Pankaj Dutta

A single-period inventory model with fuzzy random variable demand

This paper presents a single-period inventory problem in an imprecise and uncertain mixed environment. The aim of this paper is to introduce demand as a fuzzy random variable. To determine the optimal order quantity a new methodology is developed for this model in presence of fuzzy random variable demand where the optimum is achieved using a graded mean integration representation. To illustrate the model the classical newsboy problem is considered.

Continuous review inventory model in mixed fuzzy and stochastic environment

In this paper, we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting. Since demand plays an important role in such type of inventory systems, we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand. After fuzzifying the random lead-time demand we consider the annual average demand as a fuzzy random variable. We provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value. Since the expected value of a fuzzy random variable is a fuzzy quantity, a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution. A numerical example is presented to illustrate the proposed model.

Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand

This paper presents an approach for solving an inventory model for single-period products with maximizing its expected profit in a fuzzy environment, in which the retailer has the opportunity for substitution. Though various structures of substitution arise in real life, in this study we consider the fuzzy model for two-item with one-way substitution policy. This one-way substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. Again, to describe uncertainty usually probability density functions are being used. However, there are many situations in real world that utilize knowledge-based information to describe the uncertainty. The objective of this study is to provide an analysis of single-period inventory model in a fuzzy environment that enables us to compute the expected resultant profit under substitution. An efficient numerical search procedure is provided to identify the optimal order quantities, in which the utilization of imprecise demand and the use of one-way substitution policy increase the average expected profit. The benefit of product substitution is illustrated through numerical example.

Design and analysis of a closed-loop supply chain in presence of promotional offer

Closed-loop supply chain (CLSC) has been an area of increasing attention during the last decade due to its economic impact, strict legislations and social awareness. Profitability of any remanufacturing process is mainly driven by the effective and efficient acquisition of used products. In this paper, a market-driven recovery framework is proposed to acquire the used products from consumers by taking into account their buying patterns as well as the willingness to accept a promotional offer. The proposed framework is integrated with an optimisation model for a multi-period CLSC to maximise the overall profit of the system by determining the optimal discount amount along with the decision of finding optimal manufacturing, remanufacturing and disposal quantity. The findings of the study provide several insights to the decision-makers that lead to better performance of the entire closed-loop system. The analysis suggests a trade-off among manufacturing/remanufacturing cost, penalty cost for not fulfilling the legislation criterion and collection cost due to the employment of promotional offer. Sensitivity analysis is performed to observe the effect of various important parameters on the system’s performance. Finally, a comparative study has been conducted to examine the performance of the CLSC with vs. without promotional offer.

An integrated supply chain model for new products with imprecise production and supply under scenario dependent fuzzy random demand

In the present day business scenario, instant changes in market demand, different source of materials and manufacturing technologies force many companies to change their supply chain planning in order to tackle the real-world uncertainty. The purpose of this paper is to develop a multi-objective two-stage stochastic programming supply chain model that incorporates imprecise production rate and supplier capacity under scenario dependent fuzzy random demand associated with new product supply chains. The objectives are to maximise the supply chain profit, achieve desired service level and minimise financial risk. The proposed model allows simultaneous determination of optimum supply chain design, procurement and production quantities across the different plants, and trade-offs between inventory and transportation modes for both inbound and outbound logistics. Analogous to chance constraints, we have used the possibility measure to quantify the demand uncertainties and the model is solved using fuzzy linear programming approach. An illustration is presented to demonstrate the effectiveness of the proposed model. Sensitivity analysis is performed for maximisation of the supply chain profit with respect to different confidence level of service, risk and possibility measure. It is found that when one considers the service level and risk as robustness measure the variability in profit reduces.

Simulation Study of an Integrated Reverse Logistics in Fuzzy Environment

Along with forward supply chain organization needs to consider the impact of reverse logistics due to its economic advantage, social awareness and strict legislations. In this work, we develop a system dynamics framework to analyze the long-term behavior of a multi-echelon integrated forward-reverse supply chain with fuzzy demand, satisfaction rate and collection rate. The uncertainty associated with satisfaction of customers and collection of used product has been quantified using fuzzy possibility measures. In the proposed model, it is assumed that the customer can exchange their old used product with a fresh new product in a primary market or a relatively better refurbished product in a secondary market at a discounted price. From the simulation study, it is observed that the inclusion of product exchange policy reduce the order variation and bullwhip effect at both retailer and distributor level. Finally, sensitivity analysis is performed to examine the impact of various parameters, namely; satisfaction rate, collection percentage, refurbishing percentage, inventory cover time and inventory adjustment time on recovery process and bullwhip effect.

A multi-product newsboy problem with fuzzy customer demand and a storage space constraint

This article provides a fuzzy inventory model for multi-product newsboy problem subject to a storage space constraint. Common characteristics of inventory systems include uncertain demand. Several authors have examined constrained multi-item newsboy problem with stochastic demand. In this paper, a model for cases of fuzzy demands is constructed. The objective is to maximise the total resultant profit by considering fuzzy demands together with a storage space constraint. The optimisation is achieved using interval-valued expectation of a fuzzy number. Based on the bisection method, an efficient iterative algorithm is adopted to identify the optimal order quantities. The optimality conditions are justified through a numerical example.

Analysis of an EPC project: a solution to the resource constrained project scheduling problem using genetic algorithms

This study employs a generalised resource constrained project scheduling problem to estimate an optimal schedule for an engineering– procurement–construction (EPC) project. We present a decision support system using a repetitive mutation-based genetic algorithm for solving multiple resource constrained problems while scheduling the activities in a construction project. The objective is to determine the minimum makespan of the project subject to the precedence and limited resource constraints. The effectiveness of the proposed evolutionary strategy is compared with some standard problems and finally, a real-life EPC project scheduling problem of a petroleum refinery is illustrated.

Resource Constrained Multi-Project Scheduling Problem with Resource Transfer Times

Scheduling multi-project is a complex decision making process. It involves the effective and timely allocation of resources to different projects. In the case of multi-project, resources are often transferred between the projects. It consumes both time and cost, when projects are situated in different geographic locations. As a result, the net present value (NPV) of multi-projects is significantly impacted by the resource transfer time. In this paper, a new genetic algorithm (GA) approach to the multi-project scheduling problem with resource transfer times is presented, where the NPV of all projects is maximized subject to renewable resource constraints. The paper also presents a heuristic approach using two phase priority rules for the same problem. We conduct a comprehensive analysis of 60 two-phase priority rules. The proposed GA approach is compared to the heuristic approach using the well-known priority rules. An extensive computational experiment is reported.

Single-period ordering and pricing policies with markdown, multivariate demand and customer price sensitivity

Abstract This paper studies single-period ordering and markdown pricing policies for short lifecycle products (SLP) by considering differing customer price and time sensitivities. The SLP is assumed to have declining customer valuation (and price) over the selling season and multivariate demand, which is a function of the inventory level, price and time. Promotional markdown (in contrast to clearance markdown) becomes an indispensable part of a pricing policy in view of stock-dependent demand and isused as a mechanism for customer segmentation and price discrimination over time. To offer a realistic pricing, we consider the impact of highly price-sensitive customers who value the price of the product over its innovativeness and who act strategically by purchasing only during a‘sale’ at a markdown price. In this context, single-period inventory models are formulated to include markdown under two market scenarios, namely the homogenous market and thetwo-segment market – a price insensitive (PI) segment, and a price-sensitive (PS) segment. The assumption of non-overlapping segments is relaxed later, and PI customers are allowed to buy later on at a markdown price. The proposed profit-maximising models determine the optimal order size, initial price, markdown time, and price. The solution methods along with the optimality conditions are specified in detail. The results are discussed by using numerical examples, and model behavior with respect to parameters is presented along with the sensitivity analysis.The study reveals the benefits of market segmentation and markdown pricing which recognise high price-sensitive ‘bargain hunter’ customers and offers deeper discounts that yield greater profits. It also demonstrates the superiority of a markdown policy to a single pricing policy, and the benefits of considering the demand stimulating-effect of inventory.