Production Inventory Control Model Research Articles

Production inventory control model for deteriorating complementary and substitute items with shortage

Production inventory control model for deteriorating complementary and substitute items with shortage

Stability analysis of fuzzy differential equation for prey–predator system under Z-number fuzzy and granular differentiability concept

The stability analysis is one of the basic problems in the field of system, prey–predator, production inventory control, signal processing etc. The goal of stability analysis for prey–predator and production inventory control model is to determine the region of the different variables and parameters at which the system is stable or unstable. This paper explores an uncertain prey–predator model where both prey and predator populations are fuzzy variables. Also we have considered all the prey–predator parameters of the system are imprecise. This fuzzy prey–predator model is converted to an equivalent crisp model using granular differentiability approach. The condition of local stability is obtained mathematically by analysis the eigenvalues of characteristic equation. And also we introduced a production inventory model as a case study of fuzzy dynamical system to illustrate the efficiency of the result and practical aspects.

Optimal Strategies in a Production Inventory Control Model

We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch over from the different production rates but it is mandatory to switch-off when the inventory process reaches the storage maximum capacity. We consider holding, production, shortage penalty and switching costs. This model was introduced by Doshi, Van Der Duyn Schouten and Talman in 1978. In their paper they found a formula for the long-run average expected cost per unit time as a function of two critical levels, in this paper we consider expected discounted cumulative costs instead. We seek to minimize this discounted cost over all admissible switching strategies. We show that the optimal cost functions for the different production rates satisfy the corresponding Hamilton-Jacobi-Bellman system of equations in a viscosity sense and prove a verification theorem. The way in which the optimal cost functions solve the different variational inequalities gives the switching regions of the optimal strategy, hence it is stationary in the sense that depends only on the current production rate and inventory level. We define the notion of finite band strategies and derive, using scale functions, the formulas for the different costs of the band strategies with one or two bands. We also show that there are examples where the switching strategy with two critical levels is not optimal.

Production-Inventory control model for a supply chain network with economic production rates under no shortages allowed

This paper presents a new production-inventory control (PIC) model for a supply chain network (SCN) where multiple suppliers, manufacturers, and buyers are vertically integrated to provide multiple items to the market. The objective of the model is to simultaneously determine optimal replenishment quantities, replenishment cycles, and production rates in order to minimize the total network cost allowing no shortages of inventory and shutdown periods. We propose closed-form functions of the average annual inventory levels. A novel mixed-integer linear programming (MILP) formulation is developed based on these functions to solve the PIC model. In addition, an algorithm based on a decomposition approach was developed to solve a special case of the PIC model with a less computational burden. The results obtained by the algorithm are compared to the results of the existing models in literature to see if there is any improvement. A case study for designing an integrated SCN and controlling operational decisions is presented to demonstrate the application of the proposed PIC model.

An Integer Optimal Control Model of Production-Inventory System

The optimal control model of the production-inventory system has investigated in several past studies, but without taking into account the integer condition. This study suggested a new approach to find the integer solution of production-inventory control model under periodic review policy. A new approach is based on the modified some equations of Pontryagin maximum principle that used to find the solution of the non-integer model. Our numerical results showed the efficiency of the new approach by saving the paths of inventory level and production rate up to reach its goals over time. The total penalty costs of the model were the same, despite a difference in the values of initial inventory level. Also, we testified a new approach by formulating the quadratic programming problem of the production-inventory system. The solution was the same for the two problems; quadratic programming and new approach.

A fuzzy production inventory control model using granular differentiability approach

In this paper, we have created a single-period fuzzy production inventory control model on the finite time horizon. A new nonlinear demand function has been introduced, which depends on the stock, selling price and product quality. The realistic reasons come from logistical function and entry into the initial demand for the product and the reliance on uncertain advertising rates, uncertain stock rates, uncertain selling prices and uncertain product quality. In order to control and test the stability, the model needs to be defuzzified. The concept of granular differentiability has been applied to defuzzification. Granular differentiability is the new definition of fuzzy derivatives based on the function of horizontal membership. For the first time in this paper, we have used the granular differentiation method in production inventory systems. We analyzed vaguely optimized controls in terms of granular differentiation analytically and numerically.

Effect of Inflation on Two Storage Inventory Model with Time Dependent Deteriorating Items and Stock Dependent Demand

For deteriorating product, there always be a pressure on the company to maximize the profit. In the present model, an effort is made to develop a production inventory control model having two separate warehouses. In most of the study, the demand is assumed as time dependent which is not appropriate; but here authors have considered stock based demand. An approach is taken into consideration that deterioration rate different for different warehouses.

Optimal Production-Inventory Policy for a Periodic-Review Energy Buy-Back System over an Infinite Planning Horizon

This paper studies a periodic-review production-inventory control model under an energy buy-back program over an infinite planning horizon, in which a fixed setup cost and compensation levels corresponding to various market states are involved. The objective is to identify the manufacturer’s optimal production-inventory policy that can minimize his total discounted cost or long-run average cost. By using Veinott’s conditions, it is shown that such a state dependent optimal policy is of either an [Formula: see text], or partly an [Formula: see text] type.

Use of “e” and “g” operators to a fuzzy production inventory control model for substitute items

In this paper, a fuzzy optimal control model for substitute items with stock and selling price dependent demand has been developed. Here the state variables (stocks) are assumed to be fuzzy variables. So the proposed dynamic control system can be represented as a fuzzy differential system which optimize the profit of the production inventory control model through Pontryagin’s maximum principle. The proposed fuzzy control problem has been transformed into an equivalent crisp differential system using “e” and “g” operators. The deterministic system is then solved by using Newton’s forward-backward method through MATLAB. Finally some numerical results are presented both in tabular and graphical form.

Two-critical-number control policy for a stochastic production inventory system with partial backlogging

This paper deals with a production–inventory control model with partial backlogging, in which a reflected Brownian motion governs the inventory level variation. We consider a single storage facility with infinite capacity and assume that shortages are allowed and the total amount of stock-out is a mixture of backordering and lost sales. In addition, the production facility is controlled by a two-parameter (m, M) policy, which switches the production rate when the inventory level reaches the threshold values. The aim is to determine the optimal control parameters m and M by minimising the long-run total expected cost of the system. Some results are illustrated using numerical examples. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.

Production-inventory model for two-echelon closed-loop supply chain with finite manufacturing and remanufacturing rates

ABSTRACTThis research develops a two-echelon closed-loop supply chain production-inventory model consisting of a manufacturer, a remanufacturer and a retailer. The retailer faces a constant demand from the customers, which is satisfied by new and remanufactured product received from the manufacturer and the remanufacturer, respectively. The manufacturer and remanufacturer produce the product in batches with finite production rate. The manufacturer procures raw material in batches from outside supplier, and the remanufacturer receives the used product from the customers at a constant return rate. Many studies in the area of forward supply chain have established that the centralised production-inventory control models provide better results than the decentralised models. Hence, with synchronised activities of the supply chain players, this research proposes to find an optimal production-inventory policy of the players by minimising the joint total cost of the two-echelon closed-loop supply chain. Numerical illustration is presented to demonstrate the solution procedure and a sensitivity analysis is carried out to examine the impact of key parameters of the problem. Also, the total cost of closed-loop supply chain model is compared with the total cost of the corresponding forward supply chain model.

A JUMP-FLUID PRODUCTION–INVENTORY MODEL WITH A DOUBLE BAND CONTROL

We consider a production–inventory control model with two reflecting boundaries, representing the finite storage capacity and the finite maximum backlog. Demands arrive at the inventory according to a Poisson process, their i.i.d. sizes having a common phase-type distribution. The inventory is filled by a production process, which alternates between two prespecified production rates ρ1 and ρ2: as long as the content level is positive, ρ1 is applied while the production follows ρ2 during time intervals of backlog (i.e., negative content). We derive in closed form the various cost functionals of this model for the discounted case as well as under the long-run-average criterion. The analysis is based on a martingale of the Kella–Whitt type and results for fluid flow models due to Ahn and Ramaswami.

Simulation Techniques on System Dynamics Modeling of Productioninventory Control Model

The purpose of this research is to simulate the System Dynamics modeling approach in areas related to production-inventory management. Present inventory systemis based on order rate which is proportional to the discrepancy between the desired inventory and the actual inventory and time between orders are negligible. Asymptotic growth/decline are the perplexing behavior of this type of production-inventory control model. Considering the complexities of proposed inventory control model,solution approach comprises Euler's integration algorithm to simulate under the platform of system dynamics modeling. Coding is developed in C++ platform and resultsare demonstrated in Graphics mode by considering object oriented concepts. Numerical example with graphical output is presented to show the efficacy of Euler's integration algorithm in simulation for solving real life complex problems under system dynamics environment.

Overplanning factor in Toyota's formula for computing the number of kanban

To determine the number of required kanban, Toyota uses a formula based on the average demand during an order picking cycle, inflated by a constant overplanning factor β. This technical note attempts to characterize the situations where the simplicity of Toyota's formula reconciles with the established operations research paradigm of optimality. The overplanning policy examined in this paper could also be applied to other production inventory control models under uncertainty.

A one-vendor multi-buyer integrated inventory model: A comment

This paper presents a new production-inventory control (PIC) model for a supply chain network (SCN) where multiple suppliers, manufacturers, and buyers are vertically integrated to provide multiple items to the market. The objective of the model is to simultaneously determine optimal replenishment quantities, replenishment cycles, and production rates in order to minimize the total network cost allowing no shortages of inventory and shutdown periods. We propose closed-form functions of the average annual inventory levels. A novel mixed-integer linear programming (MILP) formulation is developed based on these functions to solve the PIC model. In addition, an algorithm based on a decomposition approach was developed to solve a special case of the PIC model with a less computational burden. The results obtained by the algorithm are compared to the results of the existing models in literature to see if there is any improvement. A case study for designing an integrated SCN and controlling operational decisions is presented to demonstrate the application of the proposed PIC model.

A review of: “Production-Inventory Control Models” (CWI Tract No. 30). By A. G. DE KOK. (Centre for Mathematics and Computer Science, The Netherlands, 1987.) [Pp. 214] Price Dfl33.

(1988). A review of: “Production-Inventory Control Models” (CWI Tract No. 30). By A. G. DE KOK. (Centre for Mathematics and Computer Science, The Netherlands, 1987.) [Pp. 214] Price Dfl33. International Journal of Production Research: Vol. 26, No. 12, pp. 1981-1981.

Approximations for operating characteristics in a production-inventory model with variable production rate

This paper deals with production-inventory control models with a variable production rate. The demand process is a compound Poisson process. The production rate is controlled by the well-known ( m, M)-policy. Simple and accurate approximations are given for operating characteristics of the system. It turns out that a sequential determination of M - m and m yields a rule that minimizes average costs subject to a service level constraint. Numerical results are given to show the accuracy of the approximations.

Asymptotic analysis for a production–inventory control model with renewal arrivals and exponential demands

We consider a production–inventory problem in which the production rate can be dynamically adjusted to cope with random fluctuations in demand. Customers arrive according to a renewal process, and the customer's demand is assumed to be exponentially distributed. Excess demand is backlogged. The production is controlled by a two-critical-number rule that prescribes which one of the two possible production rates must be used. Tractable expressions are given for several services measures including the fraction of demand backlogged. The analysis is based on the results for hitting probabilities in random walks, where the jump distribution has an exponential right or left tail.

Asymptotic analysis for a production–inventory control model with renewal arrivals and exponential demands

We consider a production–inventory problem in which the production rate can be dynamically adjusted to cope with random fluctuations in demand. Customers arrive according to a renewal process, and the customer's demand is assumed to be exponentially distributed. Excess demand is backlogged. The production is controlled by a two-critical-number rule that prescribes which one of the two possible production rates must be used. Tractable expressions are given for several services measures including the fraction of demand backlogged. The analysis is based on the results for hitting probabilities in random walks, where the jump distribution has an exponential right or left tail.

A Production-Inventory Control Model with a Mixture of Back-Orders and Lost-Sales

We consider a production-inventory control model of finite capacity, in which backordering up to a certain level is allowed. We assume that there exist two possible production rates. The control is based on two critical stock-levels and prescribes to change the production rate used only when one of these levels is reached. A fixed cost is associated with every switch-over. The rate at which customers arrive and the distribution of the demand of an arriving customer depend on the production rate used at that moment. A formula for the long-run average expected costs per unit time is obtained as a function of the chosen critical levels. From this formula we derive expressions for various interesting operating characteristics of this system, amongst which are the joint stationary distribution of the processes describing the production rate used and the inventory of the system and the average number of switch-overs and lost-sales per unit time.