An inventory control model with stochastic review interval and special sale offer

Periodic review inventory models are widely used in practice, especially for inventory systems in which many different items are purchased from the same supplier. However, most of periodic review models have assumed a fixed length of the review periods. In practice, it is possible that the review periods are of a random (stochastic) length. This paper presents an inventory control model in the case of random review intervals and special sale offer from the supplier. The replenishment interval is assumed to obey from two different distributions, namely, exponential and uniform distributions. Also, shortages are allowed in the term of partial backordering. For this model, its convexity condition is discussed and closed form solutions are proposed.     

An improved algorithm for the minimax distribution-free inventory model with incident-oriented shortage costs

This article reconsiders Gallego's minimax distribution-free procedure. He created a two-point distribution to serve the most unfavorable case for estimating the expected cost of lost sales. We provide a reasonable condition to insure the existence and uniqueness of the optimal solution and the convergence of Gallego's method.     

An inventory model with reliability in an imperfect production process

The paper analyzes an economic manufacturing quantity (EMQ) model with price and advertising demand pattern in an imperfect production process under the effect of inflation. If the machine goes through a long-run process, it may shift from in-control state to out-of-control state. As a result, the system produces imperfect items. The imperfect items are reworked at a cost to make it as new. The production of imperfect quality items increases with time. To reduce the production of the imperfect items, the systems have to more reliable and the produced items depend on the reliability of the machinery system. In this direction, the author considers that the development cost, production cost, material cost are dependent on reliability parameter. Considering reliability as a decision variable, the author constructs an integrated profit function which is maximized by control theory. A numerical example along with graphical representation and sensitivity analysis are provided to illustrate the model.     

An inequality model for solving interval dynamic response of structures with uncertain-but-bounded parameters

In this paper, we look into the dynamic response of structures with uncertain-but-bounded parameters. A new inequality model for determining the interval dynamic response is presented. First we propose an interval dynamic response solution theorem. An inequality model which is a mathematics programming problem is suggested by the presented theorem. Using the central difference method, we substitute the differential items of the inequality model by difference items. By solving them, the interval dynamic response can be obtained. Two examples are used to illustrate the feasibility and the efficiency of the model.     

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.     

Two storage inventory problem with dynamic demand and interval valued lead-time over finite time horizon under inflation and time-value of money

A finite time horizon inventory problem for a deteriorating item having two separate warehouses, one is a own warehouse (OW) of finite dimension and other a rented warehouse (RW), is developed with interval-valued lead-time under inflation and time value of money. Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. The demand rate of item is increasing with time at a decreasing rate. Shortages are allowed in each cycle and backlogged them partially. Shortages may or may not be allowed in the last cycle and under this circumstance, there may be three different types of model. Here it is assumed that the replenishment cycle lengths are of equal length and the stocks of RW are transported to OW in continuous release pattern. For each model, different scenarios are depicted depending upon the re-order point for the next lot. Representing the lead-time by an interval number and using the interval arithmetic, the single objective function for profit is changed to corresponding multi-objective functions. These functions are maximized and solved by Fast and Elitist Multi-objective Genetic Algorithm (FEMGA). The models are illustrated numerically and the results are presented in tabular form.     

An inventory model with returns and lateral transshipments

In this paper, we propose a single-item inventory model with returns. The model allows lateral transshipment of returns from one inventory system to another. Each inventory system is under continuous review and an (r, Q) policy is employed as the inventory control. An approximated closed-form solution of the system steady-state probability distribution is derived when Q is large. The approximated inventory cost and replenishment cost can be written in terms of this distribution. We show that the rejection rate of returns is reduced significantly when transshipment of returns is allowed between the inventory systems.     

信息熵方程求解算法及其应用

给定一个离散且有限随机变量的信息熵,求其对应的概率分布需要解多元非线性方程,文中提出了一个将n元信息熵方程化为至多(n-1)个一元非线性方程求解的算法,证明了算法的正确性,给出了算法误差估计;运用熵方程求解算法设计了一种基于信息熵的文本数字水印方案.     

A deterministic inventory/production model with general inventory cost rate function and piecewise linear concave production costs

We present a thorough analysis of the economic production quantity model with shortages under a general inventory cost rate function and piecewise linear concave production costs. Consequently, an effective solution procedure, particularly useful for an approximation scheme, is proposed. A computational study is appended to illustrate the performance of the proposed solution procedure.     

An order-revenue inventory model with returns and sudden obsolescence

This paper introduces an EOQ-like state-dependent inventory model with returns and sudden obsolescence. Returns arrive according to a MAP process governed by the underlying Markov chain. Additionally, the system is totally obsoleted at stationary renewal times. Hitting level 0 yields an order of size $Q$. We assume order, loss, and shortage costs in addition to revenue. By applying hitting-time transforms and martingales we derive the cost functionals under the discounted criterion. Numerical results, insights, and a comparative study are provided.     

A two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation

In the business transactions, the supplier usually offers a permissible delay in payment to his retailer to attract more sales. In addition, a permissible delay in payment may be applied as an alternative to price discount. Based on the above phenomena, we incorporate a permissible delay in payment into the model of Yang [1] and develop a two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation. The objective of this study is to derive the retailer’s optimal replenishment policy that maximizes the net present value of the profit per unit time. The necessary and sufficient conditions for an optimal solution are characterized. An algorithm is developed to find the optimal solution. Finally, numerical examples are provided to illustrate the proposed model. Sensitivity analysis is made and some managerial implications are presented.     

Integrating process optimization and inventory planning in cutting-stock with skiving option: An optimization model and its application

We consider a two-stage flow line where the first stage produces components for the downstream assembly stage. An integer programming model which integrates decisions at both the planning and the operation level is proposed, with the aim of minimizing production, holding and transportation costs. The model is tested on instances built on the basis of a real cutting process with skiving option, i.e., with the possibility of recombining components to obtain required parts.The implementation of the proposed methodology allows the integration of two hierarchical decision levels (short-term operations vs. mid-term planning) and functional areas (production vs. purchase of materials) within a single planning model, and provides an example of how an element of an Advanced Planning System (APS) could be designed. Moreover, the use of suitable cost figures in the model allows to correctly manage the insertion of hot orders of finite parts.     

A GA based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components

In this paper, we have considered the problem of constrained redundancy allocation of series system with interval valued reliability of components. For maximizing the overall system reliability under limited resource constraints, the problem is formulated as an unconstrained integer programming problem with interval coefficients by penalty function technique and solved by an advanced GA for integer variables with interval fitness function, tournament selection, uniform crossover, uniform mutation and elitism. As a special case, considering the lower and upper bounds of the interval valued reliabilities of the components to be the same, the corresponding problem has been solved. The model has been illustrated with some numerical examples and the results of the series redundancy allocation problem with fixed value of reliability of the components have been compared with the existing results available in the literature. Finally, sensitivity analyses have been shown graphically to study the stability of our developed GA with respect to the different GA parameters.     

An inventory model with backorders with fuzzy parameters and decision variables

The paper considers an inventory model with backorders in a fuzzy situation by employing two types of fuzzy numbers, which are trapezoidal and triangular. A full-fuzzy model is developed where the input parameters and the decision variables are fuzzified. The optimal policy for the developed model is determined using the Kuhn-Tucker conditions after the defuzzification of the cost function with the graded mean integration (GMI) method. Numerical examples and a sensitivity analysis study are provided to highlight the differences between crisp and the fuzzy cases.     

Iterative methods for solving nonlinear equations with finitely many roots in an interval

In this paper we consider a nonlinear equation f(x)=0$f\left(x\right)=0$ having finitely many roots in a bounded interval. Based on the so-called numerical integration method [B.I. Yun, A non-iterative method for solving non-linear equations, Appl. Math. Comput. 198 (2008) 691–699] without any initial guess, we propose iterative methods to obtain all the roots of the nonlinear equation. In the result, an algorithm to find all of the simple roots and multiple ones as well as the extrema of f(x)$f\left(x\right)$ is developed. Moreover, criteria for distinguishing zeros and extrema are included in the algorithm. Availability of the proposed method is demonstrated by some numerical examples.     

Optimal pricing and production in an inventory model

This paper deals with the problem of simultaneously determining the optimal price policy and production rate over a given planning horizon. For nonlinear demand functions and convex inventory and shortage cost functions the optimal solution paths are derived by using optimal control theory. The treatment of linear nonsmooth cost functions requires the use of a generalized maximum principle. The solution method is a phase portrait analysis providing insight into the optimal pricing and production policies as well as the resulting inventory paths. Moreover, it is shown that in the case of nonsmooth piecewise linear cost functions the equilibrium is approached within finite time although the model is nonlinear in the control variables. Finally it is illustrated that exogenous fluctuations in the demand rate (seasonal demand pattern) amount to cyclical optimal solutions.     

An effective heuristic for the review period in an inventory model with staggered deliveries and normal demands

Consider a single-item, periodic review, infinite-horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. Orders can arrive in every period, and the cost of receiving them is negligible (as in JIT). Every T periods, one audits the stocks and chooses a delivery schedule for each of the next T periods, thus incurring a fixed audit cost and—when one schedules actual deliveries—a fixed order cost. The problem is to find a review period T and an ordering policy minimizing the average cost. An earlier article developed an algorithm for computing an optimal T, and undertook a numerical study to evaluate various approximations. Assuming normal demands, we characterize the asymptotic behavior (for large μ/σ) of the optimal T and establish the asymptotic optimality of a heuristic, calculable on a spreadsheet. A numerical study indicates that patterns established here for large μ/σ hold for σ/μ above 2.     

Pricing and hedging in a single period market with random interval valued assets

In this article, a new financial market model, in which securities have random interval valued payoffs, is proposed. As an extension of traditional random market model, some concepts, such as robust arbitrage opportunities, risk-neutral pricing measures and robust replicative strategies, are given and discussed parallel to those in traditional market analysis. With these new concepts, problems of pricing and hedging are analyzed. It is shown that the requirement of no robust arbitrage opportunities is equivalent to the existence of risk-neutral pricing measures. Taking no robust arbitrage as the valuation principle, the problem of pricing a contingent claim with random interval valued payoff is discussed. All no robust arbitrage prices of the claim form an interval, whose endpoints can be got from the risk-neutral pricing measures or from robust replicative strategies.     

Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables

In this note, we consider a variation of the economic order quantity (EOQ) model where cumulative holding cost is a nonlinear function of time. This problem has been studied by Weiss [Weiss, H., 1982. Economic order quantity models with nonlinear holding costs. European Journal of Operational Research 9, 56–60], and we here show how it is an approximation of the optimal order quantity for perishable goods, such as milk, and produce, sold in small to medium size grocery stores where there are delivery surcharges due to infrequent ordering, and managers frequently utilize markdowns to stabilize demand as the product’s expiration date nears. We show how the holding cost curve parameters can be estimated via a regression approach from the product’s usual holding cost (storage plus capital costs), lifetime, and markdown policy. We show in a numerical study that the model provides significant improvement in cost vis-à-vis the classic EOQ model, with a median improvement of 40%. This improvement is more significant for higher daily demand rate, lower holding cost, shorter lifetime, and a markdown policy with steeper discounts.     

Formal solution of an interval system of linear equations with an application in static responses of structures with interval forces

We are concerned with the so called formal solution of an interval system of linear equations. We focus on the case where the coefficient matrix is deterministic (real) and the right-hand side is an interval vector. We show that the set of formal solutions represents a convex polyhedral set. We propose new properties of the formal solution related to its existence, uniqueness and robustness. As particular classes of problems we investigate also the situation where the coefficient matrix is an M-matrix or H-matrix. Example problems related to the structures, such as 6-bar truss and a rectangular sheet, are solved to illustrate the computational aspects of the methods.