The present study is an attempt to develop an inventory model for deteriorating items with negative exponential demand. Shortages are allowed with partial back logging. This model is different from the existing models where deterioration is a function of time. Accordingly, three different types of probabilistic deterioration functions have been considered to find the associated decision variables and also to make comparisons among them. The optimality is illustrated with numerical values of system parameters and the graphical representations are given to depict the trend. The necessary observations in obtaining optimal values of decision variables are analyzed in the light of the practical aspect of the developed model. Finally, considering the numerical values of system parameters, sensitivity analyses are carried out to study the effect of changes in most important system parameters.

The role of sustainability in supply chain is becoming critical due to increasing environment related problems and societal issues. Sustainable Supply Chain Management (SSCM) helps in reducing environmental degradation as well as social and economic implications. SSCM practices in Indian industries are in initial stage of implementation and industries find difficult to implement. Therefore, in present research, key enablers to initiate SSCM are recognized and analyzed. This research has recognized twelve enablers with the help of previous researches and expert survey. A Structural framework has been drawn with the use of Interpretive Structural Modeling (ISM) technique, to understand the relationship among the identified enablers and also to find the reliance of one on another. Further, MICMAC analysis has been employed for evaluating these identified enablers in accordance with Driving power and Dependence power. From ISM Methodology “Government policies and supportive systems” is found to be a key bottom enabler, which is important to implement the SSCM in Indian industries. For further future perspective, Decision Making Trial and Evaluation Laboratory (DEMATEL), can also be recommended for evaluation purpose. Present research may be helpful to find the importance of different enablers for successful implementation of SSCM in Indian industries.

The life of many people across the world can face various dangers with incurrence of incidents and unpredictable diseases. Incidents often require quick relief as they directly affect human lives. The process of planning, management and monitoring the flow of relief sources to injured and sick individuals is called relief logistics. When best relief services are provided through available sources, relief logistics appear. In this article, a multi-objective model for relief resources distribution facilities under an uncertain condition is investigated in two ways of demand satisfaction by considering the relief resources accessibility and demand satisfaction in a fuzzy logic. In the presented model, the concepts of cost, chance of demand satisfaction, elevation of response capability of system, discount levels for relief commodities, late satisfaction of demand, hub for accumulation of late and returned orders and special route for time significance in distribution of relief commodities are considered. For the first problem, the chance of relief resources accessibility and for the second problem, demands were investigated using fuzzy logic. Considering the conducted analysis, the demand amount is taken more in the second problem than the first one, which has led to an increase in the cost of the second problem. On one hand, the chance of demand satisfaction with no late orders is higher than the second problem. Satisfaction of demand occurs more in the second problem as well. Thus, these problems should be utilized in a way that suits the space of this problem. To solve the problem and to do the sensitivity analysis, we present a NSGA-II algorithm to deal with multi-objectiveness of the problem. A ε-Constraint method is also proposed to evaluate the performance of the proposed algorithm.

The player uses credit financing to perform profitable business. We analyze an economic order quantity model in which items have a fixed lifetime and deteriorate over time. The supplier offers the retailer a full credit period whenever the retailer orders more than or equal to a pre-specified quantity. If the retailer orders less than pre-specified order quantity, then the retailer will do partial payment to the supplier and avail of delay in payments for the remaining outstanding amount. The demand is price-sensitive. The retailer’s profit is maximized by setting appropriate retail price and replenishment time. The algorithm is developed to choose the best policy for the decision maker from the number of alternatives. Numerical data is used to validate the theoretical developments. Managerial insights are discussed. It is observed that for a given units to qualify for avail of partial credit period, increase in ordering cost decreases profit of the retailer. The increase in rate of the purchase cost to avail of delay payment suggests that to have a more profit, retailer should deplete stock before the allowable credit period.

Quantity discount is a usual term in business and has been a topic of interest for a long time, but have received very little attention. Many vendors offer different schemes to their customers to increase the existing size of order, which results in higher annual sale for the vendor and a lower purchasing price for the retailer. Therefore, the buyer adjusts his/her selling price, which influences the demand for the product. The objective of this paper is to develop an inventory model for deteriorating products with quantity discount and partial backlogging to determine the optimal ordering quantity for the retailer optimizing the total cost or profit of the associated model. A numerical example is also given to illustrate the model and its significant features.

There are many researches on project selection field, but few of them have considered environmental criteria in their studies. Moreover, there are many articles in evaluating risk but there is no article that considers value at risk concept to evaluate the amount of risk in multi project selection. We propose a multi objective mathematical model to address a situation in which several projects are candidate to be invested completely or partially. Three objective functions are considered in this paper. The first objective maximizes sum of the net present value of pure cash flow obtained from selected projects. In this objective, we consider the factor of time and its impact on value of money. In addition, we use the concept of value at risk (VAR) as the present value for the first time in project selection problems. Although green projects are more interesting, there are few articles, which address environmental issues. Hence, we consider the objective, which are related to environmental issues as the final criterion. Multi-Objective Differential Evolution algorithm (MODE) algorithm is applied to solve a problem, which is known as robust and efficient algorithm. Then computational results are compared with solutions obtained by NSGA-II algorithm which is well-known algorithm in this field with respect to seven comparison metrics.