturing firm produces three products P, Q, R using four resources R1, R2, R3 and R4. Owing to its limited resource company wants to outsource some product to subcontractor. The facilities are available five days a week for one shift consisting of eight hours per day. So total working minute available 5 × 8×60 = 2,400 min. The flow layout (Figure 1) of the product processing describe each of the three product incorporates two of four raw material 1, 2, 3 and 4. The cost of each raw material is $20. The market price of the products P, Q and R are $120, $160, and $200, respectively. The customer demand is 100 units of each one of the three products. Contractors selling price to the company for P, Q, R are $100, $120, and $190, respectively. These prices include the cost of raw materials (Table I).
Standard accounting
Standard accounting procedure decides those products that are more profitable per production time unit. To calculate the cost of each product the company's operating expenses $10,000 are divided by the number of resources and the maximum time limit per week. Thus, the cost of every minute worked at any resources equal $10000/4/2400=$1.041
The cost of each product is the sum of its raw material cost and total working minutes at all three resources multiplied by the company's minute rate ($1.041).The contribution margin per product is the difference between the selling price and the cost. Product profit per minute is determine by dividing the product profit by total work minute as follows: $2.768 for P, $2.173 for Q and $1.250 for R. P is the most preferred product to manufacture since its contribution per work minute is highest, followed by Q, making R the least preferred to manufacture. Hence, the constraint resource R2 will manufacture 100 units of product P, 100 units of product Q and but due to unavailability of time no units of product R. The throughput of each manufactured product is the difference between product selling price and raw material cost. The calculated throughput is multiplied by the numbers of unit manufactured. The throughput of each contracted unit is calculated as its selling price less the price paid to the contractor. Finally, total product throughput (Table II) is the summation of manufactured throughput and contracted throughput.
Standard theory-of-constraints
TOC decides product throughput per unit of working time at the bottleneck. We divide the throughput by the bottleneck resource R2's time. Product Q has the highest throughput per constraint minutes, i.e. $10 per constraint minute and is therefore the first preference to manufacture. Hence, we manufacture 100 units. Product R with a throughput per constraint minute ratio of $8.88 per constraint minute is next (Table III). Due to R2's constraint capacity we only manufacture 66 units and outsource 34 units. Product P's throughput per constraint minute ratio is the lowest, i.e. $6.66 per constraint minute and since no more manufacturing capacity is available we outsource the full 100 units.
Proposed approach
- The in house contribution margin is calculated as shown in the Table IV.
- The contractor's contribution margin is calculated as shown in Table V.
- The decision matrix of the problem is as shown in Table VI.
- Table VII shows the calculated value of row minimum and row maximum.
- Resource R2 is the bottleneck because it is most overloaded.
- Table VIII shows the priorities of each product. The production priority should be developed in view of each bottleneck. As shown in table resource R2 is the bottleneck. Decision maker assigns score 0.395 to the product R. In other words, product R has the highest priority and so on.
- The constraint resource at resource centre R2 makes us to produce 100 units of R, 50 units of Q and none or 0 of P as shown in the following table. There are 2,400 min available for resource 2. Producing 100 Q will leave 2,400-18 × 100 = 600 min. Producing 50 units will leave 600-50 × 12 = 0 min (Table IX).
- Now no time is available for producing another unit of product.
- The net profit is obtained by subtracting the plant's operating expenses from the total throughput. In house throughput for product R = 100×$160=$16,000. The throughput for product Q = 50×$120=$6,000 and P = 0, respectively. Contracted throughput for product Q = 50×$40=$2,000, R = 0 and P = 100×$20=$2,000. The plant's operating expenses=$10,000. Therefore, the total net profit=$16,000.
Conclusion and discussion
In recent years different approaches have been proposed to deal with outsourcing problem. An efficient assessment system is essential for appropriate model selection. In this paper Laplace criterion is used to assess the performance of each product. The result was compared (Table X) with standard accounting, TOC model. Out of these three models the standard accounting solution is inferior to standard TOC solution due to its treatment of equal weight age to all resources. Such an assumption is not realistic and only applies when all resources have identical utilization ratio. The standard TOC solution is also inferior to improved theory of constraints since it does not consider the relative value of each product. On the other hand, the proposed model, considers priority of each product. Therefore, priority of product is important as it justifies the product throughput of the organization and measures the performance of the system by optimizing in house and outsource quantity with maximum throughput. The proposed methodology described here has been analyzed and indicates several advantages:
- Laplace criterion decides the weightage of each product from the product contribution margin.
- The degree of importance for each of the products determines the profit obtained from the product-mix.
Some weakness of our proposed model might be:
- It is difficult to change the traditional method.
- It would take time to implement the approach.
- People may be reluctant to use it because they have to justify their own preferences, rather than simply saying yes or no.
It is, therefore, that the model can be widely applied for the industries will be of immense practical value. The model is valuable to contractor competing on contracts for more business. Further research is required into the application of this method in the multiple constrained resources.
Equation 1
Equation 2
Equation 3
Figure 1Resource time per product in minutes
Table IResource per product in minute
Table IIStandard accounting analysis
Table IIIStandard theory-of-constraints
Table IVIn house contribution margin
Table VContractor's contribution margin
Table VIDecision matrix-1
Table VIIDecision matrix-2
Table VIIIProduct priorities
Table IXResource load analysis
Table XSummery of three methodologies
References
Balkrishnan, J., Cheng, C.H. (2000), "Theory of constraints and linear programming: a re-examination", IJPR, Vol. 38 pp.1459-63.
Baxendale, S.J., Gupta, M. (1998), "Aligning TOC and ABC for silkscreen printing", Management Accounting, April, pp.39-44.
Boyd, J.H., Cox, J.F. (2002), "Optimal decision making using cost accounting information", IJPR, Vol. 40 pp.1879-98.
Campbell, R.J. (1995), "Steeling time with ABC and TOC", Management Accounting, January, pp.31.
Coman, A., Ronen, B. (2000), "Production outsourcing: a linear programming model for the theory-of-constraints", IJPR, Vol. 38 No.7, pp.1631-9.
Chakrabarty, P.S., Majumdar, G., Sarkar, B. (2006), "Constraint resource management and production related decision-a case study", IE(I) Journal-pr, March, Vol. 86.
Dugdale, D., Jones, C. (1996), "Accounting for throughput-Part I", Management Accounting, April, No.1996, pp.24-42.
Fox, R.E. (1988), paper presented at NAA Conference, Monville, NJ, .
Goldratt, E.M. (1988), "Computerized shop floor scheduling", IJPR, Vol. 26 No.3, pp.429-42.
Goldratt, E.M., Fox, R. (1986), The Race, North River Press, Croton-on-Hudson, NY, .
Gupta, M. (2001), "Activiybased throughput management in a manufacturing company", IJPR, Vol. 39 pp.1163-81.
Gupta, M.C., Baxendale, S.J., Macamara, K. (1997), "The integration of TOC and ABCM in a health company", Journal of Cost Management, July/August, pp.23.
Johnson, T. (1991), "Activitybased management: past, present and future", T Engg Econo, Spring, pp.219-38.
Kee, R. (1995), "Integrating activity-based costing and the theory of constraints to enhance production-related decision-making", Accounting Horizon, Vol. 9 No.4, pp.48-61.
Lee, T., Plenert, G. (1993), "Optimizing theory of constraints when new product alternatives exist", Prod. Inven, Man. J., pp.51-7.
Lockmy, A., Cox, J. (1994), Re-engineering Performance Measurement, Irwin Professional Publishing, New York, NY, .
Low, T.J. (1992), "Do we really need product cost?", The theory of constraints alternative. Corp. Cont., Vol. 5 pp.26-36.
Luebbe, R., Finch, B. (1992), "Theory of constraints and linear programming: a comparision", IJPR, Vol. 30 No.6, pp.1471-8.
Mabin, V.J., Davies, J. (2003), "Framework for understanding the complementary nature of TOC frames: insights for the product mix dilemma", IJPR, Vol. 41 pp.661-80.
Mehra, S., Inman, R.A., Tuitie, G. (2005), "A simulation-based comparision of TOC and traditional accounting perfance measure in a process industry", Journal of Manufacturing Technology Management, Vol. 16 No.3, pp.328-42.
Patterson, M.C. (1992), "The product-mix decision: a comparision of theory of constraints and labor based management accounting", Prod. Inven. Man. J., Vol. 33 pp.80-5.
Plenert, G. (1992), "Optimized theory of constraints when multiple constrained resource exist", European Journal of Operational Research, Vol. 70 No.1, pp.126-33.
Posnack, A.J. (1994), "Improper applications yield improper conclusions", Prod. Inven. Man. J., Vol. 35 pp.85-6.
Ray, A., Sarkar, B., Sanyal, S. (2007), "An integrated theory-of-constraints", Proceedings of the IEEE IEEM, .
Ronen, B., Starr, M.K. (1990), "Synchronized manufacturing as in OPT: from practice to theory", Computers and Manufacturing, August, Vol. 1990 pp.585-600.
Salafatinos, C. (1995), "Integrating the TOC and ABC", Journal of Cost Management, Fall, pp.58.
Soren, R., Ahn, H., Schmitz, C. (2005), "Optimal product mix decisions based on the theory of constraints? Exposing rarely emphasized premises of throughput accounting", IJPR, 15 January, Vol. 43 No.2, pp.361-74.
Spencer, M.S., Cox, J.F. (1995), "Optimum production technology and the theory of constraints (TOC): analysis and genealogy", IJPR, Vol. 33 No.6, pp.1495.
Srikant, M.L., Robertson, S.A. (1995), Measurements for Effective Decision-making, The Spectrum Publishing Company, Wallingford, CT, .
Srikant, M., Umble, M. (1997), Synchronous Measurement: Profit-based Manufacturing for 21st Century, The Spectrum Publishing Company, Guilford, CT, .
Taha, H.A. (2006), Operation Research, 7th ed., PHI, New Delhi, .
Umble, M., Umble, E., Murkami, S. (2006), "Implementing theory of constraints in a traditional Japanese manufacturing environment: the case of Hitachi tool engineering", IJPR, 15 May, Vol. 44 No.10, pp.1863-80.
Further Reading
Ray, A., Sarkar, B., Sanyal, S. (2007), "Production outsourcing: a goal programming approach", Proceedings of the 37th International Conference on Computers & Industrial Engineering, October 20-23, Alexandria, Egypt, .
Sarkar, B., Sarkar, K., Mukherjee, S.K. (2001), "OPT: an alternative to linear programming to solve product mix problem", Proceedings of National Seminar on Manufacturing Engineering in 21st Century, Indian Institute of Technology, Kanpur, March 1-3, .
Corresponding author
Amitava Ray can be contacted at: amit_ray_2000@yahoo.co.in