Bibhas C. Giri

Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost

This paper deals with an extended EOQ-type inventory model for a perishable product where the demand rate is a function of the on-hand inventory. The traditional parameters of unit item cost and ordering cost are kept constant; but the holding cost is treated as (i) a nonlinear function of the length of time for which the item is held in stock, and (ii) a functional form of the amount of the on-hand inventory. The approximate optimal solution in both the cases are derived. Computational results are presented indicating the effects of nonlinearity in holding costs.

An inventory model for deteriorating items with stock-dependent demand rate

Abstract This paper discusses an inventory model with an inventory-level-dependent demand rate followed by a constant demand rate for items deteriorating at a constant rate θ, where the terminal condition of zero inventory at the end of the scheduling period has been relaxed. Sensitivity of the decision variables to changes in the parameter values is examined and the effects of these changes on the optimal policy are discussed in brief.

TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment

A single-valued neutrosophic set is a special case of neutrosophic set. It has been proposed as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets in order to deal with incomplete information. In this paper, a new approach for multi-attribute group decision-making problems is proposed by extending the technique for order preference by similarity to ideal solution to single-valued neutrosophic environment. Ratings of alternative with respect to each attribute are considered as single-valued neutrosophic set that reflect the decision makers’ opinion based on the provided information. Neutrosophic set characterized by three independent degrees namely truth-membership degree (T), indeterminacy-membership degree (I), and falsity-membership degree (F) is more capable to catch up incomplete information. Single-valued neutrosophic set-based weighted averaging operator is used to aggregate all the individual decision maker’s opinion into one common opinion for rating the importance of criteria and alternatives. Finally, an illustrative example is provided in order to demonstrate its applicability and effectiveness of the proposed approach.

Production lot sizing with process deterioration and machine breakdown

Abstract The paper presents a generalized economic manufacturing quantity model for an unreliable production system in which the production facility may shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time (when it starts producing defective items) and may ultimately break down afterwards. If a machine breakdown occurs during a production run, then corrective repair is done; otherwise, preventive repair is performed at the end of the production run to enhance the system reliability. The proposed model is formulated assuming that the time to machine breakdown, corrective and preventive repair times follow arbitrary probability distributions. However, the criteria for the existence and uniqueness of the optimal production time are derived under general breakdown and uniform repair time (corrective and preventive) distributions. The optimal production run time is determined numerically and the joint effect of process deterioration, machine breakdowns and repairs (corrective and preventive) on the optimal decisions is investigated for a numerical example.

A note on a lot sizing heuristic for deteriorating items with time-varying demands and shortages

Abstract In the present article, an existing heuristic procedure is applied to an inventory of deteriorating items with (i) linearly and (ii) exponentially time-varying demands and shortages over a fixed planning horizon. In a similar problem, Hariga and Al-Alyan [Hariga M, Al-Alyan A. A lot sizing heuristic for deteriorating items with shortages in growing and declining markets. Computers & Operations Research 1997;24:1075–83] allowed shortages in all cycles except in the last one (policy-B). Here shortages are considered in each cycle and are completely backlogged (policy-A). The successive scheduling periods over an infinite time horizon are adjusted for a finite planning horizon following different adjustment policies (APs) that are proposed in an algorithmic form. Numerical examples are taken from Hariga and Al-Alyan [20] to show that the replenishment policy-A results in a lower average system cost than that of policy-B in both types of demand patterns. It is also found that the approximate results under the policy-A are closely associated with those of the optimal ones. Scope and purpose The purpose of the article is to implement an existing heuristic procedure to an inventory system of deteriorating items allowing shortages in all cycles over a finite planning horizon under linearly and exponentially time-varying demand patterns. Allowing shortages in all cycles is a significant departure from the traditional practice of allowing shortages in all cycles except the last one. With this departure, we reconsider the problem of Hariga and Al-Alyan [20] published recently in the Journal of Computers & Operations Research and find a reduction in the system cost upto 15%. The scope of applications of the heuristic is widely open for newly developed high technology products (e.g., microcomputer chips, sophisticated instruments, etc.) which have growing market demands or in the case of technologically obsolete products (e.g., spare parts of obsolete machines, etc.) having a gradually declining market demands.

Heuristic models for deteriorating items with shortages and time-varying demand and costs

Abstract In this article, we develop and analyse two heuristic models for the inventory replenishment problem in which the demand rate, deterioration rate, ordering cost, holding cost and shortage cost are all assumed to vary with time. Shortages in inventory are allowed and are completely backlogged. Our objective is to determine the optimal replenishment policy of the inventory system whether or not a finite planning horizon exists. Both the heuristic models are illustrated with the help of a numerical example. Finally, the sensitivity analysis is also presented for the heuristic rule that outperforms the other one.

Hybrid vector similarity measures and their applications to multi-attribute decision making under neutrosophic environment

In this paper, we propose new vector similarity measures of single-valued and interval neutrosophic sets by hybridizing the concepts of Dice and cosine similarity measures. We present their applications in multi-attribute decision making under neutrosophic environment. We use these similarity measures to find out the best alternative by determining the similarity measure values between the ideal alternative and each alternative. The results of the proposed similarity measures have been validated by comparing with other existing similarity measures reported in the literature for multi-attribute decision making. The main thrust of the proposed similarity measures will be in the field of practical decision making, medical diagnosis, pattern recognition, data mining, clustering analysis, etc.

Supply chain model with price- and trade credit-sensitive demand under two-level permissible delay in payments

This article develops a single-manufacturer and single-retailer supply chain model under two-level permissible delay in payments when the manufacturer follows a lot-for-lot policy in response to the retailers demand. The manufacturer offers a trade credit period to the retailer with the contract that the retailer must share a fraction of the profit earned during the trade credit period. On the other hand, the retailer provides his customer a partial trade credit which is less than that of the manufacturer. The demand at the retailer is assumed to be dependent on the selling price and the trade credit period offered to the customers. The average net profit of the supply chain is derived and an algorithm for finding the optimal solution is developed. Numerical examples are given to demonstrate the coordination policy of the supply chain and examine the sensitivity of key model-parameters.

Note on effects of joint replenishment and channel coordination for managing multiple deteriorating products in a supply chain

Table 1 Optimal results for low and high levels of deterioration rate and unit cost of the retailer Policy Optimal decisions Low deterioration rate High deterioration rate Low unit cost High unit cost I T 1

Fuzzy Economic Order Quantity model for perishable items with stochastic demand, partial backlogging and fuzzy deterioration rate

Most of the perishable inventory models in the literature assume that the rate of deterioration is a known constant. But in many practical situations, deterioration rate cannot be prescribed in advance; it may vary in a certain interval and hence can preferably be considered as a fuzzy number. The purpose of the paper is to develop and investigate an Economic Order Quantity (EOQ) model in the fuzzy sense by considering stochastic demand, partial backlogging and fuzzy deterioration rate. The proposed model is also extended to the case where the partial backlogging factor is assumed to be a fuzzy number. The minimum total cost and optimal order quantity are derived by defuzzifying the total cost through the signed distance method. Numerical examples are taken to demonstrate the developed models and compare the optimal results with those of the crisp models.