Integrated Vendor Buyer Inventory Model Research Articles

The effect of human errors on an integrated stochastic supply chain model with setup cost reduction and backorder price discount

This study develops an integrated vendor–buyer inventory model for a supply chain where quality issues and human error affect its coordination. Each lot shipped to the buyer contains defective items, with a rate which randomly changes from a lot to the other. The buyer inspects every shipped lot to segregate defective items. However, the inspection process at the buyer’s end goes wrong in the classification of defective and non-defective items. On the other hand, the buyer may run out of inventory, but in order to avoid lost sales, he/she offers a price discount on the backlogged items to his/her customers. Due to the vendor-buyer relationship, the buyer invests in reducing the setup cost of the vendor. Supply chain’s lead-time is considered variable, and two models are developed based on the probability distribution of the lead-time demand. In the first model, it is assumed that lead-time demand follows a normal distribution, while in the latter one, it does not follow any certain distribution. Two models are developed to determine the joint optimal decision variables that minimize the total cost of the supply chain. Two iterative algorithms are developed to obtain the optimal solution for both models. A set of numerical analysis and sensitivity analysis are conducted to gain insights.

An integrated vendor–buyer inventory model with transportation cost and stochastic demand

ABSTRACTThis study investigates a single-vendor–buyer model with stochastic demand and transportation cost. The transportation cost is a function of shipping weight, distance and transportation modes, namely truckload (TL) and less-than-truckload (LTL) shipments. A heuristic model is developed to minimise the integrated total relevant cost (JTRC) when the mode of transportation is limited to TL and LTL shipments. The decision variables of this study are the buyer's order quantity, the vendor's production quantity per cycle (which is m time the buyer's order quantity), and the safety stock. Numerical examples are given to illustrate the benefits of the model.

Fuzzy random integrated vendor-buyer inventory model with imperfect-quality items and controllable lead time

In this research, an integrated vendor-buyer inventory model with a random number of defective items under fuzzy random lead time demand is developed. The length of lead time affects the competitive abilities of a business directly and it can be controlled by adding a crashing cost. It is assumed that the lead time demand is normally distributed and the shortages are permitted, which are partially backlogged. In the model, lead time demand, annual demand rate, adjustable production rate, and backorder fraction are imprecise in nature and are represented by the triangular fuzzy numbers. Signed distance method is used to defuzzify the fuzzy total inventory cost. The objective is to determine simultaneously the optimal order quantity, the lead time, and the number of deliveries, which minimise the expected total average cost. An algorithm procedure of finding the optimal solution is developed. Furthermore, numerical example and sensitivity analysis are carried out to illustrate the proposed integrated model.

Minimax distribution-free procedure for integrated inventory model with backorder price discount and controllable lead time

The integrated vendor–buyer inventory model has been an object of study for a long time, but little is done about the effect of reducing lead time on the integrated inventory models with backorder price discount and defective items. The aim is to minimise the total related cost in the continuous review model by considering the order quantity, reorder point, lead-time and backorder price discount as decision variables. Moreover, we assume that the lead-time demand distribution is unknown but the mean and variance of lead-time demand are known. We apply the minimax distribution-free procedure to find the optimal solution. In the integrated system we discussed here, it assumes that, when the buyer places an order, the vendor produces m-times the order quantity in each production cycle, to reduce the set-up cost. In addition, the buyer offers a backorder price discount to the customers to motivate them for backorders. The arrival lot may contain some defective items, so its treatment is also incorporated in this paper. We develop an effective iterative procedure for finding the optimal policy and give a numerical example to illustrate the solution procedure.

An integrated vendor–buyer inventory model with imperfect items and planned back orders

In this paper, we develop a mathematical model to determine an integrated vendor–buyer inventory policy, where the vendor’s production process is imperfect and produces a certain number of defective items with a known probability density function. The vendor prepares for the repeating flow of orders of size \( {Q_{\mathrm{P}}}=nQ \) from the buyer by producing items in batches of size QP and planning to have each batch delivered to the buyers in n deliveries, each with a lot of Q units. Once the buyer receives the items, a 100 % screening process is conducted. We assume the screening process and demand take place simultaneously. We also assume that shortages are allowed and are completely back ordered. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The expected annual integrated total cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer. The results also show that even though there is a cost associated with each back order, it is profitable for the company to have planned back orders if customers are willing to wait for the next delivery when a shortage occurs.

Integrated vendor–buyer cooperative inventory model with controllable lead time, ordering cost reduction, and service-level constraint

In this study, an integrated vendor–buyer inventory model is proposed. The vendor produces a product in a batch environment and delivers it to a buyer facing normally distributed demand. In the current study, several assumptions are used that the combination of these assumptions has not been studied in previous papers. Here is the list of these assumptions: service-level constraint instead of shortage cost is used; ordering cost reduction is allowed, and decreasing lead time by a cost dependent on two factors including shortened lead time and ordering quantity is considered. An algorithm is developed to obtain the optimal solution of the proposed model. A numerical example is included to illustrate the results of the model. Also, the effects of assumptions used in this paper are evaluated and discussed.

An integrated vendor–buyer inventory model with order-processing cost reduction and permissible delay in payments

Trade credit plays an important role in financing for many businesses and industries. For the buyers, purchased inventory can be considered to be financed in whole or in part with permissible delay in payments during the purchasing process. On the other hand, both the vendor and buyer take part in order-processing cost reduction by applying information technologies, such as EDI (electronic data interchange). The order-processing cost can also be reduced by adding certain capital investments, and this will affect the lot size decisions. This article develops an integrated inventory model to determine the optimal inventory policy under conditions of order-processing cost reduction and permissible delay in payments, and shows that the total annual variable cost function possesses some kinds of convexities. A solution procedure is provided to determine the optimal order policy. Finally, a numerical example is presented to illustrate the solution procedure.

An integrated vendor–buyer inventory model with backorder price discount and effective investment to reduce ordering cost

The single-vendor single-buyer integrated production inventory system has been an object of study for a long time, but little is known about the effect of investing in reducing ordering cost on the integrated inventory models with backorder price discount and variable lead time. The purpose of this article is to investigate in the continuous review model with backorder price discount and variable lead time to effectively increase investment and to reduce the joint expected annual total cost. The integrated strategy discussed here is one in which the buyer orders a quantity, then the vendor produces n times order quantity in each production cycle, in order to reduce setup cost. In addition, the buyer offers backorder price discounts to the customers that may motivate the customers’ desire for backorders, and buyer ordering cost can be reduced through effective investment. An integrated inventory model is established to find the optimal solutions of order quantity, ordering cost, backorder price discount, lead time, and the number of shipments from the vendor to the buyer in one production run, so that the joint expected annual total cost incurred has the minimum value. Furthermore, numerical examples are used to demonstrate the benefits of the model.

An integrated vendor–buyer inventory model with quality improvement and lead time reduction

The success of the Japanese in the employment of just-in-time (JIT) production has received a great deal of attention in the past two decades. The underlying goal of JIT is to eliminate wastes, which can be achieved through various efforts such as shortening lead time and improving quality. Recently, Yang and Pan [2004. Just-in-time purchasing: an integrated inventory model involving deterministic variable lead time and quality improvement investment. International Journal of Production Research 42(5), 853–863] have studied the effects of lead time reduction and quality improvement investment on an integrated inventory model. The objective of this study is to extend Yang and Pan's (2004) model by allowing for shortages and using the reorder point as a decision variable. That is, this article develops an integrated inventory model which jointly determines the optimal order quantity, reorder point, process quality, lead time and the frequency of deliveries simultaneously. Analytical results that characterize the exact, optimal policy for the problem described above are devised to develop efficient and optimal computational procedures. Furthermore, a numerical example is given to illustrate the results.

An integrated vendor–buyer inventory model with perfect and monopolistic competitions: an educational note

AbstractCustomers encountering shortages will respond differently according to the type of commodity and the market environment. Complete backordering is only likely to occur in a monopolistic competition, whereas a complete lost sale is only likely to occur in a perfect competition. In reality, neither market environment exists. Therefore, in an environment with perfect and monopolistic markets, the consideration of partial backordering is a practical approach. In this study, we develop an integrated vendor–buyer inventory model with perfect and monopolistic competitions. Significant cost reduction can be achieved when partial backordering is considered. The inventory model can therefore be used to study the effect of partial backordering in a competitive market.