Can the desired service level be achieved when the demand and lost sales are unobserved?

In this paper we consider an inventory management problem in the retail industry with unobserved lost sales. The retailer does not know the demand for a particular product but she has access to Point-Of-Sale (POS) data. The retailer uses a fixed review period, order-up-to level system to control the inventory. The objective of the retailer is to achieve a pre-specified service level. We define the service level as the fraction of demand satisfied from inventory. However, due to the unobserved lost sales nature of the problem, the retailer cannot exactly measure the current service level. We propose a POS data-based mechanism for periodic updating of the order-up-to level. We show that the periodic updating approach yields the desired service level without using any inventory information. Once the periodic updating scheme converges, it also gives the actual demand distribution.     

Inventory competition and incentives to back-order

In this paper we consider the issue of inventory control in a multi-period environment with competition on product availability. Specifically, when a product is out of stock, the customer often must choose between placing a back-order or turning to a competitor selling a similar product. We consider a competition in which customers may switch between two retailers (substitute) in the case of a stock-out at the retailer of their first choice. In a multi-period setting, the following four situations may arise if the product is out of stock: (i) sales may be lost; (ii) customers may back-order the product with their first-choice retailer; (iii) customers may back-order the product with their second-choice retailer; or (iv) customers may attempt to acquire the product according to some other more complex rule. The question we address is: how do the equilibrium stocking quantities and profits of the retailers depend on the customers' back-ordering behaviors? In this work we consider the four alternative back-ordering scenarios and formulate each problem as a stochastic multi-period game. Under appropriate conditions, we show that a stationary base-stock inventory policy is a Nash equilibrium of the game that can be found by considering an appropriate static game. We derive conditions for the existence and uniqueness of such a policy and conduct a comparative statics analysis. Analytical expressions for the optimality conditions facilitate managerial insights into the effects of various back-ordering mechanisms. Furthermore, we recognize that often a retailer is willing to offer a monetary incentive to induce a customer to back-order instead of going to the competitor. Therefore, it is necessary to coordinate incentive decisions with operational decisions about inventory control. We analyze the impact of incentives to back-order the product on the optimal stocking policies under competition and determine the conditions that guarantee monotonicity of the equilibrium inventory in the amount of the incentive offered. Our analysis also suggests that, counterintuitively, companies might benefit from making their inventories “visible” to competitors' customers, since doing so reduces the level of competition, decreases optimal inventories and simultaneously increases profits for both players.     

Optimal order quantity and product modularity for a two-echelon returnable supply chain

This study considers a supply chain consisting of a manufacturer, a retailer, customers and a returnable and modular product with uncertain demand, in which customers return the unsatisfactory products to the retailer, and the retailer returns the unsold products to the manufacturer. We investigate the effects of the manufacturer’s refund for the retailer’s unsold products and the product modularity under the decentralised and the centralised strategies. We confirm that the order quantity and customer’s return probability both affect the optimal modularity level of the product, and that the optimal modularity level is related to the refund policy. Also, a strategic alliance between the supply chain members is more advantageous to product innovation based on modularity for a returnable chain. Finally, managerial insights and remarks are offered.     

Pull-type manufacturing systems with multiple product types

A multiple-product facility consisting of a manufacturing process and a finished product warehouse for several types of products is considered. An (R, r) continuous-review inventory control policy is applied to each type of product in the warehouse. The demand arrival process of each type is assumed to be Poisson. The processing times and the set-up times are arbitrarily distributed. We have developed an iterative procedure to approximately compute the average inventory level of each product in the warehouse under different priority schemes     

Optimal policies of a two-echelon serial inventory system with general limited capacities

We study optimal policies of capacitated two-echelon serial inventory systems under periodic review. For a system with smaller downstream capacity, we fully characterise the optimal policy as a further modified echelon base stock policy using an intuitive backward induction. The key lies in the magnitude relation between the initial upstream stock level and the downstream capacity. For a system with smaller upstream capacity, we demonstrate that the optimal policy is of a more complex structure where there can be at most four/five target levels up to which the upstream/downstream echelon tries to produce/order. The numbers of levels and their values depend on the length of remaining horizons and the amount of initial upstream inventories. We also specify these potential target levels and then suggest a way to simplify the search of optimal solutions.     

Competitive stocking and coordination in a multiple-channel distribution system

In this paper, we study a multiple-channel distribution system in which a manufacturer sells its product through an independent retailer as well as through his wholly-owned channel. The manufacturer and the retailer stock the product solely to satisfy the final customer demand of their respective channels. We focus on the stocking levels of the manufacturer's wholly-owned channel and the retail channel. We assume that each channel has a local stochastic demand, but that the products are substitutable, which means there will be spill-over customers in the event that one channel runs out of stock. We explore the channel inefficiencies induced by the presence of simultaneous vertical competition (double-marginalization) and horizontal competition (substitutability). We show that there is an overall tendency for both channels to overstock due to substitution, which intensifies under increasing substitution rates. Increasing double-marginalization, on the other hand, intensifies the tendency to overstock in the manufacturer's wholly-owned channel, but induces the retail channel to understock. We find that supply chain losses are least under moderate levels of double-marginalization and or substitution. We also investigate coordination mechanisms, and show that most of the well-known, simple contracts fail to achieve coordination in this setting. An exception to this is an appropriately designed penalty contract which can indeed coordinate the supply chain, but is hard to implement. In search of practically more appealing coordination mechanisms, we design a novel two-part compensation-commission contract, whose terms depend on the retail channel sales.     

Two-echelon spare parts inventory system subject to a service constraint

In this paper, we consider a spare parts inventory problem faced by a manufacturer of electronic machines with expensive parts that are located at various customer locations. The parts fail infrequently according to a Poisson process. To serve customers when a failure occurs, the manufacturer operates a central warehouse and many field depots that stock spare parts. The central warehouse acts as a repair facility and replenishes stock at the field depots. There is a centralized decision-maker who manages the inventory in both the central warehouse and the field depots. We develop a continuous review, base stock policy for this two-echelon, multi-item spare parts inventory system. We formulate a model to minimize the system-wide inventory cost subject to a response time constraint at each field depot. We present an efficient heuristic algorithm and study its computational effectiveness.     

A periodic review inventory model with loss-averse retailer,random supply capacity and demand

This paper studies a periodic review inventory model with random supply capacity and demand, where the retailer is loss-averse. For the single-period problem, it is shown that the retailer will not order unless the initial inventory level is less than a critical value, and the order-up-to level is generally not a constant. Moreover, the critical value and optimal order quantity are only dependent on the random demand and independent on the random capacity. We also investigate the impacts of loss aversion, price and cost on the optimal order quantity and maximum expected utility. Then a dynamic programming approach is used to analyse the retailer’s ordering policy in the multi-period case. In each period, if the initial inventory level is above a given value, an order will not be placed. Otherwise, the upper bound on the optimal order quantity is given. The numerical experiments are conducted to illustrate the optimal ordering policies.     

A multiperiod stochastic production planning and sourcing problem with service level constraints

We study a stochastic multiperiod production planning and sourcing problem of a manufacturer with a number of plants and/or subcontractors. Each source, i.e. each plant and subcontractor, has a different production cost, capacity, and lead time. The manufacturer has to meet the demand for different products according to the service level requirements set by its customers. The demand for each product in each period is random. We present a methodology that a manufacturer can utilize to make its production and sourcing decisions, i.e., to decide how much to produce, when to produce, where to produce, how much inventory to carry, etc. This methodology is based on a mathematical programming approach. The randomness in demand and related probabilistic service level constraints are integrated in a deterministic mathematical program by adding a number of additional linear constraints. Using a rolling horizon approach that solves the deterministic equivalent problem based on the available data at each time period yields an approximate solution to the original dynamic problem. We show that this approach yields the same result as the base stock policy for a single plant with stationary demand. For a system with dual sources, we show that the results obtained from solving the deterministic equivalent model on a rolling horizon gives similar results to a threshold subcontracting policy. Correspondence to: Fikri KaraesmenThe authors are grateful to Yves Dallery for his ideas, comments and suggestions on the earlier versions of this paper.     

Optimal cycle time and inventory decisions in coordinated and non-coordinated two-echelon inventory system under inflation and time value of money

In this paper, a mathematical model is developed for a coordinated and non-coordinated two-echelon inventory system comprising of a single manufacturer and a single retailer. The objective of the model is to demonstrate the optimality of cycle time and inventory decisions under the phenomena of different inflation rates at the manufacturer and retailer points. Also, it is aimed at determining the annual net revenue of the supply chain (SC). In the proposed model, the present value of the inflated ordering/set-up costs, purchase/unit costs, carrying costs and the gross revenue is computed for the retailer, manufacturer and the SC. A numerical example is devised to illustrate the optimality of decision variables and the objective function. Also, the sensitivity analysis is carried out. Results show that the present value of the annual net revenue of the retailer, manufacturer and SC decreases with increased inflation rate at the retailer and decreased inflation rate at the manufacturer simultaneously.     

Optimal Selection of Machinable Volumes

A brief review of the process planning literature is provided. One of the basic issues in process planning is the feature recognition. In the paper rather than representing a part with features, the representation using machinable volumes is emphasized. A model for the selection of machinable volumes with minimum corresponding machining costs, fixture and tool utilization costs is formulated. The model is illustrated with a numerical example. Computational results for five existing parts are presented.     

Strategies for warranty service in a dual-channel supply chain with value-added service competition

This paper studies a dual-channel supply chain composed of a manufacturer and a retailer. The manufacturer and the retailer sell homogeneous durable goods bundled with warranty service that is provided by the manufacturer, and they compete for customers by offering free value-added service. Both the warranty and value-added services can affect the purchasing behaviour of customers. We examine the warranty service decision of the manufacturer and the value-added service competition between the manufacturer and the retailer. Three types of warranty service strategies that can affect the value-added service competition are proposed. By analysing the equilibriums of the value-added service level decisions of the manufacturer and the retailer, we find that when the manufacturer increases its warranty service level, the value-added service competition will be weakened, and when the warranty service level is high enough, there is no value-added service competition. In addition, we examine the optimal warranty service strategy and warranty service level of the manufacturer under different conditions, and we find that the stronger the manufacturer’s bargaining power is, or the stronger the value-added service competition intensity is, the more motivation the manufacturer has to provide a high warranty service level. Numerical examples reveal that differentiation strategy in value-added service may hurt the profits of the manufacturer, the retailer and the entire supply chain.     

The impact of supply chain visibility when lead time is random

We study the impact of supply chain visibility on periodic review inventory control, by studying its effect on lead time, where lead time is assumed to be random. We break down the total lead time from a supplier to a retailer into individual smaller lead times, as the product is tracked moving from one intermediary location to another. (This can be achieved, for example, through the use of RFID technology.) Under optimality, we observe that the average expected cost per cycle that the retailer can achieve in the long run given supply chain visibility is no worse than that for the base periodic review model without such visibility. An example is given which shows that there is indeed cost savings in the former, as compared with the base model. Further numerical results are then given to quantify the benefits of supply chain visibility on retailer’s cost with defined simple lead-time distributions. We also report on any trends that might appear as input parameters are varied in the numerical experiments.     

Analysis of a deterministic demand production/inventory system under nonstationary supply uncertainty

In this article we investigate a periodic review inventory model under deterministic dynamic demand and supply unavailability. In a given period, supply is either available or completely unavailable with given probabilities. Supply unavailability probabilities are nonstationary over time. We show the optimality of an order-up-to level policy, and obtain a newsboy-like formula that determines the optimal order-up-to levels. Our formula would provide guidence as to the appropriate amount of inventory to stock in the face of uncertainties in the supply process.     

Optimal policy for a periodic review returnable inventory system

In this paper, we consider the inventory control problem in a periodic review returnable system. In a returnable system, containers are returned by consumers to the manufacturer for reuse. We view the returns in a given period to be a stochastic function of the number of containers out in the field. Using dynamic programming, we derive the optimal inventory control policy for the system.     

基于非线性控制理论的突发需求订货策略研究

基于非线性控制理论,建立生产商、分销商和零售商在内的三阶供应链动态订货模型,使用混沌理论的李雅普诺夫指数度量突发需求扩散产生的订货量、库存量和缺货量不确定性.通过仿真软件Simulink比较了突发需求情景下,采用APIOBPCS订货策略和OUT订货策略时的系统不确定性变化.研究发现:在降低突发需求产生的库存量、订货量和...     

The use of rush deliveries in periodic review assemble-to-order systems

We calculate optimal safety stock in a periodic review (T,S) assemble-to-order system having multiple components and multiple finished goods (FGs). Customer orders for FGs arrive according to independent Poisson processes, and cannot be neither backlogged nor lost. In case of potential component stock-out, the studied system uses rush deliveries from suppliers. For this setting, approximate expressions of the optimal safety stock that minimise the sum of inventory holding and rush ordering costs are developed. Exact optimal safety stocks are calculated using Discrete Event Simulation, and compared numerically to the approximate expressions. The model is applied to a first-tier automotive supplier and yields to a significant reduction in terms of inventory holding and rush ordering costs. A sensitivity analysis on relevant system parameters such as components demand, assembly coefficients and unit rush ordering cost is conducted.     

Loading algorithms for flexible manufacturing systems with partially grouped machines

The loading problem in a Flexible Manufacturing System (FMS) involves allocating operations and associated cutting tools to machines for a given set of parts. There may be different environments for the loading problem that result from three ways of grouping machines in an PMS, i.e., no grouping, partial grouping, and total grouping. Unlike most previous studies on the loading problem for the configurations of no grouping and total grouping, this paper focuses on the loading problem resulting from partial grouping, in which each machine is tooled differently but each operation can be processed by one or more machines. Two types of heuristic algorithms are suggested for the loading problem with the objective of minimizing the maximum workload of the machines. Performances of the suggested loading algorithms are tested on randomly generated test problems and the results show that the suggested algorithms perform better than existing ones. In addition, it is found from simulation experiments that loading plans from partial grouping give significantly better performance than those from total grouping.     

违约情形下的信用保单质押融资

为了解决制造商以及零售商均存在资金约束的供应链的融资问题,构建了零售商存在违约的情形时的信用保单质押融资模型。基于报童模型的随机规划问题和博弈论的分析方法,分析了不同利率条件下零售商的订货决策、银行的利率决策以及制造商的投保决策。分析表明,零售商控制本身的违约率,通过合理的订货量获取利润。制造商通过合理的投保水平以及批发价决策来实现本身的效益。银行确定合理的利率以及根据制造商的投保水平来确定融资额度,以求实现自身的利润。制造商以及银行都希望零售商有低的违约率。其中,信用保险对融资中的各方都是有利的。     

Dual-channel supply chain pricing decisions with a risk-averse retailer

This paper investigates a dual-channel supply chain with one risk-neutral manufacturer and one risk-averse retailer where there is only one perishable product with price-dependent stochastic demand. We choose Conditional Value-at-Risk criterion to measure the retailer’s risk-averse level, and assume that the manufacturer’s direct sales channel and the retailer’s traditional channel adopt a consistent pricing strategy. The model explores a Nash bargaining problem where the manufacturer and the retailer negotiate with each other on the wholesale price, the retail price and the order quantity when they have equal bargaining power. It is found that when demand uncertainty follows a uniform distribution, a Nash bargaining equilibrium exists and the retail price will decrease as the retailer becomes more risk averse. However, when the risk-averse indicator increases, the manufacturer’s profit on his direct channel will decrease, increase or first increase and then decrease, depending on the values of the related parameters. The profit shares of the manufacturer and the retailer under the Nash equilibrium model are related to the risk-averse indicator of the retailer. Furthermore, we perform three sets of numerical experiments to verify the effects of the retailer’s risk-averse indicator on decision-making and profit allocations under the different environmental parameters and gain several meaningful managerial insights.