Optimal replenishment cycle for perishable items facing demand uncertainty in a two-echelon inventory system

We consider a two-echelon supply chain with an upstream manufacturer and a downstream retailer for a single perishable product. The manufacturer processes raw materials into finished products, which are purchased by the retailer in each replenishment cycle. The raw materials of the manufacturer are highly perishable (i.e. perishing within hours or days), and the finished goods at the retailer face demand uncertainty and obsolescence. We model the manufacturer–retailer relationship as a Stackelberg game where the retailer is the leader and decides the replenishment cycle that minimises its mismatch cost between supply and uncertain demand. The manufacturer is the follower and decides its processing rate to minimise its unit cost for finished goods. Our results show that the raw material and finished goods lifetimes, which are interrelated through the duration of the replenishment cycle, have a significant impact on supply chain costs. Although raw material spoilage cost by itself is low, we show that short raw material lifetimes have a significant impact on the costs of both parties. Additionally, we find that while high manufacturer markups increase retailer costs, they reduce the manufacturer's costs due to large production batches.     

The consignment stock of inventories under buyer's warehouse space limitation

In this paper, coordination between a single vendor (or manufacturer) and a buyer (or retailer) via the delivery schedule in a production and distribution system is presented. A continuous deterministic model with centralised decision process is developed. To satisfy the buyer's demands, the product is delivered in discrete batches from the vendor's stock to the buyer's stock subject to consignee's warehouse space capacity constraint. A more general type of consignment stock (CS) policies is analysed. The inventory patterns and the cost structure of production distribution cycles (PDC) are described under the constraint – when the ratio α of the sizes of delayed to just in time (JIT) for the vendor deliveries is given. Also, an analysis how an upper buyer's warehouse space limit can act as a key factor for implementing the generalised CS-policies successfully. Numerical examples are presented to illustrate the performance of model and the results. A comparative study of the results shows that the generalised CS-policies performs better.     

Pricing and warranty decisions in a two-period closed-loop supply chain

For a two-period closed-loop supply chain (CLSC) consisting of a manufacturer and a retailer, Stackelberg game analyses are conducted to examine pricing and warranty decisions under two warranty models depending on who offers warranty for new and remanufactured products and the corresponding benchmark models with a warranty for new products only. Next, we identify the conditions under which warranty for remanufactured products is offered and investigate how this warranty affects the CLSC operations. Subsequently, comparative studies are carried out to examine equilibrium decisions, profitability and consumer surplus of the CLSC between the two warranty models. Analytical results show that offering warranty for remanufactured products does not affect new product pricing in period 2, but influences the pricing of new products in period 1 and remanufactured products in period 2, thereby enhancing remanufacturing, individual and channel profitability, and consumer surplus. Compared to the retailer warranty for remanufactured products, the manufacturer warranty can attain a more equitable profit distribution. If the warranty cost advantage of the manufacturer (retailer) is significant relative to that of the retailer (the manufacturer), the manufacturer (retailer) arises as a natural choice to offer warranty for remanufactured products as this decision enhances both profitability and consumer surplus.     

Multi-commodity warehouse location and distribution planning with inventory consideration

We consider the problem of designing a distribution network for a logistics provider that acquires products from multiple facilities and then delivers those products to many retail outlets. Potential locations for consolidation facilities that combine shipments for cost reduction and service improvements are considered. The problem is formulated with direct shipment and consolidation opportunities. A novel mathematical model is derived to solve a complex facility location problem determining: (i) the location and capacity level of warehouses to open; (ii) the distribution route from each production facility to each retailer outlet; and (iii) the quantity of products stocked at each warehouse and retailer. A genetic algorithm and a specific problem heuristic are designed, tested and compared on several realistic scenarios.     

Lot-sizing for a single-product recovery system with backordering

In this article, a single-product recovery system is studied. Used products are collected from customers and kept at the recoverable inventory warehouse for future recovery. The constant demand rate can be satisfied either by newly produced products or by recovered ones (serviceable inventory), which are regarded as perfectly as the new ones. Excess demand is completely backordered. Following an exact analytical approach, the optimal production and recovery policy is obtained. A numerical cost comparison of this model with the corresponding one without backordering is also performed. The results are general, as they were valid for finite and infinite production and recovery rates.     

Policy mechanisms for supply chain coordination

The problem is to determine a review period and stocking policy that are mutually beneficial to a producer and a retailer. In our model, the retailer uses a periodic review, base stock policy for ordering the item from the producer's Distribution Center (DC). Excess customer demand is assumed to be lost. A make-to-order production system supplies to the DC. We show that given a review period, unless the manufacturer agrees to share the cost of carrying a fraction of the safety stocks at the retailer, the two will not agree upon the level of stocks to be carried in the store. We prove that there is an equilibrium value for this fraction, such that the retailer and the manufacturer are always in agreement with regard to the stocking level. We then show that complete coordination on the stocking level as well as the review period can be achieved solely through carrying out negotiations on credit terms. These theoretical results are used to construct an algorithm for calculating the optimal policy parameters for a supply chain. As part of the analysis we suggest a modification of the base stock policy for the positive lag lost sales case of periodic review inventory models that consistently outperforms the base stock policy in our numerical studies.     

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.     

双渠道供应链中直销成本对销售渠道决策的影响

针对传统零售与网上直销并存的双渠道供应链系统,在制造商为Stackelberg博弈的领导者和零售商具有销售成本优势的假设下,建立了销售渠道决策模型,分析了制造商的直销成本对销售模式选址的影响。结果表明:当直销成本满足一定范围时,制造商采用直销模式可以使制造商、零售商和消费者三方共赢。     

The value of trade credit with rebate contract in a capital-constrained supply chain

We investigate the value of an innovative trade credit with rebate contract (TCRC) model in a stylised supply chain. In this supply chain, the capital-abundant manufacturer offers an integrated contract involving trade credit, minimum ordering and sales rebate contract to a capital-constrained retailer. To highlight the value of the TCRC model, we compare it with a traditional trade credit financing (TTCF) model in a ‘selling to the newsvendor model’. First, we show that equilibrium strategies exist between the manufacturer and the retailer under the TCRC or TTCF model. Second, this study investigates equilibrium selection between the TCRC and TTCF models for the individual and the supply chain. Finally, we show the manufacturer’s pricing policy, wherein the TCRC model outperforms the TTCF model for the players. Furthermore, we conduct a set of numerical experiments to show evidence for theoretical analysis and measure the operation efficiency of the TCRC model for players in the supply chain.     

Joint effects of remanufacturing channel design and after-sales service pricing: an analytical study

We conduct an analytical study on remanufacturing channel design and after-sales service pricing, which jointly affect the sustainability and profitability of the supply chain. We model a supply chain with one manufacturer and one independent retailer. The manufacturer, as the Stackelberg game leader, engages in remanufacturing to take advantage of production cost savings. The collection of the used products can be carried out by either the manufacturer or the retailer. After-sales service, for example, extended warranty, is offered with the product and is sold separately. The service provider can be either the manufacturer or the retailer. We use game theoretic models to answer an important research question: How do remanufacturing and after-sales service jointly affect channel selection decisions? We explore the benefits of joint decision making in terms of remanufacturing efficiency and after-sales service performance. We find that it is most efficient for the retailer to collect the used product for remanufacturing and to offer after-sales service, because the retailer simultaneously makes decisions regarding remanufacturing and after-sales service and thus reduces double marginalisation in the supply chain. We also demonstrate numerically how the costs of collecting used products and providing after-sales service impact channel selection decisions.     

短生命周期特征产品的二级供应链定价博弈分析

针对短生命周期产品的供应链利润最大化问题,建立并分析了二级供应链上制造商和销售商之间的非合作和合作定价博弈模型,得出供应链系统在成员合作情形下才能达到利润最大化的结论,并探讨了合作利润的分配机制,证明了在长期博弈中成员之间通过合作达到双赢的可行性。     

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.     

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.     

考虑渠道成本差异的双渠道供应链定价策略与渠道选择

根据网上渠道不同销售模式的特征,构建制造商网上直销、网上分销和网上代销3种供应链定价模型,引入渠道成本参数并分析制造商如何进行产品定价和渠道选择。研究表明,在3种渠道结构中,代销模式下产品价格最低,直销模式和分销模式下的价格受到渠道偏好的影响;随着线上或线下渠道成本增加,制造商会降低该渠道产品的批发价格,而零售价格与自身渠道成本正相关;此外,当制造商自建网上平台成本较低时,制造商选择直销模式最优;当制造商自建网上平台成本较高,且代销平台服务效率较低时,制造商应选择分销模式,否则制造商选择代销模式更优。     

产品回收再利用率对闭环供应链利润的影响

针对由单个制造商和单个零售商组成的二级闭环供应链系统,制造商委托零售商回收旧产品,然后制造商生产新产品和再制造产品,零售商销售产品.采用stackelberg博弈方法,对制造商占主导的正向供应链和闭环供应链的利润进行了比较,分析了回收再利用率对闭环供应链利润的影响.研究结果表明:在产品存在最低或强制回收要求的前提下,当其他参数不变时,回收再利用率满足一定的阈值,并且回收再利用率越大,制造商实施闭环供应链管理就越有利.     

A piecewise nonlinear model for a production system under maintenance,trade credit and limited warehouse space

Small and medium size manufacturers exist commonly in developing countries. Limited warehouse space is a characteristic in small and medium size manufacturers. In today’s business environment, many upstream companies offer a credit period to downstream companies. In production system, a manufacturer usually adopts the system maintenance when the system is in the out-of-control state. Therefore, this paper considers a production-inventory model for a manufacturer under system maintenance, trade credit and limited warehouse space. The objective is to determine the optimal production run time to minimise the total cost. We develop an algorithm based on several theorems for solving the problem described. We provide several examples to illustrate the solution procedure and discuss how system parameters affect the manufacturer’s decision behaviour. Computational analysis demonstrates that the results of the proposed model are consistent with economic insights.     

Coordinating loan strategies for supply chain financing with limited credit

In this paper, we design a supply chain financing (SCF) system with a manufacturer, a retailer and a commercial bank where the retailer is capital constrained under demand uncertainties. We formulate a multi-level Stackelberg game in which the manufacturer acts as the leader and the bank as the sub-leader. Considering the bankruptcy risks of the retailer, we analyze the optimal credit line for the commercial bank, the optimal order for the retailer and the optimal wholesale price for the manufacturer, respectively. Comparing the benchmark scenarios of no capital constraint and constrained capital without financing, interdependencies between the operational and financial decisions are explored, as well as coordination analysis of the wholesale price contract with different credit lines. Finally, by conducting numerical studies, interactions between the operational and financial decisions and the impacts of credit lines on contract coordination are illustrated. The results validate our theoretical analysis. Our analysis suggests that a suitable financing scheme with limited credit would motivate the capital-constrained retailer to order more and the wholesale price contract with finite loans would achieve coordination in the SCF system.     

两级供应链中合作广告的博弈分析

研究了由单一制造商和单一零售商组成的二级供应链的合作广告策略。采用博弈论方法构建了模型并结合数值仿真,在考虑制造商与零售商各自的广告成本的情形下,分别考察了非合作静态博弈、Stackelberg主从博弈以及Nash合作博弈下的最优广告策略。通过比较,得到了制造商和零售商选择合作情形下的广告水平、订货量和整条供应链收益均优于不合作情形的结论,制造商的全国性广告水平与自身的广告成本呈负相关,而与零售商的广告成本呈正相关,为供应链成员选择广告策略提供了理论依据。     

闭环供应链广告协调机制研究

为了研究闭环供应链中零售商回收与制造商回收时两种情形下价格决策与广告协调策略,在广告既能影响市场需求又能影响回收率的条件下,运用博弈论分别建立制造商回收与零售商回收时的广告分摊协调策略数学模型,结果表明制造商回收模式有利于零售商,零售商回收模式有利于制造商。零售商所分摊的广告费用比例在制造回收时小。制造商回收时零售商所分摊的广告费用比例与广告回收效率因子负相关,与广告营销效率因子正相关。零售商将回收时零售商所分摊的广告费用比例与回收效率因子、营销效率因子无关。最后通过仿真证明了相关结论。本文的研究为闭环供应链在不同回收模式下广告回收效率与营销效率的变化时提供相应的协调策略。     

Coordinating a three-layer supply chain with uncertain demand and random yield

The paper considers a three-layer supply chain involving one raw-material supplier, one manufacturer and one retailer. The market demand is assumed to be stochastic and productions at the raw-material supplier and manufacturer are subject to random yield. The centralised model is studied as the benchmark case. The decentralised model is solved and Nash equilibrium solutions are obtained. It is shown that buyback contract fails to coordinate such a supply chain. However, a composite contract framed combining buyback, and sales rebate and penalty contracts is shown to coordinate the supply chain. Numerical examples are provided to illustrate the developed models.