Sole versus dual sourcing under order dependent lead times and prices

In this paper, we consider a dual-sourcing model with constant demand and stochastic lead times. Two suppliers may be different in terms of purchasing prices and lead-time parameters. The ordering takes place when the inventory level depletes to a reorder level, and the order is split among two suppliers. Unlike previous works in the order splitting literature, the supply lead time between vendor and buyer as well as unit purchasing prices is considered to be order quantity dependent. The proposed model finds out the optimal reorder point, order quantity and splitting proportion, using a solution procedure. Numerical results show that neglecting the relationship between ordering batch size and lead times is a shortcoming that hides one of order splitting advantages. Moreover, connecting unit prices to order quantity can decrease the percentage saving from dual sourcing compared to sole sourcing. Furthermore, sensitivity analysis shows some managerial insights.     

A mathematical model for order splitting in a multiple supplier single-item inventory system

In this paper we develop a mathematical model which considers multiple-supplier single-item inventory systems. The lead times of the suppliers and demand arrival rate are random variables. All shortages are backordered. Continuous review (s, Q) policy has been assumed. When the inventory level hits the reorder level, the total order is split among n suppliers. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost and shortage cost is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared to the relevant models in the literature. In addition, some managerial insights are observed.     

Optimal ordering decision for deteriorating items with expiration date and uncertain lead time

The ordering policy for the retailers and the suppliers is a function of deterioration, product expiration date, the supplier’s uncertain lead time, available capital constraint and the retailer’s seasonal pattern demand. We develop a deteriorating inventory replenishment model of the system and present an algorithm to derive the retailer’s optimal replenishment cycle, shortage period, order quantity and the supplier’s managing cost. Numerical example and sensitivity analysis are given to illustrate the model.     

Integrated vendor--buyer inventory system with sublot sampling inspection policy and controllable lead time

This article investigates the impact of inspection policy and lead time reduction on an integrated vendor--buyer inventory system. We assume that an arriving order contains some defective items. The buyer adopts a sublot sampled inspection policy to inspect selected items. The number of defective items in the sublot sampling is a random variable. The buyer's lead time is assumed reducible by adding crash cost. Two integrated inventory models with backorders and lost sales are derived. We first assume that the lead time demand follows a normal distribution, and then relax the assumption about the lead time demand distribution function and apply the minimax distribution-free procedure to solve the problem. Consequently, the order quantity, reorder point, lead time and the number of shipments per lot from the vendor to the buyer are decision variables. Iterative procedures are developed to obtain the optimal strategy.     

Inventory model with a mixture of back orders and lost sales

Very few researchers have considered inventory models with partial backlogging. The models developed earlier considered a fraction of demand to be backordered while the remaining fraction is lost during the stock out period. In this paper we have developed an inventory model with partial backlogging, redefining the demand rate at a particular instant as a function of the amount of orders already backlogged at that instant of time. Infinite replenishment rate and zero lead time are assumed. Expressions for optimum order quantity and optimuim value of maximum inventory are obtained by minimizing the total system costs. The model is illustrated with a numerical example, including sensitivity analysis with respect to the backlogging parameter.     

Lot sizing under (Q, R) policy in a capcity constrained manufacturing facility

Traditional approaches to lot sizing and inventory control consider uncertainties in either the demand or manufacturing process but not both. In these models it is usually assumed that the lead times are independent and identically distributed, but this is not realistic in many practical instances. In this paper we consider the lot sizing problem for items with stochastic demands and manufacturing lead times. It is assumed that the inventory of the finished product is controlled by continuous review policy of Q,R type—order quantity, order point system—and the problem is to determine optimal Q and R. We examine the decision parameters under a variety of conditions using exact and approximate methods.     

A note on inventory replenishment policies for deteriorating items in an exponentially declining market

In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But, this approach suffers some drawbacks. In this paper we first show the inventory carrying cost is in proportion to the cost of deteriorated items, then offer a formulated approximated solution. Our formula solution is accurate enough to be taken as an optimal solution. Sensitivity analysis shows that our solution is stable. Finally, we give some numerical examples to show the applicability of our solution.Scope and purposeGhare and Schrader initiated the discussion of deteriorating items in the inventory system. After that, many researchers presented diverse models with different assumptions on patterns of deterioration with/without shortages. Demand variation has also impact on inventory policies. In order to determine the optimal lot-size, Wee and Chung & Tsai advocated that the Newton's method is an adequate method. In this paper we illustrate some drawbacks of their approach, mainly the convergence and optimality problem. Thereby, we provide a formulated approximated solution, which is accurate enough to be taken as optimal.     

Joint optimization of preventive maintenance and inventory policies for multi-unit systems subject to deteriorating spare part inventory

The interconnection of maintenance and spare part inventory management often puzzles managers and researchers. The deterioration of the inventory affects decision-making and increases losses. Block replacement and periodic review inventory policies were here used to evaluate a joint optimization problem for multi-unit systems in the presence of inventory deterioration. The deterministic deteriorating inventory (DDI) model was used to describe deteriorating inventory when deteriorating inventory data were available and the stochastic deteriorating inventory (SDI) model was used when they were not. Analytical joint optimization models were established, and the preventive replacement interval and the maximum inventory level served as decision variables to minimize the expected system total cost rate. This work proved the existence of the optimal maximum inventory level and gave the uniqueness condition under the DDI model. Numerical experiments based on the electric locomotives in Slovenian Railways were performed to confirm the effectiveness of the proposed models. Results showed the total cost rate to be sensitive to the maximum inventory level, which indicates that the research of this work is necessary. Further, the optimal preventive replacement interval was reduced and the optimal maximum inventory level was increased to balance the influence of deteriorating inventory. Monte Carlo experiments were used to show that the proposed policy is better than policies that do not take deteriorating inventory into account.     

Single period stochastic inventory problems with ordering or returns policies

In recent years, there has been an increasing adoption of returns policies in the coordination of the supply chain, where market demand is always assumed to be satisfied by manufacturing or by ordering from suppliers. However, many industries face the important decision of how to balance their inventory level. This problem has long been studied in financial institutions such as banks. This study presents an optimal inventory policy under a given stochastic demand such as a uniformly distributed demand, single-item, and single period review inventory system. The optimal inventory control policy obtained in this study is called a four-point policy: that is, when the entity’s inventory level is below a reorder point, the entity must increase his stock level by ordering and order up-to a fixed level (second point); when the entity’s inventory level is over a return point (third point); the stock level must be decreased by returns and decreased to a fixed level (fourth point); otherwise, nothing should be done. We also analyze the (K, S)-convex properties of the inventory cost function.     

Quantifying suppliers’ product quality and delivery performance: A sourcing policy decision model

This paper provides buying firms with a useful sourcing policy decision tool to help them determine an optimum set of suppliers when a number of sourcing alternatives exist. We propose a probabilistic cost model in which suppliers’ quality performance is measured by inconformity of the end product measurements and delivery performance is estimated based on the suppliers’ expected delivery earliness and tardiness. The model is then empirically tested, utilizing the parameters obtained from one US mechanical component manufacturing company. The results from the case analysis indicate that single sourcing could be a cost effective policy but is not a panacea when the buying firm pursues product quality and delivery excellence. A prerequisite condition for the success of single sourcing practices is a low incoming quality variation within a group of single-source suppliers.     

Evaluation of sourcing contracts in wood supply procurement using simulation

Procurement operations in forest companies are exposed to various risks, which may increase procurement costs. Examples of risks are the contract's unreliability and contract breach. Deterministic planning models cannot perfectly reflect the complexities of real-world applications in the presence of sourcing risks when the future is uncertain. In practice, forest industries use contracts to guarantee the wood supply. Monthly forecasts are prepared for the delivery volume and are primarily based on the experience of procurement staff and the total volume of contracts. Missed deliveries in the contracts lead to a mismatch between the supply and demand for wood fiber and increase the costs of procurement as a result of high inventory costs or expensive purchases from the open market. Previous studies on simulating the impact of sourcing risks on procurement operations have been conducted; however, none have addressed the selection of procurement contracts in the presence of sourcing risks. In forest industry, numerous suppliers are available with sourcing contracts. Each contract possesses its own characteristics such as flexibility, volume, schedule, and price of delivery. A Monte Carlo simulation approach is implemented to analyze the behavior of a deterministic planning approach. Random events are generated by formulating different types of sourcing risks, having either short- or long-term impact. The simulation is embedded with a deterministic planning model in each period. Results showed that management of sourcing risks is easier with flexible contracts than with fixed contracts, despite their higher purchasing cost.     

A continuous review inventory model with the controllable production rate of the manufacturer

Optimal operating policy in most deterministic and stochastic inventory models is based on the unrealistic assumption that lead‐time is a given parameter. In this article, we develop an inventory model where the replenishment lead‐time is assumed to be dependent on the lot size and the production rate of the manufacturer. At the time of contract with a manufacturer, the retailer can negotiate the lead‐time by considering the regular production rate of the manufacturer, who usually has the option of increasing his regular production rate up to the maximum (designed) production capacity. If the retailer intends to reduce the lead‐time, he has to pay an additional cost to accomplish the increased production rate. Under the assumption that the stochastic demand during lead‐time follows a Normal distribution, we study the lead‐time reduction by changing the regular production rate of the manufacturer at the risk of paying additional cost. We provide a solution procedure to obtain the efficient ordering strategy of the developed model. Numerical examples are presented to illustrate the solution procedure.     

A solution procedure for mixed-integer nonlinear programming formulation of supply chain planning with quantity discounts under demand uncertainty

Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.     

Integrated inventory control and inspection policies with deterministic demand

In this paper, we develop integrated inventory inspection models with and without replacement of nonconforming items. Inspection policies include no inspection, sampling inspection, and 100% inspection. We consider a buyer who places an order from a supplier. When a lot is received, the buyer uses some type of inspection policy. The fraction nonconforming is assumed to be a random variable following a beta distribution. Both the order quantity and the inspection policy are decision variables. In the inspection policy involving determining sampling plan parameters, constraints on the buyer and manufacturer risks are set in order to obtain a fair plan for both parties. A solution procedure for determining the operating policies for inventory and inspection consisting of order quantity, sample size, and acceptance number is proposed. Numerical examples are presented to conduct a sensitivity analysis for important model parameters and to illustrate important issues about the developed models.     

On conflict and cooperation in a two-echelon inventory model for deteriorating items

Four scenarios are proposed concerning cooperative behavior for inventory policies between suppliers and retailers: no information is shared; the supplier is dominant during negotiations with retailers; the retailer is dominant during negotiations with suppliers; and the supplier and retailer cooperate. Unlike other studies, we consider deteriorating items and permit completed backorders, with a fixed service rate, in the models for these four scenarios. We explore the optimality of these models and present a procedure to find the optimal solution. Numerical examples are provided to illustrate the procedure, which are also used for sensitivity analysis. The results show that the cooperation scenario with information sharing is the best way to reach a win–win position. However, some compensation programs might be required to persuade suppliers or retailers to cooperate when one of them faces a loss of profits in a cooperative scenario.     

随机供应中断和退货环境下库存的应急控制

随机供应中断和退货环境下库存变化, 失去传统上的单调性, 呈现复杂的随机波动状态, 从而, 极大地增加了控制难度. 为解决系统库存的短缺和超储问题, 本文提出一个应急控制(包括应急采购和应急处理)策略. 在库存水平的动态变化表示为Lévy过程条件下, 利用连续时间Markov链、更新过程和鞅理论, 构建了系统期望折扣总利润模型, 并设计了交叉熵法确定最优控制策略. 仿真结果表明, 中断强度和类型及退货批次和批量, 对最优应急处理水平和应急采购量均有较大影响. 而退货类型仅影响最优应急处理水平, 对最优应急采购量影响较小.     

A multi-server perishable inventory system with negative customer

In this paper, we consider a continuous review perishable inventory system with multi-server service facility. In such systems the demanded item is delivered to the customer only after performing some service, such as assembly of parts or installation, etc. Compared to many inventory models in which the inventory is depleted at the demand rate, however in this model, it is depleted, at the rate at which the service is completed. We assume that the arrivals of customers are according to a Markovian arrival process (MAP) and that the service time has exponential distribution. The ordering policy is based on (s, S) policy. The lead time is assumed to have exponential distribution. The customer who finds either all servers are busy or no item (excluding those in service) is in the stock, enters into an orbit of infinite size. These orbiting customers send requests at random time points for possible selection of their demands for service. The interval time between two successive request-time points is assumed to have exponential distribution. In addition to the regular customers, a second flow of negative customers following an independent MAP is also considered so that a negative customer will remove one of the customers from the orbit. The joint probability distribution of the number of busy servers, the inventory level and the number of customers in the orbit is obtained in the steady state. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.     

Simultaneous determination of the optimal production–inventory and product inspection policies for a deteriorating production system

In this paper, we attempt to find a method for the optimization of production–inventory and product inspection policies for deteriorating production systems. Taking advantage of the nature of a deteriorating production system, a strategy would be not to inspect the first s items of the batch. Therefore, an inspection policy which disregards the first s (DTF-s) items of the batch is proposed. Under the DTF-s policy, we do not inspect the first s produced items but inspect only those items from the (s+1)th till the end of the production run. The objective of this study was the joint determination of the production lot size and the inspection policy s, resulting in a minimization of the expected average cost per unit time. Based on this model, the underlying conditions necessary for the existence of an optimal policy are given. Two commonly used inspection strategies, no inspection and full inspection are discussed. Under both inspection strategies, an optimal production–inventory lot is bounded by the traditional economic quantity. The case of full inspection is shown to be an extension of previously reported results. The option of investing in the process of quality improvement is also discussed. Finally, numerical examples are given to illustrate the method and its advantages in the conclusion.Scope and purposeThis paper considers the relationship between production, inventory and inspection in a deteriorating production system which may transit from the “in-control” state to the “out-of-control” state after a period of operation. Once the transition to the “out-of-control” state has occurred, it is assumed that some percentage of the items produced are defective or of substandard quality. However, in many cases, defects in a defective item can only be identified by an inspection process which carries an inspection cost. Those inspected items which are found to be defective are reworked at some cost before being shipped. On the other hand, defective items which are not inspected will be passed to the customer, incurring a much larger warranty cost. In order to operate such a system economically, tradeoffs among production setup, inventory, inspection and defective cost must be analyzed. Deterioration of the production system is an inherent process in all manufacturing industries. An understanding of the relationship among production, inventory and inspection for such systems will help managers to maintain efficient and economic control of operations.     

Order allocation for multiple supply-demand networks within a cluster

Manufacturers outside an industry cluster and suppliers within cluster form a multiple sourcing supply-demand network. Two different order allocation strategies, the production capacity-based strategy and the production load equilibrium-based strategy, are studied in this paper. The respective order allocation models of multiple manufacturers versus multiple suppliers are proposed. Considering the uncertainty of demand and enterprises’ production capacity, the discrete event system simulation is used to verify that the production load equilibrium-based strategy can not only guarantee the order’s on-time delivery from the perspective of the available manufacturing resources, but also lead to promote the whole supplier group’s operation level, so as to realize the optimization of the entire supply chain.     

A fuzzy solution approach for multi objective supplier selection

In today’s severe competitive environment the selection of appropriate suppliers is a significantly important decision for effective supply chain management. Appropriate suppliers reduce purchasing costs, decrease production lead time, increase customer satisfaction and strengthen corporate competitiveness. In this study a multiple sourcing supplier selection problem is considered as a multi objective linear programming problem. Three objective functions are minimization of costs, maximization of quality and maximization of on-time delivery respectively. In order to solve the problem, a fuzzy mathematical model and a novel solution approach are proposed to satisfy the decision maker’s aspirations for fuzzy goals. The proposed approach can be efficiently used to obtain non-dominated solutions. A numerical example is given to illustrate how the approach is utilized.