A game theory approach in seller–buyer supply chain

In this paper, several seller–buyer supply chain models are proposed which incorporate both cost factors as well as elements of competition and cooperation between seller and buyer. We assume that unit marketing expenditure and unit price charged by the buyer influence the demand of the product being sold. The relationships between seller and buyer will be modeled by non-cooperative and cooperative games, respectively. The non-cooperative game is based on the Stackelberg strategy solution concept, where we consider separately the case when the seller is the leader (Seller-Stackelberg) and also when the buyer is the leader (Buyer-Stackelberg). Pareto efficient solutions will be provided for the cooperative game model. Numerical examples presented in this paper, including sensitivity analysis of some key parameters, will compare the results between different models considered.     

Optimal Production and Marketing Planning

This paper presents an integrated production, marketing and inventory model which determines the production lot size, marketing expenditure and products selling price. Our model is highly nonlinear and non-convex and cannot be solved directly. Therefore, Geometric Programming (GP) is used to locate the optimal solution of the proposed model. In our GP implementation, we use a transformed dual problem in order to reduce the model to an optimization of an unconstrained problem in a single variable and the resulting problem is solved using a simple line search. We analyze the solution in different cases in order to study the behaviour of the model and for each case, a numerical example is used to demonstrate the implementation of our analysis.     

A hybrid method of Pareto,TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments

Multi-periodic inventory control problems are mainly studied employing one of two assumptions. The first is the continuous review, where depending on the inventory level, orders can be placed at any time, and the other is the periodic review, where orders can be placed only at the beginning of each period. In this paper, we relax these assumptions and assume that the time-periods between two replenishments are random fuzzy variables. While in the model of the problem at hand the decision variables are of integer type and there are space and service level constraints, for the shortages we consider a combination of back-order and lost-sales. We show the model of this problem to be an integer-nonlinear-programming type and in order to solve it, a hybrid method of Pareto, TOPSIS and Genetic Algorithm approach is used. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology.     

Solving a dynamic cell formation problem using metaheuristics

In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed by using some traditional metaheuristic methods such as genetic algorithm (GA), simulated annealing (SA) and tabu search (TS). Most of previous researches were done under the static condition. Due to the fact that CF is a NP-hard problem, then solving the model using classical optimization methods needs a long computational time. In this research, a nonlinear integer model of CF is first given and then solved by GA, SA and TS. Then, the results are compared with the optimal solution and the efficiency of the proposed algorithms is discussed.     

An economic order quantity model with partial backordering and a special sale price

A constant unit purchase cost is one of the main assumptions in the classic economic order quantity model. In practice, suppliers sometimes offer special sale prices to stimulate sales or decrease inventories of certain items. In this paper we develop an EOQ model with a special sale price and partial backordering. We prove the convexity of the cost-reduction function if a special order is placed at the special sale price. A solution method is proposed and numerical examples are presented.     

A multi-objective production smoothing model with compressible operating times

Real life multi-product multi-period production planning often deals with several conflicting objectives while considering a set of technological constraints. The solutions of these problems can provide deeper insights to the decision makers/managers than those of single-objective problems. Some managers want to use from a production plan that is corresponding to minimum change in production policy along with minimum total cost simultaneously as possible. On the other hand, these two objectives have intrinsic conflicts such that producing in a fixed rate will cause huge costs than producing economically or according to JIT. So this paper presents a novel multi-objective model for the production smoothing problem on a single stage facility that some of the operating times could be determined in a time interval for. The model is to: (a) smooth the variations of production volume, and (b) minimize total cost of the corresponding production plan, while satisfying a set of technological constraints such as limited available time. The proposed model is developed in a real case study and is solved by a new genetic algorithm. The proposed genetic algorithm uses a novel achievement function for exploring the solution space, based on LP-metric concepts. Computational experiences reveal the sufficiency and efficiency of the proposed approach in contrast to previous researches.     

Using genetic algorithm to solve dynamic cell formation problem

In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed using genetic algorithm (GA). Previous models presented in the literature contain some essential errors which will decline their advantageous aspects. In this paper these errors are discussed and a new improved formulation for dynamic cell formation (DCF) problem is presented. Due to the fact that CF is a NP-hard problem, solving the model using classical optimization methods needs a long computational time. Therefore the improved DCF model is solved using a proposed GA and the results are compared with the optimal solution and the efficiency of the proposed algorithm is discussed and verified.