Joint Decisions On Pricing, Advertising And Inventory For Multi-Product

Joint decisions on pricing, advertising and inventory combines the enterprise marketing decision and significant inventory decision problems, which builds a bridge between the marketing management and production/procurement Department of enterprise. As a result, the internal enterprises operation management is coordinated and the operational efficiency is improved. For the enterprises who product and operate multiple products, joint decisions on pricing, advertising and inventory is vital to the operating revenue. Therefore, this paper studies the problems of joint decisions on pricing and inventory, joint decisions on advertising and inventory, joint decisions on pricing, advertising and inventory for multi-product with the deterministic demand and stochastic demand. Research on joint decision problems of pricing, advertising and inventory for multi-product with deterministic demand.In the case of deterministic demand, first, we established joint decisions on pricing and inventory model for multi-product based on EOQ without stockout and with stockout, and used branch-and-bound algorithm to solve the model. The optimal policies for multi-product are gained through numerical examples. The results showed that, due to the certainty of demand, joint decisions on multi-product and decentralized decisions on single product neither has any influence on the pricing policy. The stockout has no influence on the pricing as well. The comparative analysis on joint decisions on multi-product and decentralized decisions on single product showed that results of joint decisions are superior to the results of decentralized decisions. Second, taking into account the capacity constraints, we established an economic lot sizing model of joint decisions on dynamic pricing for multi-product. Lagrangian relaxation algorithm is proposed to solve the model, optimal joint decisions are gained. The numerical results verified the efficiency and accuracy of the Lagrangian relaxation algorithm solving the problem of joint decisions for multi-product. And the results also showed that the optimal policy of joint decisions for multi-product is better than the policy of decentralized decision for single product. Third, given the inventory capacity constraints and budgetary constraints, the joint pricing and inventory decision models for multi-product without stockout and with stockout are studied. The optimization algorithm combination of genetic algorithm and non-linear programming optimization algorithm based on dynamic programming is proposed to solve the models. The optimal policies for multi-product are obtained through numerical examples. The property of algorithm is analyzed. Fourth, in view of the effect of advertising on demand, we considered advertising costs into the joint decisions on product pricing and inventory, and build the model of joint decisions on pricing, advertising and inventory for multi-product with capacity constraint and budget constraint. The optimal pricing, production and advertising expenditure for each product are obtained through numerical examples. Numerical results showed that the advertisement influence on product demand is large, the enterprise puts into less advertising expenditure, and can achieve the purpose of promoting sales. On the contrary, if advertisement influence on product demand is less, the advertising expenditure on the product is increased. The capacity influence on profits showed that there is an optimal capacity. If the capacity is too small, you cannot meet the production schedule. Thereby, the enterprise profit is decreased as a result. If the capacity is too high, then the excess capacity can cause the loss of profit. But the budgetary constraint is proportional to the profit.In the case of stochastic demand, first, the Distribution-Free newsboy model of joint advertising and inventory for multi-product is proposed. The optimal inventory policy for multi-product under budget constraint without advertising is considered. Then the model is extended to joint decisions on advertising and inventory for multi-product. Lagrangian heuristic algorithm is proposed to solve the model. The effects of advertising on demand are analyzed through numerical examples. Which are the three different cases such as the Constant Variance Case, Constant Coefficient of Variation Case and Increase Coefficient of Variation Case. The results showed that the profits gained when advertising are higher than that when no advertising. The profit gained under CVC is largest and the profit gained under ICVC is smallest in the three different cases of advertising influences on demand. Second, the mathematical model of joint decisions on pricing, advertising and inventory for multi-product is established, and the existence of optimal solutions is analyzed. Then, the model is extended to the joint decisions on pricing, advertising and inventory for multi-product with budget constraint. Assuming random obedience negative exponential distribution, the optimal policy is attained through numerical example. Assuming the random variable is randomly generated, through numerical simulation, The random distributions of optimal pricing, ordering and advertising expenditure for each product are simulated, which can provided the decision-making references for enterprises.