Brojeswar Pal

Three-layer supply chain – A production-inventory model for reworkable items

Abstract This article develops an integrated production-inventory model considering perfect and imperfect quality items, product reliability and reworking of defective items in the environment of supply chain management. Manufacturer, supplier and retailer are the members of the supply chain where supplier delivers raw materials to the manufacturer and sends back the defective raw materials after completion of inspection at a single lot with less market price. In this system, production starts to produce good items at the beginning of the production. The production system may undergo an “out-of-control” state from an “in-control” state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more capital. The defective items produced in “out-of-control” state are reworked at a cost just after the regular production time. This model considers the impact of business strategies such as optimal order size of raw materials, production rate and unit production cost, and idle times in different sectors in a collaborating marketing system. An analytical method is employed to optimize the production rate and raw material order size for maximum expected average profit. A numerical example along with four graphical illustrations is considered and its sensitivity analysis is provided to test feasibility of the model.

Maximising profits for an EPQ model with unreliable machine and rework of random defective items

This article deals with an economic production quantity (EPQ) model in an imperfect production system. The production system may undergo in ‘out-of-control’ state from ‘in-control’ state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more costs. The defective items produced in ‘out-of-control’ state are reworked at a cost just after the regular production time. Occurrence of the ‘out-of-control’ state during or after regular production-run time is analysed and also graphically illustrated separately. Finally, an expected profit function regarding the inventory cost, unit production cost and selling price is maximised analytically. Sensitivity analysis of the model with respect to key parameters of the system is carried out. Two numerical examples are considered to test the model and one of them is illustrated graphically.

A distribution-free newsvendor problem with nonlinear holding cost

In this paper, we analyse a single-period newsvendor model to determine the optimal order quantity where the customers’ balking occurs.This scenario occurs when the customers are opposed to buy a product for various reasons, such as decreasing quality of product, product is not as good as fresh when it reaches under a threshold level, etc. The model is investigated by assuming that the holding cost function depends on order quantity and the inventory level at which customer balking occurs depends on holding cost. The model allows partial backlogging and permits part of the backlogged shortages to turn into lost sales. We develop the model without taking any specific distributional form of demand, only assuming the mean and the variance of the distribution of demand. Finally, we illustrate the model by numerical examples and compare our distribution-free model with the specific distributional form of demand.

Three stage trade credit policy in a three-layer supply chain–a production-inventory model

The main purpose of this paper is to investigate the optimal replenishment lot size of supplier and optimal production rate of manufacturer under three levels of trade credit policy for supplier–manufacturer–retailer supply chain. The supplier provides a fixed credit period to settle the accounts to the manufacturer, while the manufacturer gives a fixed credit period to settle the account to the retailer and the retailer, in turn, also offers a credit period to each of its customers to settle the accounts. We assume that the supplier supplies the raw material to the manufacturer and sends back the defective raw materials to the outside supplier after completion of inspection at one lot with a sales price. The system always produces good items in the model. Also, we consider the idle times of supplier and manufacturer. Finally, numerical examples are provided to illustrate the behaviour and application of the model with graphical simulation.

Two‐echelon manufacturer–retailer supply chain strategies with price, quality, and promotional effort sensitive demand

This study deals with the two-layer supply chain model of one manufacturer and one retailer for a single commodity where market demand is assumed to be dependent on selling price, quality of the products, and promotional effort of the retailer. We investigate the behavior of the supply chain under centralized, manufacturer Stackelberg, conditional manufacturer Stackelberg, retailer Stackelberg, conditional retailer Stackelberg, and vertical Nash model structure. The nature of the above models provides great insights to a firms manager for achieving optimal strategy in a competitive marketing system. Quite often, not all items produced in a firm are of perfect quality; some are perfect (conforming) quality and others are imperfect (nonconforming) quality. The nonconforming products are sold in a secondary shop or by other retailers. The procurement cost of finished products depends on the quality of the products due to more investment in advanced technology, better raw materials, and skilled labor, etc. The warranty policy for the products is also imposed to attract the customers to buy more. Here, both members (manufacturer and retailer) jointly share the cost of the warranty policy. The objective of this paper is to determine the optimal selling price and promotional effort of the retailer, while the optimal wholesale price and quality of the products are determined by the manufacturer so that the above strategies are maximized. Finally, numerical examples with sensitivity analysis of the key parameters are illustrated to investigate the proposed model.

Coordination contracts for competitive two-echelon supply chain with price and promotional effort sensitive non-linear demand

In this study, our objective is to analyse the effects of a competitive supply chain with single commodity, multiple retailers and a common supplier when there is a rivalry among the retailers. The market demand of the product is assumed to be price dependent and to be enhanced by providing effective promotional effort. We also assume that the suppliers wholesale price is the same for all retailers. The retailers determine their market sales price(s) and promotional efforts to optimise the profit from the perspectives of the individual and the whole supply chain. We also analyse the coordination mechanisms among the members of the chain with several contracts and find the optimal range for the contract parameters. Finally, we investigate the model by the collective numerical data and also provide the graphical illustration of the comparison among the coordination mechanisms by the contracts.

Two-echelon competitive integrated supply chain model with price and credit period dependent demand

This study considers a two-echelon competitive supply chain consisting of two rivaling retailers and one common supplier with trade credit policy. The retailers hope that they can enhance their market demand by offering a credit period to the customers and the supplier also offers a credit period to the retailers. We assume that the market demand of the products of one retailer depends not only on their own market price and offering a credit period to the customers, but also on the market price and offering a credit period of the other retailer. The supplier supplies the product with a common wholesale price and offers the same credit period to the retailers. We study the model under a centralised (integrated) case and a decentralised (Vertical Nash) case and compare them numerically. Finally, we investigate the model by the collected numerical data.

Supply chain coordination with random yield and demand uncertainty

Abstract Uncertainty is a major challenging factor in the marketing strategies of the players in a supply chain. In this study, the random yield for both the supplier and manufacturer is investigated to find the optimal decisions in the environment of demand uncertainty. To meet the effect of random yield in the supplier’s production, the manufacturer places a flexible ordering policy in a range with conditions imposed thereupon. It is also assumed that the manufacturer faces both the under-stocking and over-stocking risk. In the over-stock situation, the model is developed with the chance factor of holding and selling with salvage value for the extra products. The behavior of the model under a centralized, vertical Nash approach is analysed. A manufacturer-Stackelberg and revenue sharing contract with penalty and sharing are also discussed. The sensitivity of the key parameters is examined to test the feasibility of the model. Finally, a numerical example with graphical illustrations is provided to investigate the proposed model.