Multistage multiproduct advertising budgeting

We propose and analyze an effective model for the Multistage Multiproduct Advertising Budgeting problem. This model optimizes the advertising investment for several products, by considering cross elasticities, different sales drivers and the whole planning horizon. We derive a simple procedure to compute the optimal advertising budget and its optimal allocation. The model was tested to plan a realistic advertising campaign. We observed that the multistage approach may significantly increase the advertising profit, compared to the successive application of the single stage approach.     

A noniterative multiproduct multiperiod production planning method

Production planning for multiple products on a single production facility over a time horizon requires minimizing the sum of production costs (regular time, overtime and subcontracting) and inventory carrying costs for meeting the known demands of the products. It is shown that the problem can be formulated and solved by a simple and noniterative method of ‘column minima’ even for multiple product situations.     

On the noniterative multiproduct multiperiod production planning method

Bahl and Zionts [H.C. Bahl, S. Zionts, A noniterative multiproduct multiperiod production planning method, Operations Research Letters 1 (1982) 219-221] formulated a problem for planning multiproduct multiperiod production on a single facility. They developed a column-minima noniterative method and claimed that it gave an optimal solution. We show that the claim is incorrect.     

Optimal and heuristic algorithms for multiproduct uncapacitated facility location

We consider a generalization of the classic uncapacitated facility location problem (UFLP) in which customers require multiple products. We call this the multiproduct uncapacitated facility location problem (MUFLP). In MUFLP, in addition to a fixed cost for opening a facility, a fixed cost is incurred for each product that a facility is equipped to handle. Also, an assignment cost is incurred for satisfying a customer's requirement for a particular product at a chosen facility. We describe a branch-and-bound algorithm for MUFLP. Lower bounds are obtained by solving a UFLP subproblem for each product using a dual ascent routine. We also describe a heuristic branch-and-bound procedure in which the solutions to the subproblems at a given node might not generate a true lower bound. To generate a feasible solution, a ‘superposition’ heuristic based on solving UFLP subproblems for each product, as well as a ‘drop’ heuristic that eliminates facilities and equipment from the solution in a step-by-step manner, are given. Computational results are reported.     

Price-based planning and scheduling of multiproduct orders in symbiotic manufacturing networks

This paper addresses the problem of planning and scheduling operations when processing a multiproduct order in a Symbiotic Manufacturing Network (SMN). The order is characterized for each of its products, by linear routings of operations which can be performed in parallel by different contracting firms of the network. We first present a characterization of the decision process for planning and scheduling operations in SMN. Next, we propose a bidding scheme expressing pricetime trade-off and a multi-commodity network model that can be used to plan and schedule many types of order-based customized production. Finally, an illustrative example is detailed to permit full comprehension of the approach.     

SAA-regularized methods for multiproduct price optimization under the pure characteristics demand model

Utility-based choice models are often used to determine a consumer’s purchase decision among a list of available products; to provide an estimate of product demands; and, when data on purchase decisions or market shares are available, to infer consumers’ preferences over observed product characteristics. These models also serve as a building block in modeling firms’ pricing and assortment optimization problems. We consider a firm’s multiproduct pricing problem, in which product demands are determined by a pure characteristics model. A sample average approximation (SAA) method is used to approximate the expected market share of products and the firm profit. We propose an SAA-regularized method for the multiproduct price optimization problem. We present convergence analysis and numerical examples to show the efficiency and the effectiveness of the proposed method.     

Modelling impact of advertising and optimizing advertising policy: an application in recreation

This paper deals with the problem of the desirable level of advertising expenditure, the optimal distribution of this expenditure in time and the allocation over the media: TV, radio and newspaper for a recreation park in the Netherlands.Although the model id developed for the specific situation of this park, in principle it can be applied in all situations where the interest is in short-term (day-by-day) effects of promotional activities on sales. Examples are: other situations in the recreation and leisure business, cultural events (theatre, cinema) and sales promotions (e.g. weekend offerings) for products in supermarkets.First a model was specified and estimated that relates number of visitors to advertising effort. It also takes into account non-advertising variables that effect the number of visitors.Then this model was used in a heuristic advertising planning procedure, which by means of incremental analysis, for a given budget level searches for the optimal allocation of the advertising budget over media and time.With this procedure, ways to readjust the advertising policy were found: by allocating the budget differently over media and time and by changing the overall budget level.Several recommendations were made to the management of the park, a number of which have already been implemented.     

Planning and scheduling of multistage multiproduct batch plants operating under production campaigns

When plants are operated under stable conditions during reasonable time periods, operation with campaigns is particularly appropriate. The regular operation of the facilities simplifies the production control, the inventory management, the plant operability, etc. A?campaign includes several batches of different products that are going to be manufactured and the same one is cyclically repeated over the time horizon. In this work, a mixed integer linear programming formulation is proposed for the planning and scheduling of given multiproduct batch plants operating with campaigns. The number and size of batches for each product, the campaign composition, the assignment of batches to units and their sequencing, and the number of times that the campaign is repeated over the time horizon must be determined. Taking into account this scenario, an appropriate performance measure is the minimization of the cycle time. An asynchronous slot-based continuous-time representation for modeling the assignment of batches to units and their sequencing is employed, and a novel rule for determining the maximum number of slots postulated for each unit is proposed.     

A multiperiod model for production planning and design in a multiproduct batch environment

A general multiperiod model to optimize simultaneously production planning and design decisions applied to multiproduct batch plants is proposed. This model includes deterministic seasonal variations of costs, prices, demands and supplies. The overall problem is formulated as a mixed-integer linear programming model by applying appropriate linearizations of non-linear terms. The performance criterion is to maximize the net present value of the profit, which comprises sales, investment, inventories, waste disposal and resources costs, and a penalty term accounting for late deliveries. A noteworthy feature of this approach is the selection of unit dimensions from the available discrete sizes, following the usual procurement policy in this area. The model simultaneously calculates the plant structure (parallel units in every stage, and allocation of intermediate storage tanks), and unit sizes, as well as the production planning decisions in each period (stocks of both product and raw materials, production plans, policies of sales and procurement, etc.).     

MILP-based approaches for medium-term planning of single-stage continuous multiproduct plants with parallel units

In this paper, we address the problem of medium-term planning of single-stage continuous multiproduct plants with multiple processing units in parallel. Sequence-dependent changeover times and costs occur when switching from one type of product to another. A traveling salesman problem (TSP)-based mixed-integer linear programming (MILP) model is proposed based on a hybrid discrete/continuous time representation. We develop additional constraints and variables to ensure that subtours do not occur in the solution. The model is successfully applied to an example of a polymer processing plant to illustrate its applicability. In order to solve larger model instances and planning horizons, a rolling horizon approach is developed to reduce the computational expense. Finally, the proposed model is compared to a recently published approach through literature examples, and the results show that the computational performance of the proposed model is superior.     

The Leitmann-Schmitendorf advertising differential game

The paper revisits the advertising differential game suggested by Leitmann and Schmitendorf [1]. We put the model into perspective and discuss the related issues of (i) state separable (or linear-state) games and (ii) open-loop equilibria that are feedback equilibria which are constant with respect to state.     

Scheduling advertising slots for television

The ISCI (Industry Standard Commercial Identification) rotator problem requires the assignment of a set of commercial videotapes to slots such that multiple airings of each tape in the set are as equally spaced as possible with respect to an L₁ loss function. The contributions of this research paper are threefold. First, an enhanced branch-and-bound algorithm is presented and shown to produce optimal solutions for each of several problems that were not computationally feasible for a previously developed branch-and-bound implementation. Second, a fast simulated annealing heuristic is developed for larger problems. This heuristic has established new benchmark (best-known) solutions for 16 large ISCI rotator problems from a recently published test suite. Third, we consider alternative loss function metrics, and have found that a branch-and-bound algorithm for the L_∞ algorithm is especially scalable.     

Transfer pricing and decentralized dynamic lot-sizing in multistage,multiproduct production processes

This paper presents the use of a transfer pricing system to coordinate business units in a Wagner–Whitin type model for a decentralized lot-sizing problem in a dynamic multistage, multiproduct environment. The paper includes two major proofs: (1) a transfer pricing system enabling optimal decentralized lot-sizing is characterized. The transfer pricing system can be interpreted as a generalization of the reciprocal method or step-down allocation method in cost location accounting; and (2) based on a Wagner–Whitin type theorem and the Kakutani fixed point theorem, it is shown that such a transfer pricing system exists.     

Non-linear advertising capital model with time delayed feedback between advertising and stock of goodwill

According to the classical Nerlove-Arrow model, advertising expenditure can be considered as a capital investment to create present and future demand for the firm's products and, hence, to create present and future revenues for the firm. Advertising is assumed to influence via stock of goodwill which cumulatively counts for the effects of the firm's current and past advertising outlays. The paper presents a time delayed feedback model describing the relations between advertising and goodwill. Three different types of effects of advertising upon the dynamics of goodwill are modelled. The advertising policy of the management is incorporated into the model via a non-linear advertising function. The advertising function controls the advertising outlay e.g. by budget constraint and by the actual and target values of goodwill. The behavior of the model is analysed both analytically and numerically. Special attention is given for deriving the stability conditions for the limiting solution. The cases of repelling or chaotic limiting solutions are analysed by bifurcation and state space diagrams. Several numerical examples are given.     

Retail competition and cooperative advertising

We consider a cooperative advertising channel consisting of a manufacturer selling its product through a retailer in competition with another independent retailer. The manufacturer subsidizes its retailer’s advertising only when a certain threshold is positive. Moreover, the manufacturer’s support for its retailer is higher under competition than in its absence.     

A nonlinear Cournot duopoly with advertising

This paper aims at studying local and global dynamics in a nonlinear duopoly with quantity-setting firms and non-cooperative advertising investments that affect the degree of (horizontally) differentiated products. It concentrates on persuasive advertising in a model where each firm has limited information and uses a behavioural rule to set the quantity for the subsequent period. By using some mathematical techniques and numerical simulations, our results show the existence of weak (à la Milnor) attractors, multistability and chaotic dynamics. In the long term, firms may continuously shift from states in which they invest in advertising to states in which advertising investment is absent.     

Optimal advertising strategies with age-structured goodwill

The problem of a firm willing to optimally promote and sell a single product on the market is here undertaken. The awareness of such product is modeled by means of a Nerlove–Arrow goodwill as a state variable, differentiated jointly by means of time and of age of the segments in which the consumers are clustered. The problem falls into the class of infinite horizon optimal control problems of PDEs with age structure that have been studied in various papers either in cases when explicit solutions can be found or using Maximum Principle techniques. Here, assuming an infinite time horizon, we use some dynamic programming techniques in infinite dimension to characterize both the optimal advertising effort and the optimal goodwill path in the long run. An interesting feature of the optimal advertising effort is an anticipation effect with respect to the segments considered in the target market, due to time evolution of the segmentation. We analyze this effect in two different scenarios: in the first, the decision-maker can choose the advertising flow directed to different age segments at different times, while in the second she/he can only decide the activation level of an advertising medium with a given age-spectrum.     

New product advertising in dynamic oligopolies

The success of the introduction of a new product in a market is very sensitive to the marketing decision variables adopted by the firm. In the present paper we are concerned with the question of new product advertising in a heterogeneous oligopoly market consisting of N firms. A dynamic game is formulated to model strategic as well as sales interactions in such a market. Optimal advertising strategies are identified as open-loop Nash solutions.The comments of two anonymous referees are appreciated. The first author wishes to acknowledge support from NSERC (Grant No. OGP0037342).     

National and store brand advertising strategies

As the propensity of premium store brands (SBs) increases, retailers must consider different ways to drive sales besides promotional strategies. With this in mind, we consider a national brand (NB) and a (premium) SB co-existing in a market. Each brand has to decide the amount to invest in advertising its product and the prices to charge its customers, which can be determined separately or in unison. When either advertising expenditures or pricing decisions are set, each brand must keep in mind that the advertising efforts and revenue may spillover between the two brands, customers who intend to purchase the NB may end up purchasing the SB and vice versa. We derive an analytical model of the situations described and characterize equilibrium advertising decisions. We find that the characteristics of a premium SB may depend on which marketing/promoting instrument (advertising or pricing) is the primary method for driving demand; and in some situations an NB may be better off to not advertise at all and instead let the premium SB carry out all of the advertising.     

A metaheuristic approach to solving a multiproduct EOQ-based inventory problem with storage space constraints

This paper considers the well-known static time-continuous multiproduct economic order quantity (EOQ) based inventory management problem with the storage space constraints. This problem is modelled as a combinatorial optimization problem in the corresponding dynamic discrete time system control process. In order to solve this problem approximately, we developed two heuristics: a special heuristic based on a local search technique and a metaheuristic procedure based on the variable neighbourhood search principle. The efficiency of two heuristics is preliminary examined and compared on several randomly generated instances with the same number of products.