In this paper, we present a new formulation for the Leontief production model using quantum calculus analogue. This formulation unifies discrete and continuous Leontief production models. Also, the classical Leontief production model is obtained by choosing q = 1. In addition, briefly give an introduction to quantum calculus. We present the formulation for continuous Leontief production models as well as quantum calculus models. Moreover, we establish the weak duality theorem and the strong duality theorem for quantum calculus analogue. Furthermore, using the objective functions for the primal and the dual quantum calculus models, we can easily obtain upper and lower bounds for the value of production at any production plan. Finally, examples are provided in order to illustrate the given results.

In this paper, we derive a new formulation for an optimal investment allocation in N-regional economic model using quantum calculus analogue. This model is described as an optimal control model and formulated in both primal and dual models using quantum calculus formulation. This formulation is an extension of regional economic models. Also, the new formulation provides an exact optimal investment allocation. In addition, the classical regional economic model is obtained by choosing q=1. Furthermore, we formulate the primal and the dual regional economic models in quantum calculus. Moreover, we present a new version of the duality theorems for quantum calculus case. Finally, example is provided and solved using MATLAB. in order to show the given new results.

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Manufacturers need to have a good supply chain management system in order to achieve low inventory levels, short lead times and adjustability to meet customer demands at minimal total operation cost. The most important drawback of existing methods used to minimize inventory costs as Just-in-time (JIT) methodology or to minimize transportation and order costs as Economic Order Model (EOQ). This minimization strategy may not be able to give the best order quantity because of the relationship between inventory cost and transportation cost, In this paper, we used genetic algorithm (GA) to reduce the inventory and transportation costs together to determine the Best Order Quantity (BOQ). The main advantage of this new method, it is covers pull system, push systems, short planning horizon, and long planning horizon.

The integration of decision-making will lead to the robust of its decisions, and then determination optimum inventory level to the required materials to produce and reduce the total cost by the cooperation of purchasing department with inventory department and also with other company,s departments. Two models are suggested to determine Optimum Inventory Level (OIL), the first model (OIL-model 1) assumed that the inventory level for materials quantities equal to the required materials, while the second model (OIL-model 2) assumed that the inventory level for materials quantities more than the required materials for the next period.                                                    This study was applied in Wasit Company for Textile Manufacturing in the Textile Factory, where it produces five products, which are printed striped, plain, poplin, dyed poplin and Naba weave.  The products are made from cotton and they are passing through several stages to transfer to the final product. A genetic algorithm is used to determine the optimum quantity of the purchase a cotton and colors for each month and with minimum cost. Where the purchasing and transportation costs were either constant or variable with respect to purchased quantities while holding cost is kept constant. The results showed that the total cost of the first model is minimum than the second model because the holding cost for this model is less from the second model, while the purchasing and transportation costs from two models are equals. The percentage of purchasing cost for cotton is the biggest value, more 99% of purchasing cost for two models.