Dynamic optimal control policy in advertising price and quality

Abstract

This study presents an algorithm for deriving the long-term polices of quality level, price and advertisement for a product. The diVusion models and cost functions are combined to formulate pro® t functions capable of determining future pro® t trends. The algorithm ® rst implements the optimal control theory to derive the optimal conditions of the pro® t function. Then the genetic algorithm is employed to search for the approximate solutions of quality level, price and advertising expenditure at each period on the planning horizon (life cycle). Examples of diVerent scenarios of the model parameters are presented to describe the results obtained herein. Sensitivity analysis for the major parameters is performed to specify their eVects on pro® ts. Results in this study allow us, ® rstly, to obtain explicit solutions simultaneously with respect to quality, price and advertising policies, secondly, to propose an appropriate algorithm for solving the diVerent scenarios of the dynamic pro® t function, which consists of the diVusion function and cost function, and thirdly, to enhance the long-term pro® t performance via the polices proposed herein, that is the approximation of the best solution. NomenclatureA…t † rate of advertising expenditure at time t C…x…t †; q…t † † total cost per unit at time t for a cumulative sales volume x…t † and quality level q…t † d price parameter h quality parameter M total number of potential purchasers over the life cycle of the product P…t † unit price at time t q…t † quality level at time t, 0 < q…t † 4 1 r discount rate T period of the life cycle x…t † cumulative sales volume by time t x 0 …t †ˆg…x…t †; p…t †; q…t †; A…t † †, sales rate at time t for a cumulative sales volume x…t †, price p…t †, quality level q…t † and advertising expenditure A…t † ¬ innovation coe cient reaction coe cient for advertising ® imitation coe cient

Pricing management between partnering rivals: a coopetitive diffusion analysis

“…However, when the products of NB manufacturers and PL retailers compete head to head on the same store shelf, the determination of pricing for either rival is more complex. For example, to maintain its market share within a retail partner's store, an NB manufacturer may stimulate demand for an NB line through additional advertising (Ip et al, 2012;Lin et al, 2001) or raising the PL production price (Karray & Martín-Herrán, 2009). The retailer in response may reduce the prices on its competing PL products or eliminate shelf space for the NB products.…”

Dynamic Effort Allocation Problem Using Genetic Algorithm Approach

“…The followings are two necessary conditions that hold for an optimal solution: The corresponding Hamiltonian will be given as The necessary condition for optimality is H w1 =0 Now, The above optimization problem is solved by genetic algorithm approach (GA), which is categorized as a powerful computerized exploratory search and optimization method [23][24][25][26] GA is a popular computerized heuristic method based on the Darwin's evolutionary theory and natural genetics. Genetic Algorithm has been effectively implemented on diverse area of optimization problem like transportation, assignment problems, inventory control, job scheduling and decision-making problems based on real-life situation.…”

The warranty policy under fuzzy environment

“…In exploring the optimality of a warranty policy, many issues are proposed, such as the renewed period of warranty (Chukova and Hayakawa, 2004; Mitra and Patankar, 1997; Thomas, 1989), the cost structure for replacement (Barlow and Hunter, 1960), repair (Tilquin and Cléroux, 1975), periodic replacement of shock (Boland and Proschan, 1982), optimal time for repair (Sheu, 1993), optimal time of repair or replacement (Jhang and Sheu, 1995), minor and catastrophic failure (Sheu, 1993), optimal maintenance (Juang and Anderson, 2004; Wang and Sheu, 2003; Bai and Pham, 2004), and association between price, quality, and warranty period (Lin and Shue, 2005; Lin et al , 2001; Kotler, 1976; Peterson, 1970). Some of these studies assume that the failure process obeys a non‐homogeneous procession process (Nakagawa and Kowada, 1983; Savits, 1988; Juang and Anderson, 2004).…”