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This paper deals with the efficiency level of cereal-dairy sheep production systems in the Mediterranean Basin. It studies them in the Protected Designation of Origin “Manchego Cheese”, located in Castilla-La Mancha (Spain). Previous studies have alerted to the low productivity levels in these farms, suggesting conducting an efficiency analysis. This work evaluates technological levels by means of synthetic indexes. Two different groups were defined. Technical efficiency was estimated using Data Envelopment Analysis with metafrontier models. The higher the technological level, the higher the efficiency level. Low technology farms could increase their production at least around 23% using the technologies of the high-technology group. Thus, it could be wise to apply new technologies, as new feeding techniques, and the use of troughs of cement, dungheaps, flushing and selective breeding. Increase farm size is a way to implement these technologies. Special attention to managerial functions, mainly organisation and planning, is also advisable. The government must improve the agricultural policies. These actions could increase efficiency, resiliency and sustainability of the farms. Keywords: dairy sheep production systems, data envelopment

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This paper presents the optimal policy for an inventory model where the demand rate potentially depends on both selling price and stock level. The goal is the maximization of the profitability index, defined as the ratio income/expense. A numerical algorithm is proposed to calculate the optimal selling price. The optimal values for the depletion time, the cycle time, the maximum profitability index, and the lot size are evaluated from the selling price. The solution shows that the inventory must be replenished when the stock is depleted, i.e., the depletion time is always equal to the cycle time. The optimal policy is obtained with a suitable balance between ordering cost and holding cost. A condition that ensures the profitability of the financial investment in the inventory is established from the initial parameters. Profitability thresholds for several parameters, including the scale and the non-centrality parameters, keeping all the others fixed, are evaluated. The model with an isoelastic price-dependent demand is solved as a particular case. In this last model, all the optimal values are given in a closed form, and a sensitivity analysis is performed for several parameters, including the scale parameter. The results are illustrated with numerical examples.