Optimal sales force compensation plans: an operational procedure

This paper describes an operational procedure for identifying optimal sales force compensation plans featuring salary, commissions and/or quota/bonus. Utility-maximising salespeople's behaviours and reactions to given compensation plans are simulated, and the resulting sales, costs and long-term expected profits are assessed. Then, a search technique attempts to identify the long-term profit-maximising compensation plan structure. Operationally, the simulation model parameters are calibrated so as to reflect those of an actual sales force, and consequently the optimal compensation scheme for this specific sales force can be identified. The concept is illustrated in an actual case study.     

On Setting Optimal Sales Commissions

This paper treats the problem of determining the commission rates a company should choose to establish for each of n products sold by a salesman. It has been shown that a sales commission plan based on paying equal commission rates on the gross margins of the salesman's product lines is optimal under the assumption that sales generated as a function of time spent on a product is a deterministic increasing function of time. This paper explores a similar problem with relaxation of the deterministic assumption. It considers a stochastic sales function in order to show differences in preference functions between a company and salesman in determining optimal commissions.     

Fair vs Optimal Salesmen's Compensation Plans

This paper suggests that a "fair" compensation plan (i.e. a compensation plan which remunerates salesmen proportionally to their efforts and competence) should include commissions on sales and bonuses pending on sales increases over a reference period. It also shows that under general conditions, a straight commission plan is not a fair compensation structure to the salesmen. Finally, it discusses the conditions under which the proposed fair compensation structure can lead to a jointly optimal allocation of a salesman's time among selling activities.     

Salespeople's management of customer information: Impact on optimal territory and sales force sizes

Collecting and processing territory and account information are major aspects of a salesperson's task. To a large extent, salespeople's effectiveness depends on the amount and quality of the market information available to them (such as their customers' needs and potential, the likelihood of getting an order after some contact time, etc.). Although they are not always easy to disentangle, these information gathering and processing activities on one hand, and the effective contact time devoted to selling to clients and prospects on the other, vie for the limited time resources available to a salesperson. This paper provides a simple statistical procedure for estimating the costs of information gathering and processing by a salesperson. The model can be used by management for estimating the most profitable territory size to be assigned to each salesperson, and consequently for estimating the optimal sales force size.     

The Impact of Risk Attitude on the Optimal Compensation Plan in a Multi-product Situation

This paper examines the role of uncertainty and risk in determining the optimal commission rates a company should choose for each product of a salesman's product line. We assume that sales for each product are a stochastic function of the time (sales effort) allocated to that product. When sales are assumed to be deterministic, we achieve optimality when each product's commission is the same fraction of its gross margin. However, we determine here that when sales are stochastic this may no longer be true. Optimality conditions require explicit consideration of the utility function of the salesman and the moments of the sales response function.     

Competitive advantage through take-back of used products

Motivated by a recent antitrust ruling against Hill–Rom, one of the two dominant American suppliers of hospital beds, we develop a stylized model to investigate the consequences of used product take-back on firms, industry and customers. Our findings suggest that by taking back and reselling refurbished products, a manufacturer can increase both profit margins and sales––to the detriment of a non-interfering competitor. In our model, customers are always better off under product take-back, but it depends on the degree of competition, whether firms use the benefits of take-back primarily to increase their margins or to pass them on to the customers by lowering their prices. The first firm to offer take-back, in some cases, can deter its competitors from following this profitable strategy, especially if it has an existing advantage in terms of lower production cost or higher market share. Contrary to the claim of Hill–Rom's competitor, we find a “legitimate business justification” for Hill–Rom's reduction of new product prices.     

Optimal Salesmen's Compensation Plans: A Multiperiod Approach

Conditions to induce an income maximizing salesman to allocate his time among product lines so as to maximize the firm's long-run profits are derived. These conditions highlight the need to take explicitly into account the carryover effects of salesmen's activities in determining the relative importance of the commission rates to be paid for the various product lines.     

A Model for Advanced Reservations for Intercity Visual Conferencing Services

In this paper we describe a model for systems in which the customers usually reserve the required facilities in advance. The model has been developed for a communication network which provides visual conferencing services. We concentrate upon a network with a single pair of cities. Each customer calls the reservation office and specifies the desired day, starting time and holding time for his conference. A scheduler either satisfies the customer's request or offers him up to two alternatives which he may or may not accept. Various performance indices of the system, such as the proportion of lost customers, the proportion of rescheduled customers and the facilities' occupancy rate, are derived. Numerical examples and applications are discussed.     

Licensing radical product innovations to speed up the diffusion

We present a differential game to study how companies can simultaneously license their innovations to other firms when launching a new product. The licensee may cannibalize licensor’s sales, albeit this can be compensated by gains from royalties. Nonetheless, patent royalties are generally so low that licensing is not an attractive strategy. In this paper we consider the role of licensing to speed up the product diffusion. Word of mouth by licensee’s customers and licensee’s advertising indirectly push forward sales of the licensing company, accelerating new product diffusion. We find evidence that licensing can be a potentially profitable strategy. However, we also find that a weak Intellectual Property Right (IPR) protection can easily diminish the financial attractiveness of licensing.     

Joint pricing and ordering policy for an advance booking system with partial order cancellations

In this paper, an inventory model for deteriorating items with price-dependent demand is developed. The cycle is divided into two periods, where an advance sales period is followed by a spot sales period. In practice, customers with reservations may cancel their orders before receiving them. During the advance sales period, the rate of reservations which will not be cancelled is dependent on the length of the waiting time for the receiving order. During the spot sales period, all customers receive their orders at the time of the purchase. We prove the existence of the realistic relationship that the advance sales price is smaller than the spot sales price. We also develop some useful properties and provide an iterative procedure for solving the maximization problem. Numerical examples are given to demonstrate the effectiveness of the proposed approach and we conclude the paper with suggestions for possible future research.     

Mathematical modelling of the order-promising process for fruit supply chains considering the perishability and subtypes of products

This paper proposes a mixed integer mathematical programming model to support the complex order promising process in fruit supply chains. Due to natural factors, such as land, weather or harvesting time, these supply chains present units of the same product that differ in certain relevant attributes to customers (subtypes). This becomes a managerial problem when customers require specific subtypes in their orders. Additionally, the deterioration of the original characteristics of subtypes over time generates waste and gives rise to a shelf life-based pricing policy. Therefore, the developed model should ensure that customers are served not only the quantities and dates, but also the required homogeneity and freshness. The model aims to maximise two conflicting objectives: total profit and mean product freshness. The novelty of the model derives from considering both homogeneity in subtypes as a requirement in customer orders and the traceability of product deterioration over time. Different scenarios are defined according to the weight assigned to each objective, shelf-life length and pricing policy in a rolling horizon scheme. The numerical experiments conducted for a real orange and tangerine supply chain, show the model’s validity and the conflicting behaviour of the two objectives. The highest profit is made at the expense of the lowest mean freshness delivered, which is reinforced by the narrower the price variation with freshness. Finally, the positive impact of prolonging the product’s shelf life on both objectives is shown.     

Optimal ordering and pricing policy for an inventory system with trial periods

It is a business practice that home shopping companies offer a free trial period for their products with a goal of increasing sales. Under this policy, if for any reason customers are not satisfied with the purchase, they can return the product for a refund within the trial period. To develop inventory strategies in such environment, home shopping companies should take the return phenomenon into account so as to increase their profit. This paper considers this phenomenon and develops a seasonal inventory model to deal with the problem. Two scenarios are analyzed. In the first scenario, demand is assumed to be linearly price-dependent while in the second one, it is assumed to be exponentially price-dependent. The purpose of this research is to maximize the total profit over a given planning period by determining the optimal ordering quantity and price. The analytical results demonstrate that the optimal ordering quantity and prices are obtained using closed-form formulas.     

On the economic order quantity under conditions of permissible delay in payments

In this note, I amend Goyal's model by considering the difference between unit price and unit cost. I then establish an easy analytical closed-form solution to the problem. The theoretical results obtained here reveal the following two managerial phenomena. (1) In certain cases, the economic replenishment interval and order quantity decreases under the permissible delay in payments, which contradicts to Goyal's conclusion. It makes economic sense for some customers to order less quantity (or shorten the replenishment time interval) and to take the benefits of the permissible delay more frequently. (2) If a supplier wants to reduce his/her large level of inventory, then he/she should charge an excessive interest rate on his/her customer's outstanding amount after the credit term expires. Consequently, his/her customers will order to buy more quantity than the classical economic order quantity. As a matter of fact, these two managerial phenomena have been demonstrated in the decision making of using credit cards. For example, most credit card companies provide card holders 25 days of grace period, and charge 18–20% interest on the amount past due (ie, the second phenomenon). However, for a well-established credit card holder, he/she will take the benefit of 25 days of grace period constantly, but will not spend over his/her limit and face an excessive finance charge (ie, the first phenomenon).     

Local design vs. global design: A strategic business choice

The market for a particular product consists of many customers having different needs and wants. A local design strategy attempts to increase market share and sales revenue by designing many variants of the product to exploit these differences. Such a strategy involves increased requirements for design, manufacturing, and marketing resources. A global design strategy offers a single product concept to all customers. Thus, the choice between a local design strategy and a global design strategy poses a fundamental tradeoff to the managers in many markets. Making such a decision is a complex process as it involves many design, manufacturing and marketing factors. We present a model based on optimal control theory representing major tradeoffs that exist between a local design strategy and a global design strategy. We demonstrate, through extensive computational experiments, how the model helps to gain strategic insight into the complex tradeoffs that exist between global design strategy and local design strategy alternatives under various scenarios over the life of a product.     

Profit maximization in an inventory system with time-varying demand,partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

     

Locating emergency services with different priorities: the priority queuing covering location problem

Previous covering models for emergency service consider all the calls to be of the same importance and impose the same waiting time constraints independently of the service's priority. This type of constraint is clearly inappropriate in many contexts. For example, in urban medical emergency services, calls that involve danger to human life deserve higher priority over calls for more routine incidents. A realistic model in such a context should allow prioritizing the calls for service. In this paper, a covering model which considers different priority levels is formulated and solved. The model heritages its formulation from previous research on Maximum Coverage Models and incorporates results from Queuing Theory, in particular Priority Queuing. The additional complexity incorporated in the model justifies the use of a heuristic procedure.     

Optimal Compensation Plans for Salesmen Who Trade-off Leisure Time Against Income

This paper discusses the minimum requirements for an adequate salesmen's compensation plan structure to lead to profit maximization by inducing non-income maximizing salesmen (1) to deploy the highest profitable activity level, and (2) to optimally allocate their time among various selling activities. It is found that a commission-quota-bonus plan is such a structure. These results hold under a large set of plausible behavioral patterns of salesmen's responses to financial incentives. In addition, the analysis supports the use of challenging sales quotas for improved sales force efficiency.     

An inventory model where backordered demand ratio is exponentially decreasing with the waiting time

We analyze an inventory system with a mixture of backorders and lost sales, where the backordered demand rate is an exponential function of time the customers wait before receiving the item. Stockout costs (backorder cost and lost sales cost) include a fixed cost and a cost proportional to the length of the shortage period. A procedure for determining the optimal policy and the maximum inventory profit is presented. This work extends several inventory models of the existing literature.     

Reducing lost-sales rate on the stochastic inventory model with defective goods for the mixtures of distributions

In this paper, we assume that the demands of different customers are not identical in the lead time. Thus, we investigate a continuous review inventory model involving controllable lead time and a random number of defective goods in buyer’s arriving order lot with partial lost sales for the mixtures of distributions of the lead time demand to accommodate more practical features of the real inventory systems. Moreover, we analyze the effects of increasing investment to reduce the lost sales rate when the order quantity, reorder point, lost sales rate and lead time are treated as decision variables. In our studies, we first assume that the lead time demand follows the mixture of normal distributions, and then relax the assumption about the form of the mixture of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. By analyzing the total expected cost function, we develop an algorithm to obtain the optimal ordering policy and the optimal investment strategy for each case. Finally, we provide numerical examples to illustrate the results.     

Dynamic inventory system with pricing adjustment for price-comparison shoppers

With numerous price-comparison websites and applications, consumers today are frequently conducting price-comparison shopping. As a result, retailers face an increasing challenge in predicting consumer demand and determining the optimal product price and inventory level accordingly. To address this issue, this paper proposes an inventory model with joint decisions of price and inventory to optimize the retailer's long-run average profit under price-comparison consumer shopping. We first formulate the demand arrival process for a retailer under price-comparison shopping to be affected by not only its own price but also its competitors'. Based on this demand arrival process, we then formulate the retailer's long-run average profit and derive properties of its optimal solution. Our model focuses on capturing the impact of price-comparison consumers on a retailer's optimal price and inventory decisions. In particular, we allow competitors' prices to affect the retailer's demand via two key factors: the manufacturer's suggested price and the variability of the outside lowest price. According to our results, when the suggested price increases, the retailer should lower its price to obtain more price-comparison customers from competitors, whereas when the variability of outside lowest price increases, the retailer should raise its price to increase per unit profit from nonprice-comparison customers.