Manas Kumar Maiti

Fuzzy inventory model with two warehouses under possibility constraints

A multi-item inventory model with two-storage facilities is developed with advertisement, price and displayed inventory level-dependent demand in a fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise). The model is formulated as a single/multi-objective programming problem under fuzzy constraint. Constraints are satisfied with some pre-defined necessity and the problem is solved via the Goal Programming Method (GPM) when crisp equivalents of the constraints are available and by a fuzzy simulation-based single/multi-objective genetic algorithm (FSGA/FSMOGA) otherwise. The model is illustrated with some numerical examples and results from different methods are compared in some particular cases.

Two-storage inventory model with lot-size dependent fuzzy lead-time under possibility constraints via genetic algorithm

Multi-item inventory models with stock dependent demand and two storage facilities are developed in a fuzzy environment where processing time of each unit is fuzzy and the processing time of a lot is correlated with its size. These are order-quantity reorder-point models with back-ordering if required. Here possibility and crisp constraints on investment and capacity of the small storehouse respectively are considered. The models are formulated as fuzzy chance constrained programming problem and is solved via generalized reduced gradient (GRG) technique when crisp equivalent of the constraints are available. A genetic algorithm (GA) is developed based on fuzzy simulation and entropy where region of search space gradually decreases to a small neighborhood of the optima and it is used to solve the models whenever the equivalent crisp form of the constraint is not available. The models are illustrated with some numerical examples and some sensitivity analyses have been done. For some particular cases results observed via GRG and GA are compared.

Two storage inventory model with random planning horizon

Abstract An inventory model with stock-dependent demand and two storage facilities under inflation and time value of money is developed where the planning horizon is stochastic in nature and follows exponential distribution with a known mean. The model is a order-quantity reorder-point problem where shortages are not allowed. Two rented storehouses are used for storage – one (say RW 1 ) at the heart of the market place and the other (say RW 2 ) little away from the market place. At the beginning, the item is stored at both RW 1 and RW 2 . The item is sold from RW 1 and as the demand is stock-dependent, the units are continuously released from RW 2 to RW 1 . Replacement of the item occurs when its inventory level reaches its reorder point ( Q r ). The model is formulated to maximize the total expected proceeds out of the system from the planning horizon. A genetic algorithm (GA) is developed based on entropy theory where region of search space is gradually decreases to a small neighborhood of the optima. This is named as region reducing genetic algorithm (RRGA) and is used to solve the model. The model is illustrated with some numerical examples and some sensitivity analyses have been done.

Two storage inventory model of a deteriorating item with variable demand under partial credit period

In this paper, a two-warehouse inventory model for deteriorating item with stock and selling price dependent demand has been developed. Above a certain (fixed) ordered label, supplier provides full permissible delay in payment per order to attract more customers. But an interest is charged by the supplier if payment is made after the said delay period. The supplier also offers a partial permissible delay in payment even if the order quantity is less than the fixed ordered label. For display of goods, retailer has one warehouse of finite capacity at the heart of the market place and another warehouse of infinite capacity (that means capacity of second warehouse is sufficiently large) situated outside the market but near to first warehouse. Units are continuously transferred from second warehouse to first and sold from first warehouse. Combining the features of Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) a hybrid heuristic (named Particle Swarm-Genetic Algorithm (PSGA)) is developed and used to find solution of the proposed model. To test the efficiency of the proposed algorithm, models are also solved using another two established heuristic techniques and results are compared with those obtained using proposed PSGA. Here order quantity, refilling point at first warehouse and mark-up of selling price of fresh units are decision variables. Models are formulated for both crisp and fuzzy inventory parameters and illustrated with numerical examples.

An EPQ model with price discounted promotional demand in an imprecise planning horizon via Genetic Algorithm

An economic production quantity (EPQ) model for a newly launched product is developed in an imprecise planning horizon, i.e., lifetime of the product is fuzzy in nature. At the beginning of each cycle price discount is offered to boost the demand. Demand depends on time and price during the price discount period. After withdrawal of price discount, demand depends on price only. Here, learning effect on production and set-up cost is incorporated. Models are formulated for both the crisp and fuzzy inventory parameters. Fuzzy models are transferred to deterministic ones following possibility/necessity measure on fuzzy goal and necessity measure on imprecise constraints. Finally optimal decision is made using Genetic Algorithm (GA).

Fuzzy inventory model with two warehouses under possibility measure on fuzzy goal

Multi-item inventory model with stock-dependent demand and two-storage facilities is developed in fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise) under inflation and time value of money. Joint replenishment and simultaneous transfer of items from one warehouse to another is proposed using basic period (BP) policy. As some parameters are fuzzy in nature, objective (average profit) function as well as some constraints are imprecise in nature. Model is formulated as to optimize the possibility/necessity measure of the fuzzy goal of the objective function and constraints are satisfied with some pre-defined necessity. A genetic algorithm (GA) is developed with roulette wheel selection, binary crossover and mutation and is used to solve the model when the equivalent crisp form of the model is available. In other cases fuzzy simulation process is proposed to measure possibility/necessity of the fuzzy goal as well as to check the constraints of the problem and finally the model is solved using fuzzy simulation based genetic algorithm (FSGA). The models are illustrated with some numerical examples and some sensitivity analyses have been done.

A production inventory model with stock dependent demand incorporating learning and inflationary effect in a random planning horizon: A fuzzy genetic algorithm with varying population size approach

A production inventory model for a newly launched product is developed incorporating inflation and time value of money. It is assumed that demand of the item is displayed stock dependent and lifetime of the product is random in nature and follows exponential distribution with a known mean. Here learning effect on production and setup cost is incorporated. Model is formulated to maximize the expected profit from the whole planning horizon. Following [Last, M. & Eyal, S. (2005). A fuzzy-based lifetime extension of genetic algorithms. Fuzzy Sets and Systems, 149, 131-147], a genetic algorithm (GA) with varying population size is used to solve the model where crossover probability is a function of parents age-type (young, middle-aged, old, etc.) and is obtained using a fuzzy rule base and possibility theory. In this GA a subset of better children is included with the parent population for next generation and size of this subset is a percentage of the size of its parent set. This GA is named fuzzy genetic algorithm (FGA) and is used to make decision for above production inventory model in different cases. The model is illustrated with some numerical data. Sensitivity analysis on expected profit function is also presented. Performance of this GA with respect to some other GAs are compared.

Fully fuzzy fixed charge multi-item solid transportation problem

Graphical abstractDisplay Omitted HighlightsFully fuzzy fixed charge multi-item solid transportation problem (FFFCMISTP) is considered.FFFCMISTP with the decision variable are taken as fuzzy.New defuzzification method, fuzzy slack and surplus variable is used for FFFCMISTP.Minimization of transportation cost as well as fuzziness of the solution for FFFCMISTP is discussed. This paper presents fully fuzzy fixed charge multi-item solid transportation problems (FFFCMISTPs), in which direct costs, fixed charges, supplies, demands, conveyance capacities and transported quantities (decision variables) are fuzzy in nature. Objective is to minimize the total fuzzy cost under fuzzy decision variables. In this paper, some approaches are proposed to find the fully fuzzy transported amounts for a fuzzy solid transportation problem (FSTP). Proposed approaches are applicable for both balanced and unbalanced FFFCMISTPs. Another fuzzy fixed charge multi-item solid transportation problem (FFCMISTP) in which transported amounts (decision variables) are not fuzzy is also presented and solved by some other techniques. The models are illustrated with numerical examples and nature of the solutions is discussed.

Production policy for damageable items with variable cost function in an imperfect production process via genetic algorithm

This paper gives an appropriate solution to the contradiction faced during the inventory of displayed damageable items where both demand and damageability are stock-dependent. In this model, more stock increases the demand and ultimately fetches more profit but at the same time, invites more damage bringing down the profit amount. Moreover, the classical inventory models normally assume the production process to be perfectly reliable with a fixed set-up cost. In practice, it is not so. In this paper, an inventory model for a damageable item is formulated following profit maximization principle. Here, the unit production cost depends on production rate and is derived from the particular production function under which it is being produced. Demand for the item is directly proportional to stock and inversely proportional to unit selling price. Also, the units are kept in heaped stock and hence, likely to be damaged due to it. Flexibility of the production process, which is not perfectly reliable, is introduced in the manufacturing system by the generalized cost function. The set-up cost, the reliability of the production process, production rate and the inventory amount are the decision variables. Due to highly nonlinearity of the average profit function (i.e., objective function), it is optimized using contractive mapping genetic algorithm (CMGA) for the global optimal solution. Numerical examples are presented to illustrate the model and some useful comments/decisions are derived for a decision maker (DM). Results are obtained via greedy search algorithm (GSA) and simulated annealing (SA) also and compared with those obtained from CMGA.

A production inventory model with fuzzy production and demand using fuzzy differential equation: An interval compared genetic algorithm approach

In this paper, a production inventory model, specially for a newly launched product, is developed incorporating fuzzy production rate in an imperfect production process. Produced defective units are repaired and are sold as fresh units. It is assumed that demand coefficients and lifetime of the product are also fuzzy in nature. To boost the demand, manufacturer offers a fixed price discount period at the beginning of each cycle. Demand also depends on unit selling price. As production rate and demand are fuzzy, the model is formulated using fuzzy differential equation and the corresponding inventory costs and components are calculated using fuzzy Riemann-integration. @a-cut of total profit from the planning horizon is obtained. A modified Genetic Algorithm (GA) with varying population size is used to optimize the profit function. Fuzzy preference ordering (FPO) on intervals is used to compare the intervals in determining fitness of a solution. This algorithm is named as Interval Compared Genetic Algorithm (ICGA). The present model is also solved using real coded GA (RCGA) and Multi-objective GA (MOGA). Another approach of interval comparison-order relations of intervals (ORI) for maximization problems is also used with all the above heuristics to solve the model and results are compared with those are obtained using FPO on intervals. Numerical examples are used to illustrate the model as well as to compare the efficiency of different approaches for solving the model.