Prakash L. Abad

A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive

This paper considers the seller–buyer channel in which the end demand is price sensitive and the seller may offer trade credit to the buyer. The unit price seller charged by the seller and the length of the credit period offered by the seller to the buyer both influence the final demand for the product. Hence we consider both to be policy variables for the seller. We use the case of no credit as a benchmark in our analysis. The paper provides procedures for determiningthe seller’s and the buyer’s policies under non-cooperative as well as cooperative relationships. In the non-cooperative case, we determine for the seller the optimal unit price and the length of the credit period. For the cooperative structure, we provide a procedure for characterizingPareto efficient solutions. r 2002 Elsevier Science B.V. All rights reserved.

Optimal price and order size for a reseller under partial backordering

Abstract The problem of determining the optimal price and lot size for a reseller is considered in this paper. It is assumed that demand can be backlogged and that the selling price is constant within the inventory cycle. The backlogging phenomenon is modeled without using the backorder cost and the lost sale cost since these costs are not easy to estimate in practice. The case in which the selling price is fixed and therefore, demand is a known constant is also considered. Given the new way of modeling the backlogging phenomenon, the results for the case of constant demand are developed. Analysis is also presented for the reselling situation in which a nonperishable product is sold. Scope and purpose Perishable products constitute a sizable component of inventories. A common question in a reselling situation involving a perishable (or a nonperishable) product is: What should be the size of the replenishment? If demand for the product is sensitive to price, then another question is: What should be the selling price? Although the ability to vary price within an inventory cycle is important, in many cases, the reseller may opt for a policy of constant selling price for administrative convenience. In this paper the pricing and/or lot sizing problem faced by a reseller is modeled assuming a general deterioration rate and a general demand function. The model allows for backlogging of demand. When a product is highly perishable, the reseller may need to backlog demand to contain costs due to deterioration. In this sense, perishability and backlogging are complementary conditions. Given that the problem entails revenue and costs, a natural objective function for the model is profit per period. The conventional approach to modeling the backlogging phenomenon requires the use of the backorder cost and the lost sale cost. These costs, however, are difficult to estimate in practice. A new approach is used in which customers are considered impatient. Hence the fraction of demand that gets backlogged at a given point in time is a decreasing function of waiting time. First the subproblem in which price is fixed is solved to determine the optimal inventory policy. The subproblem represents the important case in which the reseller has no flexibility to change the selling price. Then a procedure is developed for determining the optimal quantity and the selling price for the broader problem. The procedure can be implemented on a spreadsheet.

Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale

Abstract Perishable products constitute a sizable component of inventories. Common questions in a production and selling situation involving a perishable (or a non-perishable) product are: What should be the price and what should be the size of the replenishment? When demand for the product is price sensitive, pricing and lot sizing decisions are interdependent. Similarly, when a product is highly perishable, the demand may need to be backlogged to avoid costs due to deterioration, i.e., perishability and backlogging are complementary conditions. In this paper we consider the pricing and lot sizing problem for a perishable good under finite production, exponential decay and partial backordering and lost sale. The backlogging phenomenon in the literature is often modeled using backordering and lost sale costs. These cost parameters however are not easy to estimate in practice. In this paper, we use a new approach to model backlogging of demand. In this approach, customers are viewed to be impatient. The backlogging option gets used only when it is economic to do so. We extend the analysis presented for a perishable product to the case in which the product is non-perishable.

An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup

In this paper we use an ant colony system (ACS) algorithm to solve the vehicle routing problem with simultaneous delivery and pickup (VRPSDP) which is a combinatorial optimization problem. ACS is an algorithmic approach inspired by the foraging behavior of real ants. Artificial ants are used to construct a solution for the problem by using the pheromone information from previously generated solutions. The proposed ACS algorithm uses a construction rule as well as two multi-route local search schemes. The algorithm can also solve the vehicle routing problem with backhaul and mixed load (VRPBM). An extensive numerical experiment is performed on benchmark problem instances available in literature. It is found that ACS gives good results compared to the existing algorithms.

Supplier pricing and lot sizing when demand is price sensitive

Abstract The problem of co-ordination between a vendor and a buyer is formulated as a two-person fixed threat bargaining game. The vendor decides on his lot size and the price schedule he is to offer to the buyer. The buyer decides upon his lot size and the selling price in the market. We have characterized Pareto efficient solutions and the Nash bargaining solution for the problem. We have also proposed two pricing schedules for the vendor who is supplying to a large population of buyers. The first one is based upon profit sharing. The second one resembles the classical all unit quantity discount schedule. We have thus provided for the supplier a procedure for setting all unit quantity discount schedule.

Multi-ant colony system (MACS) for a vehicle routing problem with backhauls

The vehicle routing problem with backhaul (VRPB) is an extension of the capacitated vehicle routing problem (CVRP). In VRPB, there are linehaul as well as backhaul customers. The number of vehicles is considered to be fixed and deliveries for linehaul customers must be made before any pickups from backhaul customers. The objective is to design routes for the vehicles so that the total distance traveled is minimized. We use multi-ant colony system (MACS) to solve VRPB which is a combinatorial optimization problem. Ant colony system (ACS) is an algorithmic approach inspired by foraging behavior of real ants. Artificial ants are used to construct a solution by using pheromone information from previously generated solutions. The proposed MACS algorithm uses a new construction rule as well as two multi-route local search schemes. An extensive numerical experiment is performed on benchmark problems available in the literature.

Optimal price and lot size when the supplier offers a temporary price reduction over an interval

Manufacturers and other suppliers offer temporary reduction in the price charged to resellers for a variety of reasons. Typically the trade promotion lasts for some finite time-span. In addition, in reselling situations, the end demand tends to be sensitive to selling price. Thus, when the trade promotion takes place, there is possibility that not all the quantity purchased by the reseller at discount is passed on to the final consumers at a reduced selling price. Studies to date addressing the above problem situation have assumed that the trade promotion is offered by the supplier only at one point in time. We extend the analysis to the more realistic case where the promotion lasts a finite time interval. We consider two cases: (1) using technology (e.g. point-of-sale systems), the supplier can insure that the discount is applicable to only units resold during the promotion and (2) the discount is applicable to units purchased during the promotion.

New LP based heuristics for the classification problem

Abstract Three heuristic procedures for the two group discriminant problem are developed that minimize the total expected cost of misclassification in the training sample. The approach is shown through a systematic experiment to generate near optimal solutions and to be efficient in terms of computational effort when compared to existing research.

Decentralized planning with an interdependent marketing-production system

An interdependent marketing-production planning model based on control theory is described. The interdependent model is a composition of the Vidale-Wolfe model relating advertising rates to sales rates, and the Holt, Modigliani, Muth & Simon (HMMS) production inventory planning model. An overall optimal marketing-production plan is identified using the interdependent model. This overall optimal plan (resulting from centralized planning) is then used as a reference point to measure the effectiveness of decentralized planning approaches. It is found that in some cases almost no coordination is necessary, in some cases the use of a transfer price leads to good decentralized planning, and in other cases centralized planning must be employed to achieve good results. Several examples are presented to illustrate the cases in which decentralized planning does and does not work well.

On the performance of linear programming heuristics applied on a quadratic transformation in the classification problem

Abstract We have applied LP heuristics to a quadratic transformation of the observation data in the classification problem. Four ‘real world’ research data sets in the literature have been used to test the method. These data sets include continuous, integer and binary attributes for the observations to be classified. In all four research data sets, the proposed quadratic transformation method outperformed quadratic discriminant analysis.