A production system comprised of multiple stages in tandem is considered. Each stage may be in either of two states: desirable or undesirable. Each stage may be placed under control so that it remains in the desirable state and produces the maximum fraction of conforming production units. Stages remaining uncontrolled may change randomly from the desired state to the undesired state. The controls may be mechanical or manual but involves costs which may or may not be dependent on the stage being controlled. It is desirable to find the optimal number of controls and their allocation among the stages which will maximise the net profit of production. The problem is formulated as a nonlinear mathematical program with binary variables. For the identical control cost case (independent of the stage to which control is applied), an 0(n) linear runtime algorithm is provided, wheren is the number of stages. It is shown that a “k or nothing” (wherek is the total number of controls applied) control policy is optimal and depends on a critical cost computed from the given parameters of the problem. In addition, conditions are provided under which “all or nothing” control policies are optimal. This is based on the computation of a “critical cost” and is independent of the number of stages in the system. It is shown that when these conditions are met the profit function is pointwise convex ink. Optimal solution techniques are provided and analysed for special cases in terms of the relationships between control cost and production parameters. Sensitivity analysis is provided for each of the parameters of the problem. The solutions are in general robust, with respect to these parameter variations. Numerical examples are provided throughout the paper to illustrate the relevant theorems. The paper ends with a discussion on the general control cost case and some feasible bounds on the optimal solution are offered.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
R. Britney, “Optimal screening plans for nonserial production systems”,Management Science,18, pp. 550–559, 1972.
B. J. Yum and E. D. McDowell, “The optimal allocation of inspection effort in a class of nonserial production systems”,IIE Transactions,13, pp. 285–293, 1981.
A. Garcia-Diaz, T. W. Foster and M. Bonyuet, “Dynamic programming analysis of special multistage inspection systems”,IIE Transactions,16, pp. 115–125, 1984.
C. C. Beightler and L. G. Mitten, “Design of an optimal sequence of interrelated sampling plans”,Journal of American Statistical Association,59, pp. 96–104, 1964.
E. D. Brown, “Some mathematical models of inspection along a production line”, Technical Report No. 36, Operations Research Center, MIT, 1968.
D. L. Dietrich, “A Bayesian quality assurance model for a multistage production process”, PhD thesis, University of Arizona, Department of Aerospace and Mechanical Engineering, 1971.
W. K. Woo and T. E. Metcalfe, “Optimal allocation of inspection effort in multistage manufacturing processes”,Western Electric Engineer,16, pp. 8–16, 1981.
S. S. Ercan, “Systems approach to the multistage manufacturing connected-unit situation”,Naval Research Logistics Quarterly,19, pp. 493–500, 1972.
G. F. Lindsay and A. B. Bishop, “Allocation of screening inspection effort — a dynamic programming approach”,Management Science,10, pp. 342–352, 1964.
L. S. White, “The analysis of a single class of multistage inspection plans”,Management Science,12, pp. 685–693, 1966.
L. S. White, “Shortest route models for the allocation of inspection effort on a production line”,Management Science,15, pp. 249–259, 1969.
P. M. Pruzan and J. T. R. Jackson, “A dynamic programming application in production line inspection”,Technometrics,9, pp. 73–81, 1967.
M. R. Garey, “Optimal test point selection for sequential manufacturing processes”,Bell System Technical Journal,51, pp. 291–300, 1972.
G. Eppen and E. Hurst, “Optimal location of inspection stations in a multistage production process”,Management Science,20, pp. 1194–1200, 1974.
R. R. Trippi, “An on-line computational model for inspection resource allocation”,Journal of Quality Technology,6, pp. 167–174, 1974.
R. R. Trippi, “The warehouse location formulation as a special type of inspection problem”,Management Science,21, pp. 986–988, 1975.
D. P. Ballou and H. L. Pazer, “The impact of inspector fallibility on the inspection policy in serial production systems”,Management Science,28, pp. 387–399, 1982.
M. H. Peters and W. W. Williams, “Location of quality inspection stations: an experimental assessment of five normative rules”,Decision Sciences,15, pp. 389–408, 1984.
E. Menipaz, “A taxonomy of economically based quality control procedures”,International Journal of Production Research,16(2), pp. 153–167, 1978.
A. L. Dorris and B. L. Foote, “Inspectors errors and statistical quality control: a survey”,American Institute of Industrial Engineers — Transactions,10, p. 148, 1978.
T. Raz, “A survey of models for allocating inspection effort in multistage production systems”,Journal of Quality Technology,18(4), pp. 239–247, 1986.
D. P. Ballou and H. L. Pazer, “Process improvement versus enhanced inspection in optimized systems”,International Journal of Production Research,23(6), pp. 1233–1245, 1985.
B. J. Yum and E. D. McDowell, “Optimal inspection policies in a serial production system including scrap rework and repair: an MLIP approach”,International Journal of Production Research,25(10), pp. 1451–1464, 1987.
G. Rabinowitz, “Quality control of multistage production systems”, doctoral Dissertation, Case Western Reserve University, 1989.
About this article
Cite this article
Stern, H.I., Ladany, S.P. Optimal number and allocation of controls among serial production stages. Int J Adv Manuf Technol 9, 398–407 (1994). https://doi.org/10.1007/BF01748485
- Production control
- Quality control