Optimal safety stock levels of subassemblies and manufacturing components

In order to control the time to market and manufacturing costs, companies produce and purchase many parts and components before receiving customer orders. Consequently, demand forecasting is a critical decision process. Using modular product design and super bills of materials are two effective strategies for developing a reliable demand forecasting process. They reduce the probability of stockouts in diversified production contexts. Furthermore, managing and controlling safety stocks for pre-assembled modules provide an effective solution to the problem of minimizing the effects of forecast errors. This paper develops, evaluates, and applies innovative cost-based analytical models so that the optimal safety stock of modular subassemblies and components in assembly to order and manufacturing to order systems, respectively, can be rapidly quantified. The implementation of the proposed models in two industrial case applications demonstrates that they significantly reduce the safety stock inventory levels and the global logistical cost.     

Stocking decisions for repairable spare parts pooling in a multi-hub system

This paper presents an analytical model for determining spare parts stocking levels in a single-item, multi-hub, multi-company, repairable inventory system in which complete pooling of stock is permitted among the hubs and companies. The objective is to minimize the total system cost which consists of inventory holding cost, downtime cost and transshipment cost. We develop an approximation method to compute the logistical system performance measures needed for calculating the cost function. To find the optimal stocking levels, a two-stage solution is proposed. In the first stage, the demands at all hubs are aggregated and treated as if occurring at a single location. The optimal number of total spare parts is determined by minimizing the sum of inventory holding cost and downtime cost. In the second stage, a heuristic procedure is developed to find the optimal allocation of the total spare parts to minimize the total transshipment cost.     

EOQ models for a coordinated two-level international supply chain considering imperfect items and environmental impact

For a two-level supply chain, models are presented to determine the optimal production-shipment policy for items with imperfect quality in three different scenarios: (a) both the vendor and the buyer are in the same country, (b) the vendor and the buyer are in different countries where the stochastic behavior of the exchange rate between the two countries is modeled using a mean-reverting process, and (c) environmental impact is incorporated in determining the optimal production-shipment policy by taking into account the fixed and variable carbon emission costs. The objective is to minimize the total expected cost per unit time. For each scenario, considering equal shipment size, the total expected cost per unit time is derived and the solution procedure is proposed. Numerical examples are presented and the results are discussed.     

A serial supply chain of newsvendor problem with safety stocks under complete and partial information sharing

We consider a supply chain where multiple members are serially connected. The decision is to determine the ordering quantity of a member to the next upstream member in the supply chain. The basic cost model is similar to the newsvendor problem with additional consideration to safety stock. This paper presents optimal approaches for coordination of the supply chain under both complete and partial information sharing in order to maximize the total expected benefit. For complete information sharing we develop an optimal coordination algorithm. For partial information sharing, we propose an optimal coordination algorithm based on the Alternating Direction Method and the Diagonal Quadratic Approximation Method. A numerical example is discussed to show the optimal convergence of ordering quantities and discuss the properties of the proposed algorithms.     

Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand

This paper studies alternative methods for reducing lead time and their impact on the safety stock and the expected total costs of a (Q,s) continuous review inventory control system. We focus on a single-vendor-single-buyer integrated inventory model with stochastic demand and variable, lot size-dependent lead time and assume that lead time consists of production and setup and transportation time. As a consequence, lead time may be reduced by crashing setup and transportation time, by increasing the production rate, or by reducing the lot size. We illustrate the benefits of reducing lead time in numerical examples and show that lead time reduction is especially beneficial in case of high demand uncertainty. Further, our studies indicate that a mixture of setup time and production time reduction is appropriate to lower expected total costs.     

A discounted cash flow approach to the base stock inventory model

A widespread approach to inventory modelling is to associate costs with measures of system performance and determine the control policy which minimises the long run average cost per unit time. This type of approach ignores the impact of a control policy on the timing of the cash flows associated with payments to suppliers and revenue streams from customers. The approach in this paper is to concentrate on cash flows and determine the control policy which maximises the expected net present value of the cash flows associated with a demand, valued at the time when that demand occurs. There is a Poisson demand process, a fixed lead time, unsatisfied demand is backordered and the system is controlled using a base stock policy. A solution procedure is given and a comparison is made with an equivalent simple interest model and with the standard cost model with linear holding and shortage costs.     

A JIT lot-splitting model for supply chain management: Enhancing buyer–supplier linkage

This study develops a buyer–supplier coordination model to facilitate frequent deliveries in small lot sizes in a manufacturing supply chain. The proposed model, based on the integrated total relevant costs of both buyer and supplier, determines optimal order quantity, the number of deliveries/setups, and shipping quantity over a finite planning horizon in a relatively simple JIT single buyer single supplier scenario. Under deterministic conditions for a single product, we show that the optimal delivery policy adopted by both buyer and supplier in a cooperative manner can be economically beneficial to both parties. It is shown that the optimal delivery size can be unique, regardless of the order quantity and the number of deliveries. Numerical results are also presented.     

Integrating noncyclical preventive maintenance scheduling and production planning for a single machine

This paper deals with the problem of integrating noncyclical preventive maintenance and tactical production planning for a single machine. We are given a set of products that must be produced in lots during a specified finite planning horizon. The maintenance policy suggests possible preventive replacements at the beginning of each production planning period, and minimal repair at machine failure. The proposed model determines simultaneously the optimal production plan and the instants of preventive maintenance actions. The objective is to minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. The problem is solved by comparing the results of several multi-product capacitated lot-sizing problems. The value of the integration and that of using noncyclical preventive maintenance when the demand varies from one period to another are illustrated through a numerical example and validated by a design of experiment. The later has shown that the integration of maintenance and production planning can reduce the total maintenance and production cost and the removal of periodicity constraint is directly affected by the demand fluctuation and can also reduce the total maintenance and production cost.     

Analysis of the newsboy problem with fuzzy demands and incremental discounts

This paper proposes an analysis method for the single-period (newsboy) inventory problem with fuzzy demands and incremental quantity discounts. In fuzzy environments, the availability of the quantity discount makes the analysis of the associated model more complex. The proposed analysis method is based on ranking fuzzy number and optimization theory. By applying the Yager ranking method, the fuzzy total cost functions with different unit purchasing costs are transformed into convex piecewise nonlinear functions. To effectively and efficiently find the optimal inventory policy, the proofs of two properties regarding the relative position between the price break and minimums of these nonlinear functions are proposed. The closed-form solutions to the optimal order quantities are also derived. Four cases of a numerical example are solved to demonstrate the validity of the proposed analysis method. It is clear that the proposed methodology is applicable to further cases with different types of quantity discounts and other more complicated cases. More importantly, managerial implications are also provided for decision-makers’ references.     

A heuristic algorithm for a multi-product dynamic lot-sizing and shipping problem

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order (product) placed in a period is immediately shipped by some containers in the period and the total freight cost is proportional to the number of containers used. It is also assumed that backlogging is not allowed. The objective of this study is to simultaneously determine the lot-sizes and the transportation policy that minimizes the total costs, which consist of production cost, inventory holding cost, and freight cost. Because this problem is NP-hard, a heuristic algorithm with an adjustment mechanism is proposed based on the optimal solution properties. The computational results from a set of simulation experiment are also presented.     

Evaluation of two simple extreme transshipment strategies

We consider an organization that has more than one outlet (retailer or regional warehouse) where stock is held to meet customer demands. In such a situation, transshipments can be used to improve customer service and/or reduce the aggregate stock required. Unfortunately, the determination of an optimal transshipment policy (i.e. when to transship and how much) is a complex mathematical problem. However, in earlier research the authors observed that choosing the better of two extreme policies leads to performance that is nearly as good as a more complex analysis that takes account of the future impact of a transshipment on the cost at the location sending the shipment. These extreme policies are (i) never transship and (ii) always transship when there is a shortage at one location and stock available at another. In this paper, for the case of two stocking points, we develop an analytical approach for approximately estimating the total expected costs (carrying, replenishment, transshipments and lost sales) of these two policies. This provides a mechanism for choosing between the two policies for any given set of problem characteristics. The results of a numerical experiment are shown.     

Base stock policies with degraded service to larger orders

We study an inventory system controlled by a base stock policy assuming a compound renewal demand process. We extend the base stock policy by incorporating rules for degrading the service of larger orders. Two specific rules are considered, denoted as Postpone(q,t) and Split(q), respectively. The parameter q distinguishes between regular orders (of size less than or equal to q) and larger orders. We develop mathematical expressions for the performance measures: order fill rate of the regular orders and average on-hand inventory level. We make numerical experiments where the postpone parameter t and the base stock levels of each rule are such that all customers (of both order types) are indifferent between the two rules. When comparing the difference in the average on-hand inventory levels, we can then make an assessment of the threshold value of the cost of splitting an order (which may otherwise be hard to quantify) in the rule Split(q). Our numerical results indicate that this threshold value is increasing in the variance of the order sizes. Based on the numerical experiment our conclusion is therefore that when the variance of the order sizes is low, then Postpone(q,t) seems to be a good option, while when the variance is high, then Split(q) is more competitive.     

Integrated safety stock optimization for multiple sourced stockpoints facing variable demand and lead time

The safety stock placement problem of a multi-stage supply chain comprising multiple sourced stockpoints is addressed in this paper. Each stockpoint faces variability in its downstream demand and suppliers' lead time. The maximum among these suppliers' lead time is determined by employing concepts of order statistics. It is required to find the fill rate and safety stocks at each stockpoint that leads to satisfying the end customer service level at minimum safety stock placement cost. Hence, the fill rates and the safety amounts are decided from a global supply chain perspective. Two models are proposed; a decentralized safety stock placement model and a centralized consolidation model. The decentralized model finds the safety amounts at each stockpoint required to face its underlying lead time demand variability. The consolidation model finds the consolidated safety amounts that will be kept in the relevant consolidation center at each stage. A Benders decomposition technique is developed to handle the nonlinearity and binary restrictions involved in the safety stock consolidation model. Strategies proposed by the consolidation model achieve 45.2-62% reduction in safety amounts that results in a cost savings ranging between 22.2-44.2% as compared to the strategies proposed by the decentralized model.     

The Year in Review: Economics at the Antitrust Division, 2006–2007

In this paper, we evaluate the scope of Chadwick’s claim on the superiority of competition for the market over competition in the market under incomplete information. We firstly characterize the expected outcome achieved under competition in the market at a Cournot Bayesian-Nash equilibrium. Then we characterize the optimal expected outcome achieved under a competition for the market mechanism designed by a government facing a shadow cost of public funds. We show that a regulated monopoly selected by an auction mechanism results in higher expected welfare than does duopoly competition when the entry cost is low but that the opposite holds when the market size is small and the entry cost is high for some values of the shadow cost of public funds. These results are explained by the influence of adverse selection on the entry decision at the Cournot equilibrium and by the level of expected total fixed costs in both mechanisms.      

AN INVENTORY MODEL FOR DETERIORATING ITEMS WITH STOCK-DEPENDENT DEMAND UNDER THE CONDITIONS OF INFLATION AND TIME-VALUE OF MONEY

In this paper, we incorporate the effects of inflation and time-value of money in inventory decision making when demand, at each time moment rather than being constant, is considered to be dependent upon current stock level. In addition, the shortages are neither completely backlogged nor completely lost assuming the backlogging rate to be linearly dependent on the amount of demand backlogged. We shall be concerned with finding the optimal number of replenishments and service rate to minimize the total relevant costs over a finite planning horizon. Numerical examples are presented to illustrate the proposed models.     

On the interaction between forecasting and stock control: The case of non-stationary demand

The effect of using estimated (forecast) demand parameters on the performance of an inventory control system is an intriguing and important subject. Recent research has been undertaken on this phenomenon assuming stationary demand data. In this paper we extend the research to non-stationary demands, by means of simulation. The case of a periodic order-up-to-level inventory system is considered and the experimental structure allows us to evaluate in a progressive manner the accumulated effect of using the optimal forecasting method, optimal forecast parameters and correct variance expression procedures. The results allow insights to be gained into operational issues and demonstrate the scope for improving stock control systems.     

Economic lot-sizing and dynamic quantity competition

We study a problem of dynamic quantity competition in continuous time with two competing retailers facing different replenishment cost structures. Retailer 1 faces fixed ordering costs and variable procurement costs and all inventory kept in stock is subject to holding costs. Retailer 2 only faces variable procurement costs. Both retailers are allowed to change their sales quantities dynamically over time. Following the structure of the economic order quantity (EOQ) model, retailer 1 places replenishment orders in batches and retailer 2 follows a just-in-time (JIT) policy. The objective of both retailers is to maximize their individual average profit anticipating the competitor's replenishment and output decisions. The problem is solved by a two-stage hierarchical optimization approach using backwards induction. The second-stage model is a differential game in output quantities between the two retailers for a given cycle length. At the first stage, the replenishment policy is determined. We prove the existence of a unique optimal solution and derive an open-loop Nash equilibrium. We show that both retailers follow contrary output strategies over the order cycle. The EOQ retailer, driven by inventory holding costs, decreases his market share whereas the output of the JIT retailer increases. Moreover, depending on the cost structure, the EOQ retailer might partially be a monopolist. At the first stage, the EOQ retailer determines the cycle length, anticipating the optimal output trajectories at the second stage.     

A continuous model for supply planning of assembly systems with stochastic component procurement times

This paper studies a customized product assembly scenario where some components cannot be stocked due to high component cost and risk. We consider the case where these key components are ordered after a demand has been registered with a promised delivery date. Component lead-times are stochastic and associated distribution function is known in advance. The objective is to determine the ordering time for each component such as to minimize the sum of expected holding and backlogging costs. An approach to solve this problem is proposed and the algorithm is tested on a randomly generated data set.     

Strategic safety stock placement in supply chain design with due-date based demand

We present a strategic safety stock placement model in supply chain design for assembly-type product with due-date based demand, where demand data are based on dates when company has to ship to customers rather than order receiving dates. We formulate multi-echelon stock placement by guaranteed-service model with demand propagation equations through backward explosion, where demand can be either stationary or nonstationary. The stock placement model is incorporated into network design problem and its optimization procedure is provided. We show effectiveness of the optimization procedure and other significant features of the model through numerical examples of a machinery product supply chain.     

OPTIMAL ECONOMIC TOOL REGRINDING WITH TAGUCHI'S QUALITY LOSS FUNCTION

One of the major cost components in tool economics is the cost incurred due to deviation in workpiece quality as a result of poor tool-cutting conditions. Commonly, the operating conditions of a culling tool may be restored via regrinding during periodic intervals of the tool's life. This paper proposes that optimal regrinding interval ought to be determined with respect to the optimal number of regrindings. The product of these two values defines the economic life of a tool. The objective function is the minimization of the sum of the expected costs of failure, regrinding, tool purchase, machining, and deviation in workpiece quality. The cost of deviation in workpiece quality is modelled using Tagucbi's loss function. The effect of cutting speed on tool regrinding interval is also explored.