Gerhard Tintner and Salwa Ali S. Farghali, The Application of Stochastic Programming to the UAR First Five Year Plan (1967)

Gerhard Tintner and Salwa Ali S. Farghali’s journal article examines how stochastic programming can inform economic planning when productive relationships are variable rather than fixed. Its empirical subject is Egypt’s First Five-Year Plan, covering 1960/61–1964/65, and specifically the allocation of labor and capital between agriculture and industry. The argument proceeds from a formal treatment of technical risk through a comparison of five allocation policies to a qualification of the model’s authority. Although probabilistic calculation can clarify choices, the authors ultimately argue that central planning involves uncertainty that cannot adequately be represented by known probability distributions.

The opening conceptual move replaces a single predicted outcome with a distribution of possible outcomes. Treating output/labor and output/capital coefficients as random variables makes planning more realistic than assuming that productive relationships remain fixed. The intended contribution is both computational and evaluative: to derive an objective basis for choosing among policies and to examine what “risk” means under central planning. Statistical modeling promises guidance without eliminating the difficulty of choosing among interdependent targets, resources, and conditions.

The model maximizes combined agricultural and industrial output at the end of the plan. It considers only two productive factors, capital and labor, whose annual supplies are estimated from published planning and statistical materials. Four technical coefficients represent each sector’s output relative to these inputs; they are assumed to be independent, normally distributed random variables. Crucially, the authors do not optimize over every possible allocation. They stipulate five policies in advance, each assigning fixed proportions of labor and capital to the two sectors, and compare the resulting output distributions.

Annual constraints link each sector’s output to its preceding output and the contribution of allocated inputs. Minimum-output constraints preserve the pre-plan levels. Once resources, allocation proportions, and coefficient values are specified, the programming problem becomes particularly simple:

With this very simple form, the maximization solution is obviously always obtained by a zero slack vector.

The analytical emphasis therefore falls less on solving a difficult allocation problem than on tracing the consequences of uncertain technical coefficients. For each coefficient, the authors select five standardized values, yielding 625 combinations per policy. Each combination generates an optimized terminal output; probabilities attached to the combinations then provide estimated means and dispersion measures. The procedure turns alternative allocation rules into comparable profiles of expected production and exposure to unfavorable outcomes.

The preferred policy is not simply the one with the highest expected output. Policy IV assigns three-quarters of labor to agriculture and one-quarter to industry, while dividing capital equally. Its estimated mean output is approximately 1,841.94 million Egyptian pounds, with a reported standard deviation of 77.43, lower than those of the other policies. Policy V offers a higher mean but substantially greater dispersion. The authors make their evaluative criterion explicit:

Contrasting these results, we choose to select policy IV—as the 'best'—for being the lowest in risk among the highest in mean value.

This is a judgment balancing output against risk, rather than a uniquely determined consequence of output maximization. Calling the policy “best” incorporates a preference for stability among relatively productive alternatives. The reported actual plan allocated roughly 85 percent of labor and 44 percent of capital to agriculture. Its proximity to Policy IV supplies the article’s qualified empirical support for the planners’ allocation.

That support remains conditional. Estimated actual terminal output, approximately 2,489.12 million Egyptian pounds, considerably exceeds the means generated for the five experimental policies. The authors attribute much of this gap to deficient data and to simplifying, arbitrary assumptions required by missing information. Their coefficient estimates themselves rely on selected samples chosen for sectoral suitability. They consequently defend the actual policy only insofar as their reconstructed allocations and assumptions adequately represent the planning situation.

The numerical presentation also warrants caution. Policy II’s stated mean differs from the value in its formula and comparison table. More fundamentally, a footnote reports that testing rejected the assumed normal distribution of terminal output for the selected policy, while setting that issue aside. The distributions and reported lower-probability levels therefore support an exploratory comparison more securely than a precise validation of the plan.

The conclusion shifts from measurable technical risk to uncertainty arising within plan execution:

Uncertainty prevails if the relevant probability distributions are not known.

Organizational and human factors affect technical relationships but cannot, the authors argue, be controlled or isolated for numerical study. These factors interact with production conditions, rather than merely adding an independently measurable source of variation. Their presence changes the epistemic status of the planning problem:

Furthermore, as they interact with the technical factors, they turn what would have been a situation of risk into one of uncertainty.

The article’s significance lies in this tension between formal decision support and its institutional limits. Stochastic programming makes the consequences of technical variability explicit and exposes the trade-off behind a preferred allocation. Yet the authors’ final position preserves a necessary role for planners’ choice and value judgment where probabilities cannot reliably be known. The model provides disciplined guidance, while the experience of constructing and applying it reveals why calculation cannot fully determine policy.