This paper examines the production planning and equity investment decisions of a cash-constrained farmer who processes a raw commodity into a value-added product through a closed-membership agricultural cooperative (closed co-op). The farmer is required to purchase a certain amount of shares within specific limits to join in the co-op. The equity investment entitles the right to deliver a particular amount of qualified raw commodity in proportion, and the shares are transferable and appreciable. We consider a multi-period model in which the farmer first considers a one-time decision on participation (whether to join in the co-op). If yes, the farmer determines the production capacity and the initial equity investment in addition to the periodic production planning and equity investment adjustment when yield, spot prices, and share price are uncertain. We propose the condition under which the farmer shall participate in the co-op and characterize the optimal capacity and equity investment policies in closed form. We also investigate how the transferability of shares affects the farmer’s optimal decisions and profitability by fixing the initial equity investment. Further, we examine the performance of a variety of heuristic policies when the quality requirement or the yield uncertainty is ignored. The results provide insights into a farmer’s decision making, production planning, and cash management.

本文研究了一个现金紧缺的农民的生产计划和股权投资决策，该农民通过一个封闭式成员农业合作社（封闭式合作社）将原材料加工为增值产品。要求农民在特定限制内购买一定数量的股份才能加入合作社。股权投资赋予按比例交付一定数量合格原材料的权利，股份具有可转让性和可观性。我们考虑一个多时期模型，在这种模型中，农民首先考虑一次参与决策（是否参加合作社）。如果是，则农民在确定产量，现货价格，和股价不确定。我们提出了农民参与合作社的条件，并以封闭的形式描述了最佳产能和股权投资政策。我们还研究了股票的可转让性如何通过固定初始股权投资来影响农民的最佳决策和获利能力。此外，当质量要求或产量不确定性被忽略时，我们研究了各种启发式策略的性能。结果为深入了解农民的决策，生产计划和现金管理提供了见识。我们还研究了股票的可转让性如何通过固定初始股权投资来影响农民的最佳决策和获利能力。此外，当质量要求或产量不确定性被忽略时，我们研究了各种启发式策略的性能。结果为深入了解农民的决策，生产计划和现金管理提供了见识。我们还研究了股票的可转让性如何通过固定初始股权投资来影响农民的最佳决策和获利能力。此外，当质量要求或产量不确定性被忽略时，我们研究了各种启发式策略的性能。结果为深入了解农民的决策，生产计划和现金管理提供了见识。