An Inventory Model for Perishable Products with Stock-Dependent Demand and Trade Credit under Inflation

We consider an inventory model for perishable products with stock-dependent demand under inflation. It is assumed that the supplier offers a credit period to the retailer, and the length of credit period is dependent on the order quantity. The retailer does not need to pay the purchasing cost until the end of credit period. If the revenue earned by the end of credit period is enough to pay the purchasing cost or there is budget, the balance is settled and the supplier does not charge any interest. Otherwise, the supplier charges interest for unpaid balance after credit period, and the interest and the remaining payments are made at the end of the replenishment cycle. The objective is to minimize the retailer’s (net) present value of cost. We show that there is an optimal cycle length to minimize the present value of cost; furthermore, a solution procedure is given to find the optimal solution. Numerical experiments are provided to illustrate the proposed model

Production lot size models for perishable seasonal products

Seasonal items like fruits, fish, winter cosmetics, fashion apparel, etc. generally exhibits different demand patterns at various times during the season. Production and inventory planning must reflect this property for cost effectiveness and optimization of resources. This paper presents two production-inventory models for perishable seasonal products that minimize total inventory costs. The models obtains optimal production run time and optimal production quantity for cases when the production rate is constant and when it is allowed to vary with demand. The products are assumed to deteriorate at an exponential rate and demand for them follows a three-phase ramp type pattern during the season. Numerical examples and sensitivity analysis are carried out. Production run time and production quantity obtained by the model were found to be independent of cost parameters. The variable production rate strategy was also found to give lower inventory costs and production quantity than the constant production rate strategy

Three-Echelon Inventory Model with Permissible Delay in Payments under Controllable Lead Time and Backorder Consideration

This paper proposes a three-echelon inventory model with permissible delay in payments under controllable lead time and backorder consideration to find out the suitable inventory policy to enhance profit of the supply chain. In today’s highly competitive market, the supply chain management has become a critical issue in both practice and academic and supply chain members have to cooperate with each other to bring more benefits. In addition, the inventory policy is a key factor to influence the performance of the supply chain. Therefore, in this paper, we develop a three-echelon inventory model with permissible delay in payments under controllable lead time and backorder consideration. Furthermore, the purpose of this paper is to maximize the joint expect total profit on inventory model and attempt to discuss the inventory policy under different conditions. Finally, with a numerical example provided here to illustrate the solution procedure, we may discover that decision-makers can control lead time and payment time to enhance the performance of the supply chain

An EOQ Model for a Deteriorating Item with Time Dependent Quadratic Demand and Variable Deterioration under Permissible Delay in Payment

Abstract In a recent paper, Khanra, Ghosh and Chaudhuri's (2011) presented an EOQ model for a deteriorating item with time dependent quadratic demand under permissible delay in payment. Deterioration considered in most of the EOQ models is constant, while in most of the practical cases the deterioration rate increases with time. This work is motivated by Khanra, Ghosh and Chaudhuri's (2011) paper extending their model to allow for a variable rate of deterioration when delay in payment is permissible. The time varying demand rate is taken to be a quadratic function of time. For settling the account, the model is developed under two circumstances: case-1: The credit period is less than or equal to the cycle time and case-2: the credit period is greater than the cycle time. A numerical example is provided to illustrate the model. Sensitivity analysis has also been conducted to study the effect of the parameters

A Multi-objective Mathematical Model for Sustainable Supplier Selection and Order Lot-sizing under Inflation

Recently, scholars and practitioners have shown an increased interest in the field of sustainable supplier selection and order lot-sizing. While several studies have recently been carried out on this field, far too little attention has been given to formulating a multi-objective model for the integrated problem of multi-period multi-product order lot-sizing and sustainable supplier selection under inflationary conditions. In this study, a mathematical model for multi-period multi-product lot-sizing and sustainable supplier selection under the effects of inflation is developed. The proposed model includes four objective functions which minimize total cost and maximize total social, total environmental, and total economic qualitative scores. The model attempts to simultaneously balance different costs under inflationary conditions to optimize the total cost of purchasing and other objective functions. The applicability of the proposed model is shown by an illustrative example. The results show that the proposed model can provide an effective purchasing plan for the company while monitoring the effect of inflation and assuaging its concerns regarding sustainability issues

Supply chain contracting coordination for fresh products with fresh-keeping effort

Purpose – Fresh product loss rates in supply chain operations are particularly high due to the nature of perishable products. This paper aims to maximize profit through the contract between retailer and supplier. The optimized prices for the retailer and the supplier, taking the fresh-keeping effort into consideration, are derived. Design/methodology/approach – To address this issue, we consider a two-echelon supply chain consisting of a retailer and a supplier (i.e., wholesaler) for two scenarios: centralized and decentralized decision-making. We start from investigating the optimal decision in the centralized supply chain and then comparing the results with those of the decentralized decision. Meanwhile, a fresh-keeping cost-sharing contract and a fresh-keeping cost- and revenue-sharing contract are designed. Numerical examples are provided, and managerial insights are discussed at end. Findings – The results show that (a) the centralized decision is more profitable than the decentralized decision; (b) a fresh product supply chain can only be coordinated through a fresh-keeping cost- and revenue-sharing contract; (c) the optimal retail price, wholesale price and fresh-keeping effort can all be achieved; (d) the profit of a fresh product supply chain is positively related to consumers’ sensitivity to freshness and negatively correlated with their sensitivity to price. Originality/value – Few studies have considered fresh-keeping effort as a decision variable in the modelling of supply chain. In this paper, a mathematical model for the fresh-keeping effort and for price decisions in a supply chain is developed. In particular, fresh-keeping cost sharing contract and revenue-sharing contract are examined simultaneously in the study of the supply chain coordination problem

Population Based Metaheuristic Algorithm Approach for Analysis of Multi-Item Multi-Period Procurement Lot Sizing Problem

This research study focuses on the optimization of multi-item multi-period procurement lot sizing problem for inventory management. Mathematical model is developed which considers different practical constraints like storage space and budget. The aim is to find optimum order quantities of the product so that total cost of inventory is minimized. The NP-hard mathematical model is solved by adopting a novel ant colony optimization approach. Due to lack of benchmark method specified in the literature to assess the performance of the above approach, another metaheuristic based program of genetic algorithm is also employed to solve the problem. The parameters of genetic algorithm model are calibrated using Taguchi method of experiments. The performance of both algorithms is compared using ANOVA analysis with the real time data collected from a valve manufacturing company. It is verified that two methods have not shown any significant difference as far as objective function value is considered. But genetic algorithm is far better than the ACO method when compared on the basis of CPU execution time

Optimal Inventory Policy under Permissible Payment Delay in Fashion Supply Chains

This paper investigates a retailer’s optimal inventory cycle and the corresponding time of payment in fashion supply chains where a supplier allows the payment delay. Here according to the established model we first analyze the retailer's reaction, and then find out the retailer’s optimal inventory policy and time of payment to maximize its total profit. Our result shows that it is not always the best choice for retailers of fashion supply chains to choose the discount way to replenish stocks, but the retailer can decide the optimal credit period and inventory cycle. Moreover, numerical examples are provided to illustrate the model’s feasibility and rationality

An integrated model for sustainable supplier selection and multi-period multi-product lot-sizing for packaging film industry in Iran

The emergence of sustainability issues has created increasing interest among those involved in the field of sustainable supply chain management. Companies are motivated to modify their supply chains activities based on sustainability issues to enhance their overall level of sustainability in order to fulfil demanding environmental and social legislation and to deal with increasing market forces from different stakeholder groups. Within supply chain activities, selecting appropriate suppliers based on the criteria of sustainability, e.g., economic, environmental, and societal might help companies move towards sustainable development. Although several studies have been accomplished to incorporate sustainability criteria into supplier selection problem, little attention has been paid to developing a comprehensive mathematical model that allocates the exact quantities of orders to suppliers considering lot-sizing problems. Moreover, the effect of inflation as an important issue for companies in the developing countries has been neglected in studies that examined multi-period multi-product lot-sizing along with supplier selection. In this study, a multi-objective mathematical model for sustainable supplier selection integrated with multi-period multi-product lot-sizing problem under the effects of inflation was developed. The model consists of four objective functions which are minimizing total cost, maximizing total social, total environmental score, and total economic qualitative scores. The mathematical model was developed based on the parameters discovered by preprocessing the social, environmental, and economic data of suppliers using a rule-based-weighted fuzzy approach and fuzzy analytical hierarchy process. The model attempted to simultaneously balance different costs under inflationary conditions to optimize the total cost of purchasing and other objective functions. A comprehensive framework was developed as a road map for procurement organizations in order to facilitate the allocation of optimal order quantities to suppliers in a sustainable supply chain. The proficiency and applicability of a proposed approach was illustrated using a case study of packaging films from the food industry. For each main criterion of sustainability, their related subcriteria and influencing factors were extracted from literature and the most related ones were selected by company’s experts. In this research, green competencies, environmental management system, pollution, occupational safety and health, training and education, contractual stakeholder, economic qualitative, and cost were selected by company’s experts as the main subcriteria of sustainable supplier selection. The consideration of sustainability criteria in the proposed multi-objective model revealed that a higher value of sustainable purchasing can be achieved in comparison with a single objective costbased model. In addition, the results show that the proposed model can provide a purchasing plan for the company while monitoring the effect of inflation and assuaging its concerns regarding sustainability issues

An enhanced approximation mathematical model inventorying items in a multi-echelon system under a continuous review policy with probabilistic demand and lead-time

An inventory system attempts to balance between overstock and understock to reduce the total cost and achieve customer demand in a timely manner. The inventory system is like a hidden entity in a supply chain, where a large complete network synchronizes a series of interrelated processes for a manufacturer, in order to transform raw materials into final products and distribute them to customers. The optimality of inventory and allocation policies in a supply chain for a cement industry is still unknown for many types of multi-echelon inventory systems. In multi-echelon networks, complexity exists when the inventory issues appear in multiple tiers and whose performances are significantly affected by the demand and lead-time. Hence, the objective of this research is to develop an enhanced approximation mathematical model in a multi-echelon inventory system under a continuous review policy subject to probabilistic demand and lead-time. The probability distribution function of demand during lead-time is established by developing a new Simulation Model of Demand During Lead-Time (SMDDL) using simulation procedures. The model is able to forecast future demand and demand during lead-time. The obtained demand during lead-time is used to develop a Serial Multi-echelon Inventory (SMEI) model by deriving the inventory cost function to compute performance measures of the cement inventory system. Based on the performance measures, a modified distribution multi-echelon inventory (DMEI) model with the First Come First Serve (FCFS) rule (DMEI-FCFS) is derived to determine the best expected waiting time and expected number of retailers in the system based on a mean arrival rate and a mean service rate. This research established five new distribution functions for the demand during lead-time. The distribution functions improve the performance measures, which contribute in reducing the expected waiting time in the system. Overall, the approximation model provides accurate time span to overcome shortage of cement inventory, which in turn fulfil customer satisfaction