This paper studies production planning with random yield and demand. It is a departure from previous studies of random yield in that it defines the sale price and the purchasing cost as exogenous and increasing with decreasing yield. While this behavior can be observed in various industries (e.g., citrus), the paper focuses on the olive oil industry as its application. Production of olive oil is a challenging business as olives grow every other year; thus, a risky investment is involved. A new practice among olive oil producers involves leasing farm space from farmers to grow olives. When the yield of olives is low (because of weather, disease, etc.), the oil producer gets a second chance to buy olives from other farmers at a unit cost varying with the yield. In this case, the sale price of olive oil increases in the market place because of the reduced supply. When the yield is high, the company uses some of its olives for olive oil production and some are salvaged. After olives are pressed and olive oil is produced, the company experiences an uncertain demand. The paper makes four contributions: First, it is shown that the objective function is concave in the amount of farm space leased, so that the first-order conditions provide the globally optimal solution. Second, it illustrates how the total production of olive oil changes with the yield. Third, it proves that the optimal amount of farm space leased decreases under the presence of a second (and reliable) source of supply. Finally, unlike traditional yield papers, the fourth result shows that increased yield variance does not necessarily increase the optimal amount of farm space to be leased when there is a second chance to obtain supplies.production planning, yield and demand uncertainty, stochastic programming, yield-dependent price, yield-dependent cost, olive oil production

This paper studies the role of the yield-dependent trading cost structure influencing the optimal choice of the selling price and production quantity for a firm that operates under supply uncertainty in the agricultural industry. The firm initially leases farm space, but its realized amount of fruit supply fluctuates because of weather conditions, diseases, etc. At the end of the growing season, the firm has three options: convert its crop supply to the final product, purchase additional supplies from other growers, and sell some (or all) of its crop supply in the open market without converting to the finished product. We consider the problem both from a risk-neutral and a risk-averse perspective with varying degrees of risk aversion. The paper offers three sets of contributions: (1) It shows that the use of a static cost exaggerates the initial investment in the farm space and the expected profit significantly, and the actual value gained from a secondary (emergency) option for an agricultural firm is lower under the yield-dependent cost structure. (2) It proves that although the risk-neutral firm does not benefit from fruit futures, a sufficiently risk-averse firm can benefit from the presence of a fruit futures market. The same risk-averse firm does not purchase fruit futures when it operates under static costs. Thus, fruit futures can only add value under yield-dependent trading costs. (3) Contrary to the results presented for the newsvendor problem under demand uncertainty, the firm does not always commit to a lower initial quantity (leased farm space) under risk aversion. Rather, the firm might lease a larger farm space under risk aversion.

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Motivated by an aggregate production-planning problem in an actual global manufacturing network, we examine the impact of exchange-rate uncertainty on the choice of optimal production policies when the allocation decision can be deferred until the realization of exchange rates. This leads to the formulation of the problem as a two-stage recourse program whose optimal policy structure features two forms of flexibility denoted as operational hedging: (1) production hedging, where the firm deliberately produces less than the total demand; and (2) allocation hedging, where due to unfavorable exchange rates, some markets are not served despite having unused production. Our characterization of the optimal policy structure leads to an economic valuation of production and allocation hedging. We show that the prevalence of production hedging is moderated by the degree of correlation between exchange rates. A comprehensive examination under the following four generalized settings provides the depth, scope, and relevancy that our proposed operational hedges play to facilitate aggregate planning: (1) multiple periods, (2) demand uncertainty, (3) price setting or monopolistic pricing, and (4) price setting under demand uncertainty. We show that production and allocation hedging are robust for these generalizations and should be integrated into the overall aggregate planning strategy of a global manufacturing firm.exchange-rate uncertainty, international operations management, production planning, production hedging, allocation hedging, price setting