Consignment stock policy with unequal shipments and process unreliability for a two-level supply chain

This paper considers a vendor managed inventory model with consignment stock policy in which a single vendor delivers a single product to a single buyer in unequal-sized shipments. The vendor’s production process may produce some defective items during a production run. The buyer performs a screening process immediately after receiving each delivery from the vendor and the vendor bears the warranty cost of defective item, if any. The buyer either scraps or repairs the defective items by sending them to a repair factory. The average expected profit of the integrated system is derived using renewal reward theorem and a solution procedure is suggested to determine the optimal shipment policy of the vendor. Numerical examples are taken to determine both the equal and unequal shipment policies and compare their relative performances.     

Impacts of collaborative investment and inspection policies on the integrated inventory model with defective items

For an imperfect production system, to reduce quality-related costs, a manager may consider investing capital in quality improvement. In general, the investment expense in reducing the defective rate of items is often paid by the vendor. On the other hand, the buyer may inspect the product quality as the order is received which implies it incurs an inspection cost. In a supply chain integrated system, to accomplish global optimisation, the vendor and buyer can agree to jointly invest capital to improve the imperfect production processes, and the buyer can remove the inspection programme as the defective rate reaches a certain low-level. Hence, this paper investigates the impacts of collaborative investment and inspection policies on an integrated inventory model with defective items. The objective of this study is to seek the optimal order quantity, shipping times from the vendor to the buyer per production run, and the defective rate that minimise the joint total cost per unit time. An algorithm is developed to find the optimal solution. Several numerical examples are presented to demonstrate the proposed model and solution procedure, and then several management insights are obtained from the numerical examples.     

Vendor managed inventory with consignment stock for supply chain with stock- and price-dependent demand

This paper presents a single vendor–single buyer coordinated model. The vendor produces a single deteriorating item and transfers it to the buyer in equal shipments. The model is based on vendor managed inventory with consignment stock (VMI-CS) agreement in which the vendor uses the buyer’s warehouse. The buyer stocks items both on his shelf and in his warehouse. The demand is assumed to be linearly sensitive to inventory level and selling price. The objective is to determine variables that maximise the total profit. An exact solution procedure is proposed to find the optimal solution. Numerical results show that supply chain members will benefit from the advantages of economies of scale in coordinated model with VMI-CS policy.     

A consignment stock coordination scheme for the production,remanufacturing and waste disposal problem

This paper extends the model of a production, remanufacturing and waste disposal system by adding a buyer (retailer) to the vendor’s system to form a two-level forward/reverse supply chain. The vendor and the buyer are assumed to operate according to a consignment stock policy. A mathematical model is developed for the cases when the production and remanufacturing batches are of different and equal sizes. The model also accounts for transportation, inspection and sorting costs. Numerical examples are provided and results are discussed. The results show that the collection rate of used items and the repairable rate have a significant impact on the total cost of the system and the batch sizes. It was suggested that it may not be possible to operate a system like the one described in the paper at its maximum environmental edge without receiving some incentives or tax brackets. Another possibility is for the system to undergo a continuous improvement process to reduce its operational costs, which may require additional investment.     

An optimal production and shipment policy for a single-vendor single-buyer integrated system with both learning effect and deteriorating items

The collaboration of vendor and buyer is one of the key factors for successful supply chain management. The most common strategy for a collaborative system is to propose an integrated replenishment plan aimed at maintaining a win-win partnership for both vendor and buyer. The objective of this study is to develop a production and shipment model for a system that incorporates learning effect and deteriorating items and to derive an optimal joint total cost from the integrated perspective of both vendor and buyer. A simple solution procedure is presented to determine the optimal production time and number of deliveries. A numerical example is provided to illustrate the proposed model. A sensitivity analysis is conducted to study the effect of changes in the related parameters on the optimal solution. This paper shows that the proposed integrated model can result in a significant cost reduction as compared with the independent decisions made by either vendor or buyer.     

Vendor-managed inventory with consignment stock agreement for single vendor–single buyer under the emission-trading scheme

This paper presents a joint economic lot size (JELS) model for coordinated inventory replenishment decisions under the vendor-managed inventory (VMI) with consignment stock (CS) agreement and an emission-trading scheme. The paper assumes a single product that flows along a two-level supply chain system, with a single vendor and a single buyer. The total cost of the system is the performance measure, which is the sum of the vendor’s and the buyer’s total costs. The total cost includes the set-up and order costs, inventory holding costs, greenhouse gases (GHG) emissions tax and penalty costs. A mathematical model is proposed to determine: (1) the vendor’s production lot size quantity; (2) the number of shipments sent by the vendor to the buyer in a cycle; and (3) the production rate that minimises the total cost of the supply chain. Some numerical examples are carried out, as well as comparisons with the traditional JELS model for a classic two-level supply chain. Results show that the performance of the system is better when it is operated under a VMI with CS agreement, which is capable of reducing the traditional inventory holding costs and, for some values of given parameters, the GHG emissions tax and penalty costs.     

A closed-loop supply chain with stochastic product returns and worker experience under learning and forgetting

This paper addresses a single-manufacturer single-retailer closed-loop supply chain with stochastic product returns considering worker experience under learning and forgetting in production and inspection of returned items at the manufacturer. Customer demand is assumed to be dependent linearly on the retail price, and it is fulfilled by using both manufactured and remanufactured products. The manufacturer delivers the buyer’s order quantity in a number of equal-sized batches. The optimal number of shipments, the shipment size and the retail price are determined by maximising the average expected profit of the closed-loop supply chain. It is observed from the numerical study that high learning effects in production and inspection lead to high recovery rates of used products, which, besides an economic advantage, may have a positive effect on the environment. Even though forgetting has an adverse effect, the average expected profit of the closed-loop supply chain is much higher than that of the basic model which ignores worker learning.     

A single-vendor single-buyer production-inventory model with controllable lead time and service level constraint for decaying items

This paper presents a production-inventory model in a single-vendor single-buyer system for decaying items which deplete with constant decay rate. It is assumed that the lead time demand follows a normal distribution and shortages are backordered. Also, buyer's lead time can be reduced at an added cost. A model has been formulated to find the optimal order quantity, lead time and the number of shipments from the vendor to the buyer during one production cycle while minimising the total expected cost per unit time of the vendor-buyer integrated system. It is often difficult to estimate the stock-out cost in inventory systems. Therefore, instead of having a stock-out term in the objective function, a service level constraint is included in the model. Due to mathematical complexities involved, it is difficult to establish the solutions analytically. An iterative procedure is developed to find the optimal solution using LINGO 10, and a numerical example is given to illustrate the results of the proposed model. Furthermore, the effects of key parameters are also studied to provide the insight into the structure of the solution. In addition, the savings of buyer and vendor are investigated from implementation of joint optimisation model over the model in which they minimise their own cost independently.     

Another look at the single-vendor single-buyer integrated production-inventory problem

This paper considers a supply chain in which a ‘vendor’ supplies a product to a ‘buyer’. The vendor manufactures the product at a finite rate and periodically ships the output to the buyer. The buyer then consumes the product at a fixed rate. Costs are attached to manufacturing batch set up, the delivery of a shipment and stockholding at the vendor and buyer. The objective is to determine the production and shipment policy which minimizes long-run total average cost—assuming the vendor and buyer collaborate and find a way of sharing the consequent benefits. Most previous work has been based on the assumption that unit stockholding costs increase as stock moves down the supply chain, but recent research has suggested that the opposite may sometimes hold. We show how the optimal batch production and shipment policy may be derived when unit stockholding costs increase as stock moves down the chain and shipments are not necessarily equal in size.     

A study of an integrated inventory with controllable lead time

The Japanese experience of Just-in-Time (JIT) production has shown that there are advantages and benefits associated with the efforts to reduce inventory lead time and the associated inventory cost. The length of lead time directly affects the customer service level, inventory investment in safety stock, and the competitive abilities of a business. In most of the literature dealing with inventory problems, either a deterministic model or probabilistic model, lead time is viewed as a prescribed constant or a stochastic variable, and is not subject to control. However, in many practical situations, lead time can be reduced by an additional cost. Moreover, the successful implementation of JIT production in today's supply chain enviromnent requires a new spirit of cooperation between the buyer and the vendor (Goyal and Srinivasan 1992). A desirable condition in long time purchase agreements in such a manufacturing environment is the frequent delivry of small quantities of items so as to minimize inventory holding cost for the buyer. The vendor also needs to minimize his or her total inventory costs. An integrated inventory model that allows the two trading parties to form a strategic alliance for profit sharing may prove helpful in breaking down the traditional barriers. This paper presents an integrated inventory model with controllable lead time. The model is shown to provide a lower total cost and shorter lead time compared with those of Banerjee (1986) and Goyal (1988), and is useful for practical inventory problems.     

基于供需一体化协同控制的供应链库存模型

根据供需一体化协同库存控制策略，构建了一个一体化库存模型。在模型里，假定提前期需求是随机的且服从正态分布，允许在提前期内发生缺货，并产生缺货成本；假定提前期是可控的，能够通过增加成本缩短提前期。该模型通过同时计算最优订货量、再订货点、提前期以及运送批次．使供需一体化库存总成本最小。实例分析证明该模型能够达到节约成本的目的。     

The supplier–buyer integrated production-inventory model with random yield

This paper revisits the traditional supplier–buyer integrated production-inventory model which deals with the problem of a manufacturer (supplier) supplying a product to a retailer (buyer) serving the consumer market with constant stationary demand. The product is manufactured in batches at a finite rate. The supplier's production batch is depleted by the buyer's replenishment orders at periodic intervals. The buyer's inventory is then consumed by the market demand at a fixed rate. The problem is the simultaneous computation of the manufacturer's production lot-size and the buyer's replenishment order quantity, i.e. the integrated production-inventory policy parameters. The key characteristic considered in this paper is that the manufacturing process is imperfect, and, hence, there are defective items in each production lot. As a result, each replenishment order shipped to the buyer includes defective products and the non-defective percentage in each such shipment is random. Considering the case where the supplier replenishes the buyer via equal-sized shipments, we develop an analytical expression of the total expected cost for the supplier–buyer system under consideration, with and without a considerable inspection time. We first examine the case where the inspection time is negligible, and then we present a generalisation to consider the inspection time explicitly. Our goal is to model the impact of random yield on the system performance. Our findings are useful for computing the integrated production-inventory policy parameters while considering the supply uncertainty due to an imperfect manufacturing process. Through numerical examples, we quantify the impact of supply with random yield on the system performance and illustrate its relationship with the demand and production rate.     

Integrated product and container inventory model for a single-vendor single-buyer supply chain with owned and rented returnable transport items

This study considers a single vendor supplying a single retailer with a finished product packed in returnable transport items (RTIs), such as containers, pallets or crates, to facilitate its safe shipment. Once received at the retailer’s site, the RTIs are emptied, cleaned, repaired if needed and returned to the vendor to be used for the next shipment. Because of unexpected events, such as damage of RTIs and/or shortage of labour to empty RTIs, the RTI return time is considered stochastic in this study. In case the return of empty RTIs is delayed, the vendor has the option to rent RTIs from a nearby service provider to avoid disruptions in the delivery schedule and finished product shortages at the buyer’s premise. We formulate the problem of coordinating the flow of both the finished product and RTIs and minimising the supply chain wide costs as a mixed-integer non-linear programme. For a convex objective function, we develop an efficient solution procedure that generates the optimal replenishment cycle, the optimal number of RTIs and the optimal number of trucks. The general optimisation model and the solution procedure are illustrated for the case where the RTI return time is exponentially distributed. In addition, we conduct an experimental study to assess the impact of the problem parameters on the decision variables. It is found that renting RTIs is especially beneficial in case both shortage cost and the risk of late RTI returns are high. In addition, the average RTI return time is found to be critical for the performance of the supply chain.     

An optimal consignment stock production and replenishment policy with controllable lead time

This paper considers a single-vendor and single-buyer production system in which the lead-time is controllable with an extra investment under a long-term agreement between the two trading partners. The vendor produces at a finite rate, ships the outputs in lots of equal size within a production cycle, and delays those shipments for a certain period when the buyer’s inventory approaches the capacity limits. Therefore, the arrival of these shipments does not lead to an increase in the buyer’s inventory. Meanwhile, the buyer holds the payment until the complete consumption of the products. The holding cost consists of a storage component and a financial component. A joint EOQ/EPQ model is then established under cases where the buyer’s unit storage holding cost might be greater or less than that of the vendor to jointly determine the number of shipments, the size of each shipment, the number of delayed shipments, and the lead time that minimise the yearly joint total expected cost (JTEC) of the system. An efficient solution procedure is provided to solve the non-linear integer optimisation model that defined the system under consideration. A method to determine the integer global optima from the real global optima is also presented. Two numerical experiments are conducted to illustrate the procedure and the results show that considering the combined effect of adopting a consignment stock policy and lead time crashing opportunities may lead to a better result than any of these two policies considered separately.     

Integrated inventory models with fuzzy annual demand and fuzzy production rate in a supply chain

The successful implementation of Just-in-time (JIT) production in today's supply chain environment requires a new spirit of cooperation between the buyer and the vendor. An integrated inventory model with such a consideration is based on the total cost optimization under a common stock policy and business formula. However, the supposition of known annual demand in most related literature may not be realistic. This paper proposes the inclusion of fuzzy annual demand and/or the production rate, and then employs the signed distance, a ranking method for fuzzy numbers, to find the estimate of the common total cost in the fuzzy sense, and subsequently derives the corresponding optimal buyer's quantity and the integer number of lots in which the items are delivered from the vendor to the purchaser. Numerical examples are provided to illustrate the results of proposed models.     

An integrated inventory model involving manufacturing setup cost reduction in compound Poisson process

The collaboration of vendor and buyer is one of the key factors for successful supply chain management. The most common strategy for a cooperative system is to propose an integrated replenishment plan. Almost all inventory models assume that setup cost is deterministic and is not subject to control. However, in many practical situations, setup cost can be reduced at an added investment. The paper assumes that setup cost can be reduced at an added investment and shortage is permitted during the lead time. This article relaxes the assumption that the demand of lead time is deterministic and is assumed to be a compound Poisson process. A model is derived to determine an optimal integrated inventory policy with controllable setup cost. The expected annual integrated total cost function is derived and a solution procedure is established to find out the optimal solution. Finally, a numerical example is provided to illustrate the solution procedure.     

Operational and environmental decisions for a two-stage supply chain under vendor managed consignment inventory partnership

Supply-chain-based organisations are nowadays facing intense pressure to abide to environmental regulatory requirements while they are striving to be responsive to customers’ needs at the least cost possible. As supply chain activities are among the top contributors to carbon emissions, several recent research works have investigated the impact of carbon regulation policies on economic and environmental supply chain performance. This paper presents integrated economic and environmental models for the one-vendor one-buyer supply chain problem under a vendor managed consignment inventory (VMCI) arrangement. Through the developed models, we study the impacts of two carbon reduction policies, namely carbon cap and carbon tax policies, on supply chain wide costs and carbon emissions. We first provide a much simpler and more compact formulation for the basic single-vendor single-buyer supply chain under VMCI agreement. We also present an environmental-based VMCI model where reduction of carbon footprint is considered as the only objective function. We then extend these two basic models to include each of the two carbon emissions reduction policies. We identify structural properties for the optimal solutions of the two hybrid economic and environmental models and propose algorithms to generate optimal solutions. The results of the computational experiments reveal that the implementation of carbon reduction policies, through carbon cap and carbon tax, may call for the adjustment of the vendor’s production and buyer’s delivery quantities to reduce carbon footprint without significantly increasing the operational costs.     

Consignment stock theory with a fixed batch manufacturing process

This paper deals with stock control in a supply chain. The focus is on consignment stock (CS), an innovative collaborative relationship, which can create a win–win situation between the vendor and the buyer. Recently some analytical formulations have been proposed to optimise CS, and the present paper extends these models by considering a new critical factor: a fixed batch production process at the vendor's plant. This kind of production is typical if there are batch processing machines that can hold and simultaneously process a finite number of items, such as kilns for long heat treatment. Specifically, we consider a deterministic single-vendor single-buyer system. The buyer consumes a single product at a constant rate and is replenished by the vendor who produces in batches and incurs set-up costs. Each batch is dispatched to the buyer in a number of shipments, some of which may take place while production is still running. To minimise total operating costs (that is, manufacturing, replenishment and holding), two alternative production and shipment policies are proposed and analytically formulated as integer optimisation models. A step by step heuristic procedure to obtain the optimal solution is finally presented and demonstrated through numerical examples.     

An integrated inventory model for a single vendor and single buyer with order-processing cost reduction and process mean

Co-ordination in a supply chain is an effective way to improve channel performance. This paper considers a supply chain in which a vendor supplies a product to a buyer. In this paper, we develop a model that integrates the single vendor single buyer problem with order-processing cost reduction and process mean. A solution procedure is provided to determine the optimal order policy. Finally, a numerical example is presented to illustrate the solution procedure.     

The optimal production and quality policy for the vendor in a trade

Arranging an inspection schedule for the production process and taking inspection and burn-in tests to screen out defective items in a production lot before items are shipped to the buyer are widely used by the vendor, such that the defective percentage in an outgoing batch satisfies the quality requirement specified in the contract between them. For an inspection schedule, the number of inspections and the length of time intervals between two inspections are influential to both the precision of detecting the manufacturing process and the inspection cost. As to the inspection test, it is not perfect, so there are two types of errors (Types I and II). Nevertheless, compared with inspection test, burn-in is usually costly. Hence, how to make a suitable trade-off between these three treatments (i.e., inspection schedule, inspection test, and burn-in test) such that the outgoing batch satisfies the purchaser's quality requirement with low cost is an important issue. The main purpose of this paper is to deal with the problem of determining the optimal inspection schedule and the optimal mixed policy of inspection and burn-in, where the average outgoing quality is used as the measure of quality. More specifically, by using the criterion of maximizing the expected profit that the vendor makes in a trade, a nonlinear programming problem is built to determine (a) the number of inspections undertaken in the production process, (b) the times at which the production process is inspected, (c) the total number of items that the vendor should produce (or the production run time), (d) the number of items for inspection, the number of items for burn-in, and the number of items that need neither inspection or burn-in, and (e) the optimal burn-in time for those needing burn-in testing. An example is provided to illustrate the proposed method.