Abstract:
The production-inventory models are traditionally adopted for manufacturing systems. A relatively new area of production-inventory planning is related to livestock growing process. This research aims to propose a class of production-inventory model for new items titled growing items. In such a case, a rancher orders a quantity of newborn livestock like chicks or lambs, grow them to an appropriate weight during the growing period, slaughter them and then sells them to the meat market. The goal is to calculate the economic order quantity of the growing items at the start of a growing cycle, the optimal length of the growing cycle and the optimal total profit. We, in this research, extend the previous work to the case of joint growing and deteriorating items, where livestock grows at growing period, and, additionally, the slaughtered livestock may be deteriorated during the sales period. Moreover, since some amount of slaughtered livestock is waste and should be disposed, a weight reduction factor is considered when livestock is slaughtered. The inventory models are constructed for this case, a heuristic solution algorithm is presented, a numerical example is discussed, and finally, sensitivity analysis is carried out to investigate the applicability of the problem.
Machine summary:
In such a case, a rancher orders a quantity of newborn livestock like chicks or lambs, raises them to an appropriate weight during the growing period, slaughters them and then sells them to the meat market.
The inventory level for growing items The purchasing cost per cycle, when we purchase newborn livestock in each cycle and each one bears weight , is obtained as: (View the image of this page) Since decision variables in the model are (i) order quantity for newborn livestock and (ii) weight of livestock slaughtering , we should remove all other dependent variables like in .
(View the image of this page) Figure 2: The inventory level for joint growing and deteriorating items The setup, purchasing, and feeding costs are the same as the previous model as follows.
(View the image of this page) To obtain the optimal values for and , we should solve the system of equations resulting from setting the partial derivative of with respect to and to zero, as follows(View the image of this page) The same procedure is carried out for the second model (joint growing and deteriorating items), as follows: (View the image of this page) 3.
Results of implementations (View the image of this page) As an analysis of the first model, the results obtained reveal that the rancher should order 345, 822 and 349 lambs for power, exponential and quadratic feed intakes at the start of each growing cycle and slaughter them when they reach weight 24.
Conclusions This research proposed production-inventory models for joint growing and deteriorating items as an extension of the work presented by Rezaei (2014).