Optimal inventory control of lumpy demand items using (s,S) policies with a maximum issue quantity restriction and opportunistic replenishments

This paper presents a modified (s, S) inventory model which describes the characteristics of an inventory system with lumpy demand items. A maximum issue quantity restriction of w units and a critical inventory position of A units are incorporated into the inventory control policy. Customer orders with demand sizes larger than the maximum issue quantity will be filtered out from the inventory system and satisfied by using special replenishment orders in order to avoid disruption to the inventory system. The option of opportunistic replenishments is introduced to further minimize the total replenishment cost. An opportunistic replenishment is initiated if the level of the current inventory position is equal to or below the critical level when a customer demand with a size exceeding the maximum issue quantity arrives, which does not only initiate a direct shipment to the customer, but also raises the inventory position to S. Two effective algorithms are developed to determine the optimal values of w, A, s and S simultaneously. The first algorithm is based on the branch-and-bound tree search technique, and the second one is based on the concept of genetic algorithms. Numerical examples are used to illustrate the effectiveness of the algorithms developed. The effects of changes in the cost and system parameters on the optimal inventory control policy are also studied by using sensitivity analysis.     

The evolution of family level sales forecasts into product level forecasts: Modeling and estimation

It is frequently the case that sales forecasts are available at the detailed product level for only a relatively short time horizon. For the rest of the forecast horizon, only aggregate sales forecasts at the product family level are available. The problem addressed in this paper is how to fit a forecast simulation model to a history of these aggregate and disaggregate forecasts. Our approach to develop such a model is to combine a forecast update model with a forecast disaggregation model. The forecast update model is called the Martingale model of forecast evolution. The parameters of the two models must be estimated from historical forecast data. It is this statistical parameter estimation problem that occupies the major part of our investigation. We recommend an estimation technique based on the method of moments.     

Forecasting service parts demand for a discontinued product

Stochastic demand forecasting methods for service parts of a discontinued product are proposed. The identified four major factors are the number of product sales, the discard rate of the product, the failure rate of the service part, and the replacement probability of the failed part. During a given period, typically a year, the number of failed service parts is estimated using the first three factors, and then the demand for those service parts is obtained with the use of the last factor. A stochastic model is derived to estimate the demand in a certain prediction interval, and the closed-form solutions in the case of a constant failure rate are provided. An approximate model is proposed to render actual computation possible when the part failure time is not distributed exponentially. Numerical data from the automotive industry are used to validate the model.     

Adaptive exponential smoothing versus conventional approaches for lumpy demand forecasting: case of production planning for a manufacturing line

Production planning in a lumpy demand environment can be tenuous, with potentially costly forecasting errors. This paper addresses the issue of selecting the smoothing factor used in lumpy demand forecasting models. We propose a simple adaptive smoothing approach to replace the conventional industrial practice of choosing a smoothing factor largely based on the analyst or engineer's experience and subjective judgment. The Kalman filter approach developed in this study processes measurements to estimate the state of a linear system and utilises knowledge from states of measurements and system dynamics. Performances of an array of forecasting models that have been shown to work well in lumpy demand environments are compared with respect to the proposed adaptive smoothing factor and the conventional smoothing constant across a spectrum of lumpy demand scenarios. All models using the adaptive smoothing factor based on Kalman filter weighting function generate smaller errors than their conventional counterparts, especially under high lumpiness demand environments. Our proposed approach is particularly useful when production management is concerned about simplicity and transferability of knowledge due to constant personnel turnaround and low retention rate of expertise.     

An application of cost-effective fuzzy inventory controller to counteract demand fluctuation caused by bullwhip effect

This paper develops a fuzzy inventory model to counteract the demand fluctuation in supply demand networks, which combines fuzzy logic controller with (s,?S) policy based on economic order quantity (EOQ) model. Following a literature review and a discussion of counteractions to the bullwhip effect and the obstruction of general counteraction in supply demand networks, a multi-echelon fuzzy inventory model in supply demand networks is proposed. A simulation model with one- and two-echelon supply demand network is built and tested for (s, S) policy based on the classical EOQ model and the proposed fuzzy inventory model. Based on the simulation, results of the relevance performance are presented and discussed, which show that the proposed multi-echelon fuzzy inventory model provides not only a cost-effective management of inventory (e.g. lower inventory levels and cost) in market uncertainty, but also another effective alternative for counteracting demand fluctuation. In particular, the proposed multi-echelon fuzzy inventory model shows benefit in counteracting demand fluctuation in multi-echelon supply demand networks. Finally, some conclusions and suggestions for further research works are presented.     

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.     

Deep reinforcement learning for selecting demand forecast models to empower Industry 3.5 and an empirical study for a semiconductor component distributor

A semiconductor distributor that plays a third-party role in the supply chain will buy diverse components from different suppliers, warehouse and resell them to a number of electronics manufacturers with vendor-managed inventories, while suffering both risks of oversupply and shortage due to demand uncertainty. However, demand fluctuation and supply chain complexity are increasing due to shortening product life cycle in the consumer electronics era and long lead time for capacity expansion for high-tech manufacturing. Focusing realistic needs of a leading distributor for semiconductor components and modules, this study aims to construct a UNISON framework based on deep reinforcement learning (RL) for dynamically selecting the optimal demand forecast model for each of the products with the corresponding demand patterns to empower smart production for Industry 3.5. Deep RL that integrates deep learning architecture and RL algorithm can learn successful policies from the dynamic and complex real world. The reward function mechanism of deep RL can reduce negative impact of demand uncertainty. An empirical study was conducted for validation showing practical viability of the proposed approach. Indeed, the developed solution has been in real settings.     

Optimal introduction time decision for holiday products with uncertain market demand

In this paper, we investigate how retailers with different risk preferences determine the optimal introduction time and order quantity for holiday products to maximise performance in environments characterised by uncertain market demand. Specifically, both the market demand and the accuracy of sales forecasts are assumed to be affected by the timing of the introduction, which in turn affects the order quantity and subsequent performance. The results suggest that as the level of uncertainty in the market demand increases, as the retailer’s power in the industry increases and as the coefficient of elasticity of the competitive demand over introduction time is larger, the retailer prefers to set a later introduction time and to order smaller quantities, to reduce the risk of overstocking. Moreover, a risk-averse retailer will set a later introduction time and order smaller quantities than a risk-neutral retailer. Indeed, the more risk-averse the retailer is, the later will be the introduction time and the smaller the quantity ordered. The managerial implications are presented for decision-makers with different risk preferences regarding the interconnections between important factors and introduction time and inventory decisions for holiday products in environments characterised by uncertain market demand.     

Allocation flexibility for agribusiness supply chains under market demand disruption

This paper develops a multi-commodity multi-period optimisation model to analyse market demand disruption risk in agribusiness supply chains. It investigates the role of allocation flexibility and the effectiveness of multiple risk management strategies for achieving allocation flexibility. A robust optimisation formulation is used to obtain risk-averse solutions for an objective combining expected profit and risk. Numerical results are presented for a real-life case study of Zespri’s kiwifruit supply chain. The results show that allocation flexibility is effective for mitigating market demand disruption risk. Three proposed risk management strategies, namely diversified demand market, backup demand market and flexible rerouting, improve both expected profit and risk measures. While diversified demand market and backup demand market strategies are equally important for all decision-makers, flexible rerouting is especially significant for less risk-averse decision-makers.     

Value of information exchange and synchronization in a multi-tier supply chain

We investigate the value of various information exchange mechanisms in a four-echelon supply chain under a material requirements planning framework. In the absence of any information sharing, each echelon would develop its own forecasts and plan its inventories based on the history of actual demand from its downstream customer (or echelon). Through a simulation study, we compare this policy with policies where each echelon has access to (i) the end-user demand history and (ii) the planned order schedule of the downstream echelon. Among all the demand information exchange mechanisms, planning inventories based on the planned downstream order schedules resulted in the lowest average inventory level for the entire supply chain. However, use of end-user demand history to forecast and plan inventories at all echelons resulted in the lowest total cost. In addition to the information exchange mechanisms, a simple synchronized replenishment system was considered and evaluated in the study. In the synchronized system, the retailer determines a fixed order interval and the upper echelons replenish only at integer multiples of this interval. The study found that synchronized inventory replenishments among the echelons, even without any exchange of demand information, can bring about more benefits and cost reduction than any of the information exchange mechanisms.     

A rolling horizon simulation approach for managing demand with lead time variability

This paper proposes a rolling horizon (RH) approach to deal with management problems under dynamic demand in planning horizons with variable lead times using system dynamics (SD) simulation. Thus, the nature of dynamic RH solutions entails no inconveniences to contemplate planning horizons with unpredictable demands. This is mainly because information is periodically updated and replanning is done in time. Therefore, inventory and logistic costs may be lower. For the first time, an RH is applied for demand management with variable lead times along with SD simulation models, which allowed the use of lot-sizing techniques to be evaluated (Wagner-Whitin and Silver-Meal). The basic scenario is based on a real-world example from an automotive single-level SC composed of a first-tier supplier and a car assembler that contemplates uncertain demands while planning the RH and 216 subscenarios by modifying constant and variable lead times, holding costs and order costs, combined with lot-sizing techniques. Twenty-eight more replications comprising 504 new subscenarios with variable lead times are generated to represent a relative variation coefficient of the initial demand. We conclude that our RH simulation approach, along with lot-sizing techniques, can generate more sustainable planning results in total costs, fill rates and bullwhip effect terms.     

Active demand management for substitute products through price optimisation

This paper presents a systematic mathematical programming approach for active demand management in process industries. The proposed methodology aims to determine optimal pricing policies as well as output levels for substitute products, while taking into consideration manufacturing costs, resource availability, customer demand elasticity, outsourcing and market competition. First, profit maximisation analytical formulae are derived for determining Nash equilibrium in prices for a duopolistic market environment where each company produces only one product. An iterative algorithm is then proposed so as to determine the decision-making process by solving a series of non-linear mathematical programming (NLP) models before determining the Nash equilibrium in prices for the competing companies. The proposed algorithm is extended in order to accommodate the case of multi-product companies, each one selling a set of substitute products at different prices. The applicability of the proposed methodology is demonstrated by a number of illustrative examples.     

On the demand distributions of spare parts

Spare parts have become ubiquitous in modern societies, and managing their requirements is an important and challenging task with tremendous cost implications for the organisations that are holding relevant inventories. Demand for spare parts arises whenever a component fails or requires replacement, and as such the relevant patterns are different from those associated with ‘typical’ stock keeping units. Such demand patterns are most often intermittent in nature, meaning that demand arrives infrequently and is interspersed by time periods with no demand at all. A number of distributions have been discussed in the literature for representing these patterns, but empirical evidence is lacking. In this paper, we address the issue of demand distributional assumptions for spare-parts management, conducting a detailed empirical investigation on the goodness-of-fit of various distributions and their stock-control implications in terms of inventories held and service levels achieved. This is an important contribution from a methodological perspective, since the validity of demand distributional assumptions (i.e. their goodness-of-fit) is distinguished from their utility (i.e. their real-world implications). Three empirical datasets are used for the purposes of our research that collectively consist of the individual demand histories of approximately 13,000 SKUs from the military sector (UK and USA) and the Electronics Industry (Europe). Our investigation provides evidence in support of certain demand distributions in a real-world context. The natural next steps of research are also discussed, and these should facilitate further developments in this area from an academic perspective.     

Issues on the reduction of demand variance in the supply chain

To streamline an agile manufacturing system of a global firm facing a high demand of market service, supply chain management (SCM) plays an important role. In SCM, a phenomenon called ‘the bullwhip effect’ has attracted considerable attention. This study examines the bullwhip effect caused by order variance from retailers. It shows that based on portfolio theory, supplier's demand variance can be reduced by adjusting the order quantities of retailers through co-ordination. The results indicate that our approach can be a useful means for alleviating the bullwhip effect.     

Quantity discounts in single-period supply contracts with asymmetric demand information

We investigate how a supplier can use a quantity discount schedule to influence the stocking decisions of a downstream buyer that faces a single period of stochastic demand. In contrast to much of the work that has been done on single-period supply contracts, we assume that there are no interactions between the supplier and the buyer after demand information is revealed and that the buyer has better information about the distribution of demand than does the supplier. We characterize the structure of the optimal discount schedule for both all-unit and incremental discounts and show that the supplier can earn larger profits with an all-unit discount.     

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.     

Integrated DNC: A case study

With the development of CNC, communication and CIM technology, the connotation and functions of DNC have been greatly enlarged. In order to describe the features and development of contemporary DNC, a new concept, integrated DNC, is presented in this paper. The connotation of integrated DNC and other relative concepts are discussed. Four control architectures of integrated DNC are proposed, including bi-hierarchies, tri-hierarchies, quadri-hierarchies and acrossshops architectures. A case study of integrated DNC is introduced.     

A study on capacity allocation scheme with seasonal demand

This paper studies a game-theoretical capacity allocation problem in a two-echelon supply chain comprised of one supplier and N retailers. With demand fluctuating seasonally and significantly, supply is sufficient in low-demand periods but is insufficient in high-demand periods, especially when the supplier’s capacity decreases in high-demand periods. Retailers compete for the supplier’s capacity in high-demand periods, but do not want to absorb the supplier’s redundant capacity in low-demand periods. A turn-and-earn allocation scheme is proposed to encourage retailers to increase their order quantity in low-demand periods. Under the turn-and-earn allocation scheme, in high-demand periods, the supplier is willing to offer a guaranteed portion of supply capacity for the primary retailer. The remaining capacity in high-demand periods is allocated based on orders retailers placed in low-demand periods. In response, the retailers will decide how much they should order in low-demand periods. Then, a competitive game based on Nash equilibrium among the supplier and her retailers is analysed. In order to solve the problem of unreasonable distribution of interest caused by competition, a contract is designed to make it possible for subsidy to be transferred from the supplier to the retailers. Usually, the supplier and her primary retailer can both be better off under turn-and-earn allocation compared with fixed allocation, and the system efficiency in Nash solution is close to it in optimal solution. A numerical study is also conducted to discuss the parties’ sensitivity to different demand level and guaranteed allocation portion of capacity.     

Mean-based error measures for intermittent demand forecasting

To compare different forecasting methods on demand series, we require an error measure. Many error measures have been proposed, but when demand is intermittent some become inapplicable because of infinities, some give counter-intuitive results, and there is no agreement on which is best. We argue that almost all known measures rank forecasters incorrectly on intermittent demand series. We propose several new error measures with almost no infinities, and with correct forecaster ranking on several intermittent demand patterns. We call these ‘mean-based’ error measures because they evaluate forecasts against the (possibly time-dependent) mean of the underlying stochastic process instead of point demands.     

MILP-based campaign scheduling in a specialty chemicals plant: a case study

Supply chain management in chemical process industry focuses on production planning and scheduling to reduce production cost and inventories and simultaneously increase the utilization of production capacities and the service level. These objectives and the specific characteristics of chemical production processes result in complex planning problems. To handle this complexity, advanced planning systems (APS) are implemented and often enhanced by tailor-made optimization algorithms. In this article, we focus on a real-world problem of production planning arising from a specialty chemicals plant. Formulations for finished products comprise several production and refinement processes which result in all types of material flows. Most processes cannot be operated on only one multi-purpose facility, but on a choice of different facilities. Due to sequence dependencies, several batches of identical processes are grouped together to form production campaigns. We describe a method for multicriteria optimization of short- and mid-term production campaign scheduling which is based on a time-continuous MILP formulation. In a preparatory step, deterministic algorithms calculate the structures of the formulations and solve the bills of material for each primary demand. The facility selection for each production campaign is done in a first MILP step. Optimized campaign scheduling is performed in a second step, which again is based on MILP. We show how this method can be successfully adapted to compute optimized schedules even for problem examples of real-world size, and we furthermore outline implementation issues including integration with an APS.