scholarly journals Profit maximization in an inventory system with time-varying demand, partial backordering and discrete inventory cycle

2021 ◽  
Author(s):  
Luis A. San-José ◽  
Joaquín Sicilia ◽  
Manuel González-de-la-Rosa ◽  
Jaime Febles-Acosta
Keyword(s):  
Profit Maximization ◽  
Inventory System ◽  
Future Research ◽  
Mathematical Programming Problem ◽  
Inventory Problem ◽  
Integer Multiple ◽  
Basic Period ◽  
Partial Backordering ◽  
Demand Rate ◽  
Varying Demand

AbstractIn this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

scholarly journals Multi-item fuzzy inventory problem with space constraint via geometric programming method

2006 ◽  
Vol 16 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Kumar Mandal ◽  
Kumar Roy ◽  
Manoranjan Maiti
Keyword(s):  
Space Constraint ◽  
Geometric Programming ◽  
Profit Maximization ◽  
Inventory Model ◽  
Programming Method ◽  
Unit Price ◽  
Selling Price ◽  
Inventory Problem ◽  
Set Up ◽  
Fuzzy Inventory

In this paper, a multi-item inventory model with space constraint is developed in both crisp and fuzzy environment. A profit maximization inventory model is proposed here to determine the optimal values of demands and order levels of a product. Selling price and unit price are assumed to be demand-dependent and holding and set-up costs sock dependent. Total profit and warehouse space are considered to be vague and imprecise. The impreciseness in the above objective and constraint goals has been expressed by fuzzy linear membership functions. The problem is then solved using modified geometric programming method. Sensitivity analysis is also presented here.

scholarly journals An inventory model for deteriorating items under time varying demand condition

2013 ◽  
Vol 8 (1) ◽  
pp. 1273-1278
Author(s):  
Srichandan Mishra ◽  
S.P. Mishra ◽  
N. Mishra ◽  
J. Panda
Keyword(s):  
Time Horizon ◽  
Cost Minimization ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Time Varying ◽  
Infinite Time ◽  
Infinite Time Horizon ◽  
Demand Rate ◽  
Demand Condition ◽  
Varying Demand

In this paper we discuss the development of an inventory model for deteriorating items which investigates an instantaneous replenishment model for the items under cost minimization. A time varying type of demand rate with infinite time horizon, exponential deterioration and with shortage in considered. The result is illustrated with numerical example.

Ordering Policy in a Two-Warehouse Environment for Deteriorating Items under Inflationary Conditions

2014 ◽  
pp. 320-338
Author(s):  
Chandra K. Jaggi ◽  
Sarla Pareek ◽  
Aditi Khanna ◽  
Ritu Sharma
Keyword(s):  
Global Economy ◽  
Aggregate Demand ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Inventory Problem ◽  
Inventory Costs ◽  
Ordering Policy ◽  
Demand Rate ◽  
Warehousing Systems ◽  
The Cost

In this chapter, the two-warehouse inventory problem is considered for deteriorating items with constant demand rate and shortages under inflationary conditions. In today’s unstable global economy, the effects of inflation and time value of money cannot be ignored as it increases the cost of goods. To safeguard from the rising prices, during the inflation regime, the organization prefers to keep a higher inventory, thereby increasing the aggregate demand. This additional inventory needs additional storage space that is facilitated by a rented warehouse. Further ahead, in the real business world, to retain the freshness of the commodity, most of the organizations adopt the First-In-First-Out (FIFO) dispatching policy. FIFO policy yields fresh and good conditioned stock thereby resulting in customer satisfaction, especially when items are deteriorating in nature. However, the two warehousing systems usually assume that the holding cost of items is more in Rental Warehouse (RW) than the Owned Warehouse (OW) due to modern preserving techniques. Therefore, to reduce the inventory costs, it is economical to consume the goods of RW at the earliest. This approach is termed the Last-In-First-Out (LIFO) approach. The objective of the present chapter is to develop a two warehouse inventory model with FIFO and LIFO dispatching policies under inflationary conditions. Further, comparison between FIFO and LIFO policies has been exhibited with the help of a numerical example. Sensitivity analysis has also been performed to study the impact of various parameters on the optimal solution.

Optimal Strategies for Deteriorating Inventory Systems Under Trapezoidal Type Demand

2018 ◽  
pp. 1-31
Author(s):  
Kunal Tarunkumar Shukla ◽  
Mihir S. Suthar
Keyword(s):  
Sensitivity Analysis ◽  
Continuous Function ◽  
Optimal Strategy ◽  
Piecewise Linear ◽  
Optimal Strategies ◽  
Literature Survey ◽  
Inventory Systems ◽  
Future Research ◽  
Partial Backlogging ◽  
Demand Rate

In this chapter, we study different inventory systems with trapezoidal demand rate, i.e., demand rate is a piecewise linear and continuous function. This chapter presents mathematical formulations of optimal replenishment policies for items with trapezoidal demand rate. Section 1 presents detailed literature survey for inventory systems with ramp type and trapezoidal type demand. In Section 2, Formulation technique for inventory system of items, which follows trapezoidal type demand rate. Section 3 presents effect of deterioration in model discussed in Section 2. Optimal strategy for deteriorating items with expiration dates under trapezoidal type demand and partial backlogging is discussed in Section 4. In Section 5, sensitivity analysis is carried out and chapter is concluded along with future research scope in Section 6.

Some Studies in Multi-Storage Inventory System

2016 ◽  
pp. 176-200
Author(s):  
Shyamal Kumar Mondal
Keyword(s):  
Planning Horizon ◽  
Inventory System ◽  
Mixed Integer ◽  
Lot Size ◽  
Continuous Release ◽  
Demand Rate ◽  
Cycle Lengths ◽  
Holding Cost ◽  
Inventory Holding ◽  
And Storage

In this chapter, a multi-storage inventory system has been considered to develop a deterministic inventory model in finite planning horizon. Realistically, it is shown that due to large stock and insufficient space of existing own warehouse (OW); excess items are stored in single rented warehouse (RW). Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. Here, the replenishment cycle lengths are of equal length, the demand rate is a continuous linear increasing function of time and partially backlogged shortages are allowed in all cycles. In each cycle, the replenishment cost is assumed to be dependent linearly on lot size and the stocks of RW are also transported to OW in continuous release pattern. The model is formulated as a constrained non-linear mixed integer cost objective function under single management. Finally, results with a sensitivity analysis have been shown with the help of a real coded GA.

scholarly journals A New Green Efficiency-Based Carbon Taxing Policy and Its Effects on a Production-Inventory System with Random Carbon Emissions and Green Investment

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Tapan Kumar Datta
Keyword(s):  
Carbon Tax ◽  
Profit Maximization ◽  
Inventory System ◽  
Environmental Benefits ◽  
Independent Random Variables ◽  
Model Parameters ◽  
Green Technologies ◽  
Numerical Examples ◽  
Production Inventory ◽  
Production Inventory System

In this study, the author proposes a new carbon taxing policy. This proposed carbon tax has two tax components. The first component is constant, and the second component depends on the green efficiency of production. The green efficiency of production is measured by the average amount of emissions per unit production in an assessment year. The green efficiency-based tax component can be reset every year. Lesser average emission rate indicates better green efficiency. The second component of this proposed carbon tax forces the firm to improve the green efficiency of production, which results in cleaner production. The author incorporates this new carbon tax policy in a production-inventory system with a price-sensitive demand rate. A rule is provided for the implementation of this new tax. Emissions during setup, production, and storage are considered as independent random variables. The firm has the opportunity of investing in green technologies to improve green efficiency. A profit maximization policy is adopted to solve the developed model. A solution algorithm is also provided. The model is illustrated by numerical examples with randomly generated model parameters. The results of numerical examples show the environmental benefits of the proposed carbon tax.

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