A study of an EOQ model with public-screened discounted items under cloudy fuzzy demand rate

This article deals with an economic order quantity inventory model of imperfect items under non-random uncertain demand. Here we consider the customers screen the imperfect items during the selling period. After a certain period of time, the imperfect items are sold at a discounted price. We split the model into three cases, assuming that the demand rate increases, decreases, and is constant in the discount period. Firstly, we solve the crisp model, and then the model is converted into a fuzzy environment. Here we consider the dense fuzzy, parabolic fuzzy, degree of fuzziness and cloudy fuzzy for a comparative study. The basic novelty of this paper is that a computer-based algorithm and flow chart have been given for the solution of the proposed model. Finally, sensitivity analysis and graphical illustration have been given to check the validity of the model.

An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price

Traditionally, the inventory models available in the literature assume that all articles in the purchased lot are perfect and the demand is constant. However, there are many causes that provoke the presence of defective goods and the demand is dependent on some factors. In this direction, this paper develops an economic order quantity (EOQ) inventory model for imperfect and perfect quality items, taking into account that the imperfect ones are sent as a single lot to a repair shop for reworking. After reparation, the items return to the inventory system and are inspected again. Depending on the moment at which the reworked lot arrives to the inventory system, two scenarios can occur: Case 1: The reworked lot enters when there still exists inventory; and Case 2: The reworked lot comes into when the inventory level is zero. Furthermore, it is considered that the holding costs of perfect and imperfect items are distinct. The demand of the products is nonlinear and dependent on price, which follows a polynomial function. The main goal is to optimize jointly the lot size and the selling price such that the expected total profit per unit of time is maximized. Some theoretic results are derived and algorithms are developed for determining the optimal solution for each modeled case. It is worth mentioning that the proposed inventory model is a general model due to the fact that this contains some published inventory models as particular cases. With the aim to illustrate the use of the proposed inventory model, some numerical examples are solved.

A consignment stock policy for a two-level supply chain with imperfect quality items

A consignment stock is a type of supply-chain coordination for the management of supply-chains in which there is a joint vendor and buyer policy that is mainly focused on having the vendor manage the buyer's inventory. This thesis aims to investigate the consignment stock strategy in a single-vendor single-buyer supply-chain context considering imperfect items that may be produced from an imperfect production process. It develops a flexible mathematical model that allows for managerial decisions with regards to imperfect items and seeks to minimize costs (maximize profits) of the supply-chain. Such managerial decisions include scrapping items at a cost, selling them for a marginal profit to a secondary market, applying re-work, and/or applying minor setups to restore the production process. Results show that the introduction of imperfect items increases the batch size and reduces the number of shipments. Minor setups were shown to reduce cost, increase the number of shipments and reduce its size.

A consignment stock policy for a two-level supply chain with imperfect quality items

A consignment stock is a type of supply-chain coordination for the management of supply-chains in which there is a joint vendor and buyer policy that is mainly focused on having the vendor manage the buyer's inventory. This thesis aims to investigate the consignment stock strategy in a single-vendor single-buyer supply-chain context considering imperfect items that may be produced from an imperfect production process. It develops a flexible mathematical model that allows for managerial decisions with regards to imperfect items and seeks to minimize costs (maximize profits) of the supply-chain. Such managerial decisions include scrapping items at a cost, selling them for a marginal profit to a secondary market, applying re-work, and/or applying minor setups to restore the production process. Results show that the introduction of imperfect items increases the batch size and reduces the number of shipments. Minor setups were shown to reduce cost, increase the number of shipments and reduce its size.

Single-manufacturer and multi-retailer supply chain model with pre-payment based partial free transportation

In this paper, a supply chain model between a manufacturing firm and a group of retailers has been developed. Manufacturing firm produces simultaneously both perfect and imperfect items which are separated by screening process. Then the perfect items are transferred to the retailers' showroom/warehouse located in different places and a part of imperfect items are repaired by rework process. Retailers receive the products from the manufacturer with paying partial pre-payment to ensure the replenishment of order. On the other hand, the manufacturer provides partial free transportation facility to the retailers due to pre-payment. The corresponding problem has been formulated mathematically as a profit maximization problem and then solved it analytically. As an illustration of this supply chain model, three numerical examples have been considered and solved. Finally, post optimality analyses have been carried out to investigate the effects of changes of different parameters on the optimal policy.

A profit jump inventory model for imperfect quality items with receiving reparative batch and order overlapping in dense fuzzy environment

This paper presents an economic order quantity (EOQ) inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a dense fuzzy environment Here, the imperfect items are identified by screening and are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterwards, the items are returned to the supplier to be reworked. Also, discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error free. An order overlapping scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. However, we assume the total monthly demand quantity as the dense fuzzy number because of learning effect. Moreover, first of all a profit maximization deterministic model is developed and solve by classical method. Fuzzifying the final optimized function via dense fuzzy demand quantity we have employed extended ranking index rule for its defuzzification. During the process of defuzzification we make an extensive study on the paradoxical unit square of the left and right deviations of dense fuzzy numbers. A comparative study is made after splitting the model into general fuzzy and dense fuzzy environment. Finally numerical and graphical illustrations and sensitivity analysis have been made for its global justifications.

An inventory model for deteriorating items with imperfect quality under advance payment policy

In the business world, it is generally observed that the supplier gives cash discount due to advance payment. The buyer may either pay off the total purchase cost or a fraction of the total purchase cost before receiving the products. If the buyer makes full payment then he receives a cash discount instantly. If the buyer pays a fraction of the total purchase cost, then (s)he receives the cash discount while paying the remaining amount at the time of receiving the lot. Moreover, in most of the inventory models, it is generally assumed that the delivered lot contains only perfect items. But in reality, presence of imperfect items in the received lot cannot be overlooked as it will affect total profit of the system. Thus, the study of inventory models considering the presence of imperfect items in the lot makes the model more realistic and, it has received much attention from inventory managers. This paper develops a model that jointly considers imperfect quality items and the concept of advance payment scheme (full and partial). The objective is to determine optimal ordering quantity in order to maximise the total profit of the system. The necessary theoretical results showing the existence of global maximum is derived. The model is illustrated with the help of numerical examples, and sensitivity analysis is carried out on some important system parameters to see the effects on the total profit of the system. The study shows that full advance payment scheme is beneficial for the buyer.