Deterministic Inventory Model Research Articles

Fuzzy multi-objective deterministic inventory model with time dependent demand and holding cost under Pythagorean fuzzy goal programming approach

Fuzzy multi-objective deterministic inventory model with time dependent demand and holding cost under Pythagorean fuzzy goal programming approach

Optimal inventory policies for finite horizon deterministic inventory models for non-instantaneous deteriorating items and permissible-delay in payment

This paper is concerned with the search for the optimal inventory policy for a finite horizon inventory model with time-varying demand, non-instantaneous deteriorating items, and permissible delay in payment. The optimal inventory policy consists of the determination of the number and timing of replenishment schedules that minimise some total inventory costs. The search for such policy is formulated as a mixed integer nonlinear programming problem (MINLP). It turns out that the non-instantaneous deterioration phenomenon coupled with permissible delay in payment introduce non-smoothness in the objective function of the MINLP. This leads to failure of direct applications of known solution methods to the MINLP. To circumvent this problem, a methodology is proposed for solving fully the MINLP problem. It is shown, through careful mathematical analysis, that earlier results on similar problems can be adapted to solve this problem. Conditions under which the solution of the MINLP is unique are identified. Moreover, convexity with respect to the number of replenishment orders is established. This makes the search for the optimal inventory policy handy. Numerical experiments are also conducted to test the applicability, to identify the key elements and to provide managerial insights to the model.

A polynomial of degree five representing the selling price of an inventory of deteriorating items with a linear degradation rate, constant holding cost, and demand-dependent selling price

The study suggests a deterministic inventory model as opposed to a probabilistic one. With just odd powers considered, the model's demand rate is a degree five polynomial of the selling price. The keeping expense is assumed to stay constant. Time has an impact on how quickly things degrade. The backlog and shortages are both acceptable. The inventory model used a single article inventory. It is assumed that there is no lead time. In this study, the differential equation's solution was used to determine the best values. The model is numerically validated, and in a maple application, convexity is displayed as a two-dimensional graph.

A deterministic inventory model for deteriorating products with shortages and price dependent demand rate

Purpose of the study: The proposed model shows a deterministic approach of the inventory management in which the rate of the deterioration of the inventory commodities is proportional to time, demand rate is a function of selling price and inventory holding cost both, ordering cost and deterioration rate are all function of time. Here shortages are allowed during the lead time and completely backlogged. The optimum replenishment policy is to be determined which minimizes the total cost. The rate of deterioration has been considered as non-instantaneous and that follows the two parameters Weibull distribution. In the proposed model we aim to find optimal value of the inventory level to minimize the total effective cost.
 Methodology: The optimal solution will have to be obtained by using Mathematica Software and has been illustrated using a numerical example.
 Main Findings: Since lowering the selling price would result in increase in purchase of items by the customers, hence the selling price is the major criteria to determine their buying capacity.
 Applications of this study: If researchers go on taking several kinds of variable costs etc., then hopefully they may find a new area of study in their research.

Inventory Model for Order Quantity Optimization with Partial Backlogging on Greater Demand at The Beginning

This article discusses the model of inventory with greater demand at the beginning which allows shortages. During the shortage period, it is assumed that there is a backlogged demand, and the remainder is considered lost sales. This research is completed by using the deterministic inventory model method, namely the EOQ model. The result of using the EOQ method is to determine the inventory lot size and length, with the goal of minimizing the total cost of inventory and generating maximum profits related to the inventory model. An numerical example is given to show the use of this model.

Understanding complex dynamics in inventory management with endogenous demand under social interactions: a chaos perspective

This paper investigates the system dynamics and performances of a deterministic inventory model with endogenous demand transitions determined by consumers' purchase behaviours and managers' order decisions under social interactions. With known demand transitions, the manager makes order decisions to maximise the single-period profit by the optimal order policy or commits to a fixed quantity by the constant order policy. With unknown demand transitions, the demand-chasing order policy is adopted. The impacts of various endogenous factors on the system dynamics and performances are examined. It is found that the equilibrium demand can exhibit stability, periodic cycles, and chaos in the long-run dynamics. Strong social interactions can lead to instabilities in demand processes and impair the profitability of the inventory system. The value of information on endogenous demand transitions increases if social interaction intensities and/or sizes of loyal customers become larger. The results suggest that endogenous factors stemming from managers' decision-making, consumers' purchase behaviours, and their interplay can cause persistent and unpredictable demand fluctuations leading to instability and profit losses. Managers should understand the underlying causes of demand variations and the impacts of endogenous factors to improve operational effectiveness in inventory management.

Constrained Stochastic Inventory Control Models for Multi-Item with Variable Demand

Constrained multi-item inventory system with variable demands are considered. The demand rates of five selected multi-item - Cowbell, Milo, SMA, Cerelac and Golden Morn were modeled as Weibull, Normal and Lognormal probability distributions respectively with the aid of chi-squared multinomial goodness-of-fit test. The respective probability distributions with estimated location parameters: 491.55, 536.92, 10.5, 2.1926 and 5.3103 were used as the basis of probabilistic inventory models to obtain dynamic EOQ for each item under each constraint subject to Kuhn, Karush and Tucker (KKT) conditions as against the use of simple averages in deterministic inventory models. The optimal values of these constraints: available warehouse space (124sq.ft), specified level of inventory (94 units), limited capital (76,671.52 naira) and number of orders (1/month) were obtained using the optimal EOQ values to establish optimal inventory level and constraints level/capacity for each item in order to avoid shortage or excess stock.

A Deterministic Inventory Model with Time-varying Demand for Items with Static Deterioration Rate

A Deterministic Inventory Model with Time-varying Demand for Items with Static Deterioration Rate

Optimal policies for a deterministic continuous-time inventory model with several suppliers: when a supplier incurs no set-up cost

The subject is a deterministic continuous-time continuous-state inventory control model. Stock is replenished by ordering from one of a number of suppliers incurring a different cost per item and a different set-up cost. Taking the cost of procurement into account, the objective is to minimize the total discounted cost over an infinite planning horizon. The size of the order that is to be placed and the supplier with which it is to be placed are to be decided. Earlier studies of the problem have relied substantially on the assumption that the set-up cost of every supplier is strictly positive. Removing this restriction calls for a significant modification of the adopted approach. This is realized in the present study. It is shown that there is a stable unique optimal policy of a type that encompasses (s, S) and generalized (s, S) policies. Conditions that are necessary and sufficient for it to reduce to each of these types are established. The case of two suppliers is studied in detail, properties of the solution are investigated, numerical examples illustrating various aspects are included, and the connection with antecedent results is assessed.

Cost optimization inventory model for deteriorating items with trapezoidal demand rate under completely backlogged shortages in crisp and fuzzy environment

Recently, various deterministic inventory models were developed for deteriorating items with the uniform demand pattern (either increasing or decreasing) throughout the cycle. However, such types of models are not suitable for many real business problems. In particular, the demand patterns of various items are not steady throughout the cycle. In many inventory models, ordinarily, the demand rises first, then it becomes static and finally decreases, and such types of demands can be portrayed by considering trapezoidal functions. Moreover, the costs associated with the inventory become imprecise due to several socio-economical factors. As a result, the optimal solution obtained by the classical inventory model may not fit the actual scenario. Keeping this in view, we develop here an inventory model for deteriorating items having the trapezoidal type of demand function in both crisp and fuzzy environments by considering three possible cases of shortages which are completely backlogged. Furthermore, in view of the comparative study of both scenarios, different data sets of constraints are examined for optimal results. Also, it is observed that the optimal results of the fuzzy model are more appropriate to real-world inventory problems. Finally, in order to strengthen the present investigation, the managerial insight of fluctuation in parameters is presented analytically via sensitivity analysis.

Analysis of a JIT Stochastic Inventory System for deteriorating items

This paper provides insights into the management of perishable products from a simulation-inventory modeling perspective. By studying a just-in-time (JIT) inventory system under a single-setup multiple-delivery setting, we propose a new simulation-optimization approach for analyzing JIT purchasing agreements between a single supplier and a single retailer when dealing with randomness. Our findings show that using deterministic inventory models in a stochastic environment can be particularly useful for modeling and optimizing complex inventory systems, i.e., when difficulties arise in characterizing randomness through an analytical model.

Two warehouse inventory model for deteriorating items with fixed shelf-life stock-dependent demand and partial backlogging

In inventory management self life expiration date has a unique role. In the practice there are many goods and services such as food, medication remain safe and suitable for human consumption until it exist their shelf life. In this paper, we implemented a fixed shelf life of a deterministic inventory model for decaying items in two warehouses system with partial backlogging. The demand rate is considered stock dependent means that demand inclined by display of the stock level. In two warehouse system we are considering one own warehouse and second warehouse is on rented basis. The preservation facility is good in rented warehouse than own warehouse. Due to various preserve conditions, deterioration rate in two warehouses may be differs. In addition, backlogging rate is time dependent which is inversely proportional to the waiting time for the next cycle. The model is also justified by the numerical examples under two cases and also sensitivity analysis is carried out with various parameters by using MATLAB R16b.

An Optimal Policy for Items with Linear Demand Rate, Variable Deterioration Rate Under Shortage and Lead-Time

In this research, we have developed a deterministic inventory model for an item having linear demand in variable deterioration rate. The shortage is allowed and fully backlogged. In developing the model, we have assumed that lead time is not equal to zero. Here we developed an optimal policy that minimizes that the total average cost. The model is illustrated by a suitable numerical example and sensitivity analysis has been carry- out.

A deterministic inventory model of aluminium refreshment cans in reverse supply chain

A deterministic inventory model of aluminium refreshment cans in reverse supply chain

Impact of delay in payment, shortage and inflation on an EOQ model with bivariate demand

The major challenge of inventory decision makers is to determine an inventory optimization strategy that ensures the right balance between keeping abundant on hand inventory to meet the demand of the customers and optimizing costs related to holding inventory. This article analyzes on providing a general deterministic inventory model in which the rate of demand is determined by price and time over the ordering cycle time. The traditional assumption of zero ending invento ry level is relaxed to a non-zero ending inventory level. Shortages are allowed which are partially backlogged. We develop models with partial backlogging and without backlogging. The aim is to maximize the profit per unit time, assuming delay in payment and inflation. An algorithm is proposed to find the optimal selling price, optimal stockout period, optimal replenishment cycle time and the optimal ending inventory level. All the possible special cases of these two models are also discussed. The numerical examples, graphical representation, and sensitivity analysis are given to illustrate the practical application of the proposed model.

The nature of optimal policies for deterministic finite-horizon inventory models

This paper concerns a general formulation for a longstanding problem. This is the problem of determining a replenishment schedule that minimises the total cost of stocking and holding an inventory in a deterministic finite-horizon inventory model. The formulation permits the treatment of seemingly unrelated models in a single framework. These include classical lot-size models, batching models, repair models, recovery models and others. Admissible control policies are restricted to a partition of some closed interval on the real line. The solution of a mixed integer nonlinear programming problem (MINLP) delivers the optimal partition. It is shown that the MINLP possesses an optimal solution under very mild conditions. The theory of submodular functions on a lattice is the key to handling the integer variable. This theory permits the recovery and generalisations of earlier results on the interleaving property of optimal partitions and a convexity property of the value of the objective function. Past intractable inventory models with demand driven by a general differential equation and in the absence and in the presence of shortages and inflation are solved. This generalises a number of existing results in the literature.

Inventory Model with Inflation under Credit Period and Shortage

In this study, an deterministic inventory model based on the concept of permissible delay in payments is discussed. Demand is assumed to be price dependent, and a constant price function represents it. Shortages are allowed and partially backlogged. In the realistic environment, it observed that there are several items like dry fruits, vegetables, grocery, and fruits, etc. which deteriorate after a time gap. So this model is also based on non-instantaneous deterioration. This study aims is to optimize the optimal order level and selling price to maximize the retailer`s total profit. Finally, numerical examples solved by using a proposed algorithm to show the validity of the model and sensitivity analysis done on parameters..

A deterministic production inventory model with defective items, imperfect rework process and shortages backordered

The basic assumption of the conventional inventory models is that all items produced are of perfect quality. In practice, some defective items are produced due to process deterioration or other factors. This paper develops a mathematical model for an imperfect production inventory system. It is assumed that the defective items produced in the regular production process consist of scrap, imperfect quality and reworkable items. The rework process is accomplished immediately when the regular production process ends, and the rework process produces scrap, imperfect quality and as-good-as perfect items. A numerical example is provided to illustrate the developed model, and a sensitivity analysis is carried out. It was found that producing scrap and imperfect quality items through the reworking is crucial, since this assumption effects optimal policy. Managerial insights are also presented based on the numerical examples.

A Periodic Review Deterministic Inventory Model with Exponential Rate of Demand for Deteriorating Items and Partial Backlogging

A Periodic Review Deterministic Inventory Model with Exponential Rate of Demand for Deteriorating Items and Partial Backlogging

A deterministic inventory model in reverse supply chain

Purpose The purpose of this paper is to present a unique model for the production–recycling–reuse of aluminium refreshment cans. It is presumed that disposed-off 250-ml aluminium cans are collected from the retail outlet. The cans are thereafter arranged into non-tainted and tainted categories. Design/methodology/approach The current model considers all the factors, i.e. producing, recycling and remanufacturing, whereas the previous models provide emphasis only one factor. Six procedures were considered in the improvement of the mathematical model. Findings In this paper, a recycling–reuse model that remanufactures non-tainted aluminium beverage cans and uses regrind from damaged non-tainted aluminium beverage cans mixed with parent aluminium material in the production of new cans was developed and analysed to reduce the amount of aluminium beverage cans that are disposed off in a scrapyard. The model is assumed to have no shortcomings, and the different percentages regarding the classes of cans are taken to be deterministic. Originality/value The model incorporates several unique aspects, including accounting for the cost of land use and associated environmental damage through the calculation of a present value that is charged to the manufacturer.