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.     

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.     

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.     

Learning and screening errors in an EPQ inventory model for supply chains with stochastic lead time demands

This paper investigates the role of variable lead time, learning in production and screening errors in a vendor–buyer supply chain with defective items. The vendor–buyer supply chain is modelled for supplying a single item considering that the lots from vendor may contain some defective items. It is assumed that demand during lead time follows a normal distribution. Moreover, the production time at vendor’s facility is assumed to follow learning whereas buyer’s screening for defective items is prone to errors as well. Numerical examples are presented to illustrate the impact of different variables in the model. The analysis shows that delay in transportation lead time forces the buyer to carry more inventories to avoid shortages. Further, Type I error has a major impact on this cost. It was found that learning in production keeps on reducing the total cost of the supply chain up to a threshold.     

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.     

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.     

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.     

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.     

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.     

The optimal production and shipment policy for the single-vendor singlebuyer integrated production-inventory problem

This paper considers the problem of a vendor (manufacturer) supplying a product to a buyer (customer). The vendor manufactures the product in batches at a finite rate and ships the output to the buyer. The buyer then consumes the product at a fixed rate. The objective is to minimize the mean total cost per unit time of manufacturing set-up, stock transfer and stock holding. Previously published work has concentrated on finding optimal solutions from within given classes of policy. We derive the structure of the globally-optimal solution, set out an algorithm for obtaining it and illustrate the process with two numerical examples.     

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。     

A coordinated two-phase approach for operational decisions with vehicle routing in a single-vendor multi-buyer system

This study considers a two-echelon system in which a vendor produces a product at a finite production rate and supplies it to several buyers facing independent normally-distributed demands. The product is delivered to the buyers using a set of different speed vehicles with identical capacity and different operating costs. The issues of lead time reduction and the service level constraint on the buyers have been incorporated in the model. A model is formulated to determine the optimal production–inventory policy, vehicle routes and vehicle type for each route by minimising the related production, inventory, lead time crashing and transportation costs of the system while satisfying the service level constraint on each buyer. A coordinated two-phase iterative approach is proposed to solve the model. Finally, a numerical example is included to describe the solution approach and illustrate the results.     

A systematic literature review of remanufacturing scheduling

This paper studies a vendor–buyer integrated inventory system with buyers’ variable demand and warehouse space limitation where the consignment stock (CS) replenishment operates under a controllable lead time. Within any cycle, the production rate, the number of shipments and the shipping size are all fixed. Based upon the CS policy, the vendor agrees to maintain the buyer’s inventory to be above a safety level and less than the buyer’s space limitation. Due to the uncertainty in the demand, shortages/over stocks are sometimes inevitable. In such cases, penalties are incurred to discourage such occurrence. The holding cost consists of a storage component and a financial component, and the lead time is controlled with an extra investment which is a function of both the shipment size and the reduced time. Two-constraint, five-variable mix-integer optimisation models are established to describe the CS system. Two doubly-hybrid meta-heuristic algorithms are employed to solve the models that are complex and difficult to solve with available techniques. Two numerical examples are used to illustrate the solution procedure and the analysis of the computational results reveals the effects of some important parameters used for the annual joint total expected cost of the integrated system. The computational efficiency and quality of the solutions are evaluated by comparing them with other existing and popular methods. The results founds in all comparative evaluation are very encouraging and competitive.     

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.     

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.     

Modelling on vendor-managed inventory policies with equal and unequal shipments under GHG emission-trading scheme

This paper studies five different stock control policies in the supply chain management. The lead time can be shortened by extra investment between two entities. The vendor produces a single product and delivers the order quantity in a number of unequal shipments to the buyer. The unit holding cost is divided into financial and storage components. The vendor takes care of financial component until the products are sold to the end customers to encourage them to buy more products. In order to reduce emissions from production and to protect the environment, some legislative actions have been taken such as implementing taxes and penalties. The cost function also includes these taxes and penalties. The optimal solutions of this constrained mixed integer non-linear programming problem are obtained by using the Genetic Algorithm (GA). Numerical examples are employed and comparison works are carried out with other existing literatures. Results show that the performance of the system is better when it is operated under unequal shipment policies and vendor-managed inventory (VMI) agreement.     

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.     

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 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.     

Consignment and vendor managed inventory in single-vendor multiple buyers supply chains

In this paper we model a consignment (CS) and vendor-managed inventory (VMI) policy for a single vendor and multiple buyers supply chain with known demand. We study three vendor–buyers partnerships: (i) the vendor and the buyers act independently, (ii) the vendor enters in a vendor-managed inventory consignment (VMI&CS) partnership with the buyers and (iii) the vendor and the buyer belong to a vertically integrated firm where a single decision maker decides about the ordering policies. We use relationships (i) and (ii) to study the benefits of the VMI&CS agreement. We provide analytical and numerical results. We find that such an agreement is more beneficial when the vendor has a flexible capacity. It is also more attractive to buyers when they have significant order costs and the vendor's setup cost is not large. Finally we find that under VMI&CS the vendor will tend to make more frequent shipments with smaller lots.