In this paper, we establish an economic production quantity (EPQ) based inventory model by
considering various types of non-perfect products. We classify products in four groups of
perfect, imperfect, defective but reworkable and non-reworkable defective items. The demand
is a power function of price and marketing expenditure and production unit cost is considered to
be a function of lot size. The objective of this paper is to determine lot size, marketing
expenditure, selling price, set up cost and inventory holding cost, simultaneously. The problem
is modeled as a nonlinear posynomial geometric programming and an optimal solution is
derived. The implementation of the proposed method is demonstrated using a numerical
example and the sensitivity analysis is also performed to study the behavior of the model.

Nowadays electronic commerce plays an important role in many business activities, operations, and transaction processing. The recent advances on e-businesses have created tremendous opportunities to increase profitability. This paper presents a multi-objective marketing planning model which simultaneously determines efficient marketing expenditure, service cost and product & apos; s selling price in two competitive markets. To solve the proposed model, we discuss a multi-objective geometric programming (GP) approach based on compromise programming method. Since our proposed model is a signomial GP and global optimality is not guaranteed for the problem, we transform the model to posynomial form. Finally, the solution procedure is illustrated via a numerical example and a sensitivity analysis is presented.

This paper studies inventory and pricing policies in a non-cooperative supply chain with one supplier and several retailers who are involved in producing, delivering and selling a single product. We consider inventory policies in an information-asymmetric vendor managed inventory. The study consists of different scenarios where a supplier produces the product at the wholesale price to multiple retailers. The retailers also distribute the product in dispersed and independent markets at retail selling prices. The demand rate for each market is a non-decreasing concave function of the marketing expenditures of both local retailers and the manufacturer, but a non-increasing and convex function of the retail selling prices. The primary purpose is to determine wholesale price, marketing expenditure for supplier and retailers, replenishment cycles for the product, and backorder quantity to maximize the total profit for both groups of supplier and retailers. All scenarios are modeled as a Stackelberg game where the manufacturer is the leader and the retailers are the followers. A numerical study has been presented to demonstrate the influences of decision variables and/or parameters in various scenarios. Finally, sensitivity analysis is performed to study the impact of different parameters on total profitability.

Vendor Managed Inventory (VMI) is one of the effective techniques for managing the inventory in supply chain. VMI models have been proven to reduce the cost of inventory compared with traditional ones under some conditions such as constant demand and production expenditure. However, the modeling of the VMI problem has never been studied under some realistic assumptions such as price dependent demand. In this paper, three problem formulations are proposed. In the first problem formulation, we study a VMI problem with one buyer and one supplier when demand is considered to be a function of price and price elasticity to demand, and production cost is also a function of demand. The proposed model is formulated and solved in a form of geometric programming. For the second and the third models, we consider VMI problem with two buyers and two suppliers assuming that each buyer centre is relatively close to the other buyer centre. Each supplier has only one product which is different from the product of the other supplier. Two suppliers cooperate in customer relationship management and two buyers cooperate in supplier relationship management as well, so the suppliers send the orders of two buyers by one vehicle, simultaneously. For the third model, an additional assumption which is practically applicable and reasonable is considered. For all the proposed models, the optimal solution is compared with the traditional one. We demonstrate the implementation of our proposed models using some numerical examples.