Analysing consumer segments to budget for loyalty and promotion programmes and maximize market share

This paper seeks to provide a framework and benchmark for the allocation of marketing budget between promotion and loyalty programmes using an approach that combines a Markov-type market share model and the Lagrange multiplier method to maximize market share. The Lagrange multiplier method, that takes into account the market share and the loyalty effect observable in preceding periods along with the estimated promotional effects, permits the allocation to be optimized and future market share to be maximized. Then, loyalty-based consumer segment are used to explain why the budgeting exercise can achieve the maximization objective. To this end, the study uses consumer panel data concerning three categories, namely, adult milk powder, shampoo, and detergent. It extends previous research on loyalty-based segmentation by focusing on the budget allocation between the two options of loyalty enhancement and promotion programming. A Budget Allocation Grid for Loyalty-based Segmentation is proposed as an aid to understand budget allocation between loyalty and promotion programmes based on the relative sizes of exclusive-loyalty and variety-seeking segments.     

Planning the supply of rewards with cooperative promotion considerations in coalition loyalty programmes management

Coalition loyalty programmes (CLPs) are owned and operated as for-profit enterprises. We consider the ordering decisions of rewards that arise in this context, under a general setting in which not only is the demand for rewards uncertain, but also the CLP firm offers bonus points, a very common cooperative promotion mechanism used in loyalty programmes. The rewards are acquired either at a wholesale ‘discounted’ cost or at a wholesale ‘non-discounted’ cost by the CLP firm from its multiple commercial partners and supplied to customers seeking to redeem their accumulated ‘reward points’, subject to commercial partners’ capacities for offering rewards, the firm’s overall budget for purchasing rewards, and its control policy on points liability. We formulate the problem as a stochastic linear programme with recourse and solve it using a sampling-based heuristic solution procedure previously discussed in the literature. We report on the managerial applicability of our model in dealing with the redemption budget spending resulting from changes in demand variability, changes in the redemption budget, and the control of liability levels within a reasonable range.     

The single-mode rate equations for semiconductor lasers with thermal effects

A mathematical model describing the coupling of electrical,optical and thermal effects in semiconductor lasers is introduced.Numerical and asymptotic solutions are derived, including expressionsfor key physical quantities such as the initial time delay,the frequency of spike oscillation and the temperature rise,together with its influence on the photon density, the electronconcentration and the threshold current. The consequences ofthermal effects in reducing efficiency are thus quantified.     

The impact of data collection on fill rate performance in the (R,s, Q) inventory model

In this paper we consider the determination of the reorder point s in an (R, s, Q) inventory model subject to a fill rate service level constraint. We assume that the underlying demand process is a compound renewal process. We then derive an approximation method to compute the reorder level such that a target service level is achieved. Restrictions on the input parameters are given, within which this method is applicable. Moreover, we will investigate the effects on the fill rate performance in case the underlying demand process is indeed a compound renewal process, while the demand process is modelled as a discrete-time demand process. That is, the time axis is divided in time units (for example, days) and demands per time unit are independent and identically distributed random variables. It will be shown that smooth and erratic behaviour of the inter-arrival times have different impacts on the performance of the fill rate when demand is modelled as a discrete-time process and in case the underlying demand process is a compound renewal process.     

The impact of distance on location problems

Various features influencing the formulation of a locational decision problem include the problem representations performance criteria, availability of data, the restrictions imposed, and the computational aspects. Although there is a great need for in-depth analyses of the impact of these factors-both individually and jointly - we have as a first step primarily focused on the influence of distance on modelling with respect to e.g. computational tractability and on the quality of the solutions obtained.While most papers on locational decision problems are concerned with the mathematical/technical aspects, we have preferred a non-mathematical exposition aiming at a target group of O.R. practitioners and regional planners.     

The impact of customer returns on pricing and order decisions

In this paper, we address the simultaneous determination of price and inventory replenishment when customers return product to the firm. We examine cases when the quantity of returned product is a function of both the quantity sold and the price, in single and multi-period problems, with and without uncertainty in demand.     

The impact of process deterioration on production and maintenance policies

This paper examines a single-stage production system that deteriorates with production actions, and improves with maintenance. The condition of the process can be in any of several discrete states, and transitions from state to state follow a semi-Markov process. The firm can produce multiple products, which differ by profit earned, expected processing time, and impact on equipment deterioration. The firm can also perform different maintenance actions, which differ by cost incurred, expected down time, and impact on the process condition. The firm needs to determine the optimal production and maintenance choices in each state in a way that maximizes the long-run expected average reward per unit time.     

The impact of price skimming on supply and exit decisions

Stochastic inventory control theory has focused on the order and/or pricing policy when the length of the selling period is known. In contrast to this focus, we examine the optimal length of the selling period—which we refer to as market exit time—in the context of a novel inventory replenishment problem faced by a supplier of a new, trendy, and relatively expensive product with a short life cycle. An important characteristic of the problem is that the supplier applies a price skimming strategy over time and the demand is modeled as a nonhomogeneous Poisson process with an intensity that is dependent on time. The supplier's problems of finding the optimal order quantity and market exit time, with the objective of maximizing expected profit, is studied. Procedures are proposed for joint optimization of the objective function with respect to the order quantity and the market exit time. Then, the effects of the order quantity and market exit time on the supplier's profitability are explored on the basis of a quantitative investigation. Copyright © 2014 John Wiley & Sons, Ltd.     

The growth rate of partial maxima on subsequences

The growth rate of partial maxima for iid. random variables is considered with respect to subsequences. The results show that in a certain class of random variables only the maximal growth rate is connected with the growth of the subsequence.     

The impact of investment lags on investment decision

This paper suggests a valuation framework for an investment project through the concept of real options. Generally, in real asset world, decision time and its payment time are not identical. This so-called investment lag problem should be considered when valuing real assets. When investment lags exist, firms’ accommodation capacities play important roles. In this paper, the real effect of investment lag on investment value is tested upon various conditions. We show the valuation process of real assets under the risk-neutral world. The closed-form formula is also provided for valuing real assets, including R&D project.     

The impact of 2-neighborhoods on graph structure

Connected regular graphs of diameter greater than 2 with 2-neighborhoods isomorphic to a certain graph Δ of diameter 2 are studied. Regular graphs of diameter 2 with 2-neighborhoods isomorphic to the distance-regular graph Δ of diameter 3 are also studied. It is prowed that 2-locally Schrikhande graphs do not exist. Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 892–897, December, 1997. Translated by S. S. Anisov     

The impact of product substitution on retail merchandising

We analyze the impact of product substitution on two key aspects of retail merchandising: order quantities and expected profits. To perform this analysis, we extend the basic news-vendor model to include the possibility that a product with surplus inventory can be used as a substitute for out of stock products. This extension requires a definition and an approximation for the resulting effective demand under substitution. A service rate heuristic is developed to solve the extended problem. The performance of this heuristic is evaluated using an upper bound generated by solving the associated Lagrangian dual problem. Our analysis suggests that this heuristic provides a tractable and accurate method to determine order quantities and expected profits under substitution. We apply this heuristic to examine how the level of demand uncertainty and correlation, and the degree of substitution between products affect order quantities and expected profits under substitutable demand. In addition, we use the heuristic to better understand the mechanism by which substitution improves expected profits.     

The impact of loops on the game of cops and robbers on graphs

In the game of cops and robbers on graphs, the cops and the robber are allowed to pass their turn if they are located on a looped vertex. This paper explores the effect of loops on the cop number and the capture time. We provide examples of graphs where the cop number almost doubles when the loops are removed, graphs where the cop number decreases when the loops are removed, graphs where the capture time is quadratic in the number of vertices and copwin graphs where the cop needs to move away from the robber in optimal play.     

The shape of the yield and its impact on inventory decisions

We consider an inventory model with stochastic demand, positive lead time and random yield where ordering decisions are made according to a linear inflation rule. In case of a positive lead times the complexity of such inventory systems increases distinctly. Due to positive lead times, the inventory position contains no longer a term for outstanding orders but the estimated quantity of goods to be delivered after a known positive lead time period, which differ from the realized deliveries. Thus, a forecast error occurs in each period. In previous research this forecast error was assumed to be normally distributed which is not an appropriate assumption in case of symmetric yield. Since yield skewness can’t be neglected, we propose to fit a skew normal distribution or a generalized extreme value distribution on the forecast error to account for the yield skewness. A numerical study reveals that the proposed approaches are excellent and outperform existing ones.