Kripasindhu Chaudhuri

An EOQ model with stock-dependent demand, shortage, inflation and time discounting

Abstract This paper develops a finite time-horizon deterministic economic order quantity (EOQ) inventory model with shortages, where the demand rate at any instant depends on the on-hand inventory (stock level) at that instant. The effects of inflation and the time value of money are taken into account, considering two separate inflation rates: namely, the internal (company) inflation rate and the external (general economy) inflation rate. The results are discussed with a numerical example and particular case of the model is discussed in brief. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.

Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost

This paper deals with an extended EOQ-type inventory model for a perishable product where the demand rate is a function of the on-hand inventory. The traditional parameters of unit item cost and ordering cost are kept constant; but the holding cost is treated as (i) a nonlinear function of the length of time for which the item is held in stock, and (ii) a functional form of the amount of the on-hand inventory. The approximate optimal solution in both the cases are derived. Computational results are presented indicating the effects of nonlinearity in holding costs.

A deterministic EOQ model with delays in payments and price-discount offers

Abstract It is the purpose of this paper to model the retailer’s profit-maximizing strategy when confronted with supplier’s trade offer of credit and price-discount on the purchase of merchandise. Generally, retailers have to face many types of demands for different kinds of goods. In real situation, retailers have to correlate between the selling price and supplier’s trade offer, keeping in mind profit-maximization strategy. In the proposed model, all increasing deterministic demands are discussed analytically, numerically and graphically in the environment of permissible delay in payment and discount offer to the retailer.

A deterministic inventory model for deteriorating items with stock-dependent demand rate

Abstract A deterministic inventory model is developed by assuming that the demand rate is stock-dependent and the items deteriorate at a constant rate θ. The expression for the average net profit π over one production run is derived and its optimization with respect to the decision variables Q (initial stock) and T (duration of a production cycle) is carried out. This leads to two highly nonlinear equations which are solved by using a subroutine NEQNF in IMSL (MATH Library) in CYBER 180/480A computer system. The optimal solution so derived is compared with that for the no-deterioration (θ = 0) case. Sensitivity of the optimal solution to changes in parameter values is examined. Several aspects of the functional form for the demand rate are considered in a separate section. Finally, the salient features of the problem and its solution are discussed in brief.

An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages

An order level inventory system for deteriorating items has been developed with demand rate as a ramp type function of time. The finite production rate is proportional to the demand rate and deterioration rate is time proportional. The unit production cost is inversely proportional to the demand rate. The model with no shortage case in inventory is first solved. The inventory shortage is discussed next. Results are illustrated with two numerical examples for two models along with its sensitivity.

An inventory model for deteriorating items with stock-dependent demand rate

Abstract This paper discusses an inventory model with an inventory-level-dependent demand rate followed by a constant demand rate for items deteriorating at a constant rate θ, where the terminal condition of zero inventory at the end of the scheduling period has been relaxed. Sensitivity of the decision variables to changes in the parameter values is examined and the effects of these changes on the optimal policy are discussed in brief.

Economic Order Quantity model with Weibull deterioration distribution, shortage and ramp-type demand

A single-item single-period Economic Order Quantity model for deteriorating items with a ramp-type demand and Weibull deterioration distribution is considered. The shortages in inventory are allowed and backlogged completely. The model is developed over an infinite planning horizon and the optimal replenishment policy is derived by minimizing the total inventory cost per unit time. The numerical solution of the model is obtained, and the sensitivity of the parameters involved in the model is also examined.

A bioeconomic model of harvesting a multispecies fishery

The paper deals with the problem of combined harvesting of two competing fish species, each of which obeys the law of logistic growth. It is shown that the open-access fishery may possess a bionomic equilibrium which drives one species to extinction. An analysis of the dynamic behaviour of the system reveals that its non-trivial critical point is either an asymptotically stable node or an unstable saddle point depending on the values of the biological parameters. Further, the nature of the trivial critical point (origin) is found to depend on the biotechnical productivity (btp) of each species. It is also proven that the dynamic system does not possess any limit cycles. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equilibrium case by using Pontryagins maximal principle. Biological and economic interpretations of the results associated with the optimal equilibrium solution are explained. The significance of the results derived in the paper are then discussed.

A note on an order-level inventory model for a deteriorating item with time-dependent quadratic demand

An order-level inventory problem is discussed with the demand rate being represented by a continuous, quadratic function of time. It is assumed that a constant fraction of the on-hand inventory deteriorates per unit of time. The solution of the model is discussed both for infinite and finite time-horizon. A numerical example is taken up to illustrate the solution procedure and sensitivity analysis is also carried out. The rationale for the time-dependent quadratic demand is discussed.

Joint pricing and ordering policy for a deteriorating inventory

An inventory model is developed for a deteriorating item with a price-dependent demand rate. The rate of deterioration is taken to be time-proportional and a power law form of the price-dependence of demand is considered. The model is solved analytically and is illustrated with a numerical example.