Inventory policy for an item with inflation induced purchasing price,selling price and demand with immediate part payment

In this paper, an inventory policy for an item is presented with inflation and selling price dependent demand under deterministic and random planning horizons allowing and not allowing shortages. In addition, there is a provision for (i) an immediate part payment (variable) to the wholesaler, (ii) borrowing some money from money lending source for the immediate part payment, (iii) earning a discount on purchasing price and relaxation on credit period from the wholesaler against the advance payment and (iv) delay in payment for the rest allowed by wholesaler. The payment to the source is made at the end of the business period with some interest charged. Against the above conjectures, inventory models under the finite (crisp) and random planning horizons have been formulated with respect to the retailer’s point of view for maximum profit. The nonlinear optimization method – Generalized Reduced Gradient (GRG) method is used to find the optimal solutions and the corresponding maximum profits for the different sets of given numerical data. Some sensitivity analyses are made and presented graphically. As particular cases, the results of the crisp models and the case without shortages are obtained from those of the stochastic model and the case with shortages respectively.     

Inventory control and pricing for perishable products under age and price dependent stochastic demand

Multistage stochastic programming (SP) with both endogenous and exogenous uncertainties is a novel problem in which some uncertain parameters are decision-dependent and others are independent of decisions. The main difficulty of this problem is that nonanticipativity constraints (NACs) make up a significantly large constraint set, growing very fast with the number of scenarios and leading to an intractable model. Usually, a lot of these constraints are redundant and hence, identification and elimination of redundant NACs can cause a significant reduction in the problem size. Recently, a polynomial time algorithm has been proposed in the literature which is able to identify all redundant NACs in an SP problem with only endogenous uncertainty. In this paper, however, we extend the algorithm proposed in the literature and present a new method which is able to make the upper most possible reduction in the number of NACs in any SP with both exogenous and endogenous uncertain parameters. Proving the validity of this method is another innovation of this study. Computational results confirm that the proposed approach can significantly reduce the problem size within a reasonable computation time.     

A two-warehouse production model for deteriorating inventory items with time-dependent demands

A two-warehouse inventory model for deteriorating items with time-dependent demand has been developed. Compared with previous models, the model involves a free form time-dependent demand and a finite replenishment rate within a finite planning horizon. Rather than the heuristic approach of equal production cycle times adopted by Lee and Ma, an approach which permits variation in production cycle times is adopted to determine the number of production cycles and the times for replenishment during a finite planning horizon. Numerical examples are provided to illustrate the application of the model and the results indicate that the performance of the proposed approach is superior to that of the heuristic approach of Lee and Ma.     

Base stock policy with retrial demands

In this work, we consider a continuous review base stock policy inventory system with retrial demands. The maximum storage capacity is S. It is assumed that primary demand is of unit size and primary demand time points form a Poisson process. A one-to-one ordering policy is adopted. According to this policy, orders are placed for one unit, as and when the inventory level drops due to a demand. We assume that the demands occur during the stock-out periods enter into the orbit of infinite size. The lead time is assumed to be exponential. The joint probability distribution of the inventory level and the number of demands in the orbit are obtained in the steady state case. Various system performance measures in the steady state are derived. The results are illustrated with suitable numerical examples.     

Inventory and coordination issues with two substitutable products

This study considers a two level supply chain in a newsboy setting with two substitutable products. Demands for the two products are assumed independent as long as both are available. If, however, a product stocks out, some of its demand is transferred to the available one with a known probability which ultimately creates a dependence on the amount of purchased items. The retailer is allowed to return some or all of the unsold products to the manufacturer with some credit. The expected chain profit, the retailer’s and the manufacturer’s profit expressions are derived under general conditions. Special cases are inspected to investigate the conditions under which channel coordination is achieved. It is demonstrated that channel coordination can not be achieved if unlimited returns are allowed with full credit, a result that agrees with the findings of Pasternak [B.A. Pasternack, Optimal pricing and return policies for perishable commodities, Market. Sci. 4 (1985) 166–176] for the single item case. For the cases of unlimited returns with partial credit, the conditions for coordination are derived for one way full substitutions. For exponential demand explicit expressions for the channel and retailer’s expected profit functions are provided.     

The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands

By showing that there is an upper bound for the price of anarchyρ(Γ) for a non-atomic congestion game Γ with only separable cost maps and fixed demands, Roughgarden and Tardos show that the cost of forgoing centralized control is mild. This letter shows that there is an upper bound for ρ(Γ) in Γ for fixed demands with symmetric cost maps. It also shows that there is a weaker bound for ρ(Γ) in Γ with elastic demands.     

Inventory models with managerial policy independent of demand

This paper is an extension of two papers. The first of these, published in European Journal of Operational Research, 2007, 112-120 is by Deng et al. (2007) and concerns inventory models for deteriorating items with ramp type demand. The second, published in Computer & Industrial Engineering, 2009, 1296-1300 is by Cheng and Wang (2009) and concerns inventory models for deteriorating items with trapezoidal type demand. The purpose of this paper is threefold. First, this paper will show that the optimal solution is independent of the demand considered in the two previous papers. Second, several replenishment cycles were considered during the finite time horizon, to balance the set-up cost with the sum of the deteriorated cost, holding cost, and shortage cost. Third, this paper will examine the same numerical example in Cheng and Wang (2009) to show that this new approach will result in the saving of 84.39%.     

Inventory model with stochastic lead-time and price dependent demand incorporating advance payment

Inventory model for an item is developed in stochastic environment with price-dependent demand over a finite time horizon. Here, probabilistic lead-time is considered and shortages are allowed (if occurs). In any business, placement of an order is normally connected with the advance payment (AP). Again, depending upon the amount of AP, unit price is quoted, i.e., price discount is allowed. Till now, this realistic factor is overlooked by the researchers. In this model, unit price is inversely related with the AP amount. Against this financial benefit, the management has to incur an expenditure paying interest against AP. Taking these into account, mathematical expression is derived for the expected average profit of the system. A closed form solution to maximize the expected average profit is obtained when demand is constant. In other cases model is solved using generalized reduced gradient (GRG) technique and stochastic search genetic algorithm (GA). Moreover, results of the models without and with advance payment are presented and solved. The numerical examples are presented to illustrate the model and the results for two models obtained from two methods are compared in different cases. Also, some parametric studies and sensitivity analyses have been carried out to illustrate the behavior of the proposed model. It is observed that advance payment has positive effect on the system.     

An EOQ model for perishable products with discounted selling price and stock dependent demand

A single item economic order quantity model is considered in which the demand is stock dependent. After a certain time the product starts to deteriorate and due to visualization effect and other aspects of deterioration the demand becomes constant. In that situation a discount on selling price provides significant increment in demand rate. In this paper we investigate how much discount on selling price may be given during deterioration to maximize the profit per unit time and whether a pre-deterioration discount affects the unit profit or not. A mathematical model is developed incorporating both pre- and post deterioration discounts on unit selling price, where analytical results reveal some important characteristics of discount structure. A numerical example is presented and sensitivity analysis of the model is carried out.     

Optimal policy and stability regions for the single product periodic review inventory problem,with stationary demands

In this paper we present rules concerning the optimal policy and stability regions for the single product periodic review inventory problem with stationary demands, over a finite horizon. The key parameter to the whole study is the Lot-Sizing Index (LSI) introduced by Blackburn and Millen. Two algorithms are presented. The first one constructs stability regions which are expressed as intervals of the LSI parameter, covering the whole range of its values. The proposed algorithm is very simple to understand and implement, and most importantly, it provides a solution table which can be used by the decision maker to easily determine the optimal policy for any problem with a given horizon and any possible combination of its cost parameters, namely any LSI value. The second proposed algorithm determines the optimal policy for any given LSI value; it constitutes a completely different approach to that of the Wagner–Whitin algorithm and requires very little computational effort.     

A priori policy evaluation and cyclic-order-based simulated annealing for the multi-compartment vehicle routing problem with stochastic demands

We develop methods to estimate and exactly calculate the expected cost of a priori policies for the multi-compartment vehicle routing problem with stochastic demands, an extension of the classical vehicle routing problem where customer demands are uncertain and products must be transported in separate partitions. We incorporate our estimation procedure into a cyclic-order-based simulated annealing algorithm, significantly improving the best-known solution values for a set of benchmark problems. We also extend the updating procedure for a cyclic order’s candidate route set to duration-constrained a priori policies.     

Lot sizing for products with finite demand horizon and periodic review inventory policy

This paper analyzes and develops an efficient algorithm for solving a simple generalization of the classical economic order quantity (EOQ) model where the demand horizon is finite and a periodic review inventory policy is followed. Such problems could arise in production shops where the product under consideration is going to be discontinued and/or replaced by some other product after a certain known number of periods. Such problems could also arise as subproblems in large prodution-inventory problems were demand rate is constant in some periods and varying in others.     

A boundary element method to price time-dependent double barrier options

In this paper we propose a new method for pricing double-barrier options with moving barriers under the Black-Scholes and the CEV models. First of all, by applying a variational technique typical of the boundary element method, we derive an integral representation of the double-barrier option price in which two of the integrand functions are not given explicitly but must be obtained solving a system of Volterra integral equations of the first kind. Second, we develop an ad hoc numerical method to regularize and solve the system of integral equations obtained. Several numerical experiments are carried out showing that the overall algorithm is extraordinarily fast and accurate, even if the barriers are not differentiable functions. Moreover the numerical method presented in this paper performs significantly better than the finite difference approach.     

(s, S) Inventory systems with lost sales and Markov renewal demands

In the study of stochastic inventory systems it is generally assumed that the demand epochs are renewable in nature. The present paper deals with a single-item (s, S) inventory model with a finite number of different types of demands, in which the demand epochs form a Markov renewal process. The lead times are exponentially distributed and the demands that occur during stockout periods are not backordered. For this model the transient and limiting inventory level distributions are computed. Also the theory of point processes is used to obtain the mean reorder and shortage rates and their limiting values. For the special case of renewal demands, the problem of minimizing the long-run expected cost rate is analysed.     

Exact solution ofP n time-dependent equations with time-dependent cross-sections for slab geometry

Monoenergetic, time-dependentP _n equations with time-dependent cross-sections are solved using the method of the generalized Lie series. The variables are separated in the solution obtained. This solution is given in a closed form for the case of time-dependent cross-sections. a few numerical results are given for the case ofP ₃ approximation and compared with those obtained by the time-dependentS ₄ code.     

Exact solution of theP 1 time-dependent equations with time-dependent cross-sections for slab and spherical geometry

The monoenergetic, one-dimensional, time-dependentP ₁ equations with time-dependent cross sections are solved using the technique of the generalized Lie series. A few numerical results are given and compared with those obtained by theS ₂ method.     

Optimal periodic replacement policy for repairable products under free-repair warranty

This paper investigates the effects of a free-repair warranty on the periodic replacement policy for a repairable product. Cost models are developed for both a warranted and a non-warranted product, and the corresponding optimal periodic replacement policies are derived such that the long-run expected cost rate is minimized. For a product with an increasing failure rate function, structural properties of these optimal policies are obtained. By comparing these optimal policies, we show that the optimal replacement period for a warranted product should be adjusted toward the end of the warranty period. Finally, examples are given to numerically illustrate the impact of a product warranty on the optimal periodic replacement policy.     

Structured products equilibria in conic two price markets

A novel equilibrium theory is developed for two price markets permitting investors to trade personally designed structured products. Classical market clearing is enhanced for structured products where the market allows these products to be freely bought at ask prices or sold for bid prices. Competitive pressures lead the market to lower the ask prices and raise the bid prices with the market offering individual investors the widest possible set of acceptable risks provided the aggregate counter cash flow held by the market is consistent with a more conservative prespecified set of acceptable risks. We learn that in equilibrium heterogeneous investors inherit a common hedging objective of maximizing the bid prices of the final structured product sold to market or equivalently minimizing the ask price of what is bought.