Demand Classes Research Articles

On the effect of two popular service-level measures on the design of a critical level policy for fast-moving items

This paper studies the effect of two service-level measures on the design of a critical-level policy for fast-moving items, where rationing is used to provide differentiated service levels to two classes of demand – high priority and low priority. Using the threshold-clearing mechanism under a strictly increasing non-negative demand to allocate backorders when multiple outstanding orders exist, we formulate service-level problems under type-I, fill-rate, and mixed service-level constraints to determine the optimal parameters of a continuous review (Q, r) policy with constant threshold value C to rationing the low-priority class. Based on several monotone properties, we proposed global search algorithms to solve the service-level problems, which guarantee reaching the globally optimal solution for any desired level of accuracy. Further results and a computational study demonstrate how these different models fare against each other in practice.

Economic Analysis of TWDM PONs: A Sustainability and Policy-Making Perspective

The time- and wavelength-division-multiplexed (TWDM) passive optical network (PON) is a popular choice for future access technology. However, a comprehensive understanding of its economics is still beyond the reach of the current literature. For example, it is not clearly understood which techno-economic factors make this technology sustainable. Similarly, the role of the government in influencing the users' welfare has also remained opaque. In this paper, we uncover these important issues. Portraying the operator as a profit maximizer, we develop a mathematical model that encapsulates both economic and technical aspects of the network. Within this framework, the profit maximization problem of an operator turns out to be a mixed-integer nonlinear program that, in general, is exponentially complex. Fortunately, using a widely accepted assumption on user demand, we reduce this to a discrete optimization. Moreover, for a large class of demands, a polynomially complex algorithm is developed to solve this problem. For homogeneous linear demands, we analytically characterize the system parameters that ensure the sustainability of the network in the long run. In addition, the influence of different system parameters on the economic outcomes is studied. Our investigation reveals several policy-making insights. For example, it unveils a fundamental trade-off between the number of users and the aggregated welfare. Also, it suggests that the leasing of fibers isa better deployment policy for the government as compared to the other alternatives. Finally, we show that the architectural details of the network play a key role in deciding the economics. In particular, one variant of the PON is shown to be more viable than another.

Joint pricing and lot-sizing for a perishable item under two-level trade credit with multiple demand classes

Abstract This paper addresses the differential pricing and lot-sizing problem for a perishable item with multiple demand classes under a two-level trade credit. The distributer sells a single perishable product at different prices to various markets and offers a varied credit period to customers. In the proposed model: (1) the demand rate at each market depends on the selling price, credit period and the price of other complementary and substitute products and (2) the time and temperature parameters affect the deterioration rate. A bi-objective model is developed, which aims to jointly maximize the total profit and minimize the total inventory to assess the supply chain’s inventory performance with multiple demand classes under switching cost constraints. Since most of the parameters are imprecise in nature, a tailored possibilistic programming method based upon the fuzzy measure Me is devised to construct the deterministic counterpart. Several theoretical results are derived which demonstrate the existence and uniqueness of the solution. An efficient search procedure based on the model’s properties is developed to find the pricing and lot-sizing decisions. Then, an efficient multi-objective programming method is used to find efficient compromise solutions. Finally, illustrative examples along with a number of sensitivity analyses are provided to show applicability of the proposed approach and study the influence of key parameters on the model’s performance.

A stochastic multi-channel revenue management model with time-dependent demand

Abstract E-commerce has seen rapid growth in recent years and many firms (e.g., airline companies) sell directly to their customers through different online channels or agents (e.g., Expedia, Ctrip, Qunar, elong) by paying different proportional fees. Besides the firm's revenue management decision of dynamically allocating its limited inventory to different demand classes, it may also get a different margin for selling the same product through different channels (at the same price). This paper examines the firm's optimal channel control strategy with combining its revenue management decision. We propose a multi-period multi-channel continuous-time model with time-dependent arrival rates. The market prices are different in different periods. The firm needs to decide the protection levels for all periods and the channel control strategy in each period. By developing a stochastic (Hamiltonian) channel control system and using the Maximum Principle, the optimal channel control rules are found and a threshold channel control policy is proposed. Based on the channel control policy, we show that there exist the unique optimal protection levels for all periods.

A continuous cost evaluation approach for periodic review inventory systems with threshold rationing policy

Abstract This study analyzes an inventory problem with two stochastic demand classes in a periodic review inventory setting, in which a firm reviews its inventory position periodically and fulfills two Poisson demand classes continuously during periods. This study simultaneously assumes positive lead time and full backorders. An inventory policy consisting of order-up-to policy and threshold rationing policy is adopted, in which the firm places an order to raise its inventory position to order-up-to level in a fixed length of review interval and the inventory is rationed with a threshold level. Specifically, the total demand is served on a first-come first-served basis (FCFS) if its available inventory is above the threshold level. Otherwise, only the high-priority demand class is served. With such an inventory policy, this study provides a novel approach to evaluate the exact long-run expected inventory costs by assuming a threshold backorder clearing mechanism. This evaluation approach can easily incorporate FCFS policy. Furthermore, a method is provided to find the optimal policy parameters. Numerical experiments show that, relative to the FCFS policy and separate policy, the rationing policy can generate significant cost savings.

Managing Perishable Inventory Systems With Age-Differentiated Demand

We consider a periodic-review perishable inventory system with multiple demand classes, each characterized by a different lost-sales cost and a least freshness requirement. Demands of different classes in the same period can be correlated, while demands across periods are independent but not necessarily identical. In each period, the firm jointly makes the decisions regarding inventory issuing, rationing, production/ordering, and disposal. The objective is to minimize the total discounted expected cost over the entire planning horizon including linear ordering cost, inventory holding/lost-sales cost, expiration cost and disposal cost. By establishing new properties of multimodularity, we are able to explore some monotonicity and bounded sensitivity properties of the optimal policies and show that the optimal inventory issuing policy follows the first-in-first-out (FIFO) rule. The optimality analysis enables us to propose a novel heuristic, called adaptive approximation approach, which can be recursively calculated through a single-dimension dynamic program. Numerical studies demonstrate that our proposed approximation approach is nearly optimal with the average optimality gap 0.30% and significantly outperforms existing heuristics studied in the literature. Another important observation from numerical studies is that ignoring customers' freshness requirements can lead to a significant increase in total costs. Our heuristic idea can also be applied to the setting with the last-in-first-out (LIFO) issuing rule and still performs rather well.

Managing Perishable Inventory Systems with Multiple Demand Classes

In this paper, we study a multi-period stochastic perishable inventory system with multiple demand classes that require products of different ages. The firm orders the product with a positive leadtime and sells it to multiple demand classes, each only accepting products with remaining lifetime longer than a threshold. In each period, after demand realization, the firm decides how to allocate the on-hand inventory to different demand classes with different backorder or lost-sale cost. At the end of each period, the firm can dispose inventory of any age. We formulate this problem as a Markov decision process and characterize the optimal ordering, allocation, and disposal policies. When unfulfilled demand is backlogged, we show that the optimal order quantity is decreasing in the inventory levels and is more sensitive to the inventory level of fresher products, the optimal allocation policy is a sequential rationing policy, and the optimal disposal policy is characterized by a set of thresholds. For the lost-sale case, we show that the optimal allocation and disposal policies have the same structure but the optimal ordering policy may be different. Based on the structure of the optimal policy, we develop an efficient heuristic that is at most 4% away from the optimal cost in our numerical examples. Using numerical studies, we show that the ordering and allocation policies are close to optimal even if the firm cannot intentionally dispose products. Moreover, ignoring the difference between demand classes and using a simple allocation policy (e.g., FIFO) can significantly increase the total cost. We examine how the firm can improve the control of perishable items and show that the benefit of decreasing the leadtime is more significant than that of increasing the lifetime of the products or that of decreasing the acceptance threshold of the demand. The analysis is extended to systems with age dependent disposal cost and stochastic supply.

Optimal lateral transshipment policies for a two location inventory problem with multiple demand classes

We consider an inventory model for spare parts with two stockpoints, providing repairable parts for a critical component of advanced technical systems. As downtime costs for these systems are expensive, ready–for–use spare parts are kept in stock to be able to quickly respond to a breakdown of a system. We allow for lateral transshipments of parts between the stockpoints upon a demand arrival. Each stockpoint faces demands from multiple demand classes. We are interested in the optimal lateral transshipment policy. There are three ways in which a demand can by satisfied: from own stock, via a lateral transshipment, or via an emergency procedure. Using stochastic dynamic programming, we characterize and prove the structure of the optimal policy, that is, the policy for satisfying the demands which minimizes the average operating costs of the system. This optimal policy is a threshold type policy, with state-dependent thresholds at each stockpoint for every demand class. We show a partial ordering in these thresholds in the demand classes. In addition, we derive conditions under which the so-called hold back and complete pooling policies are optimal, two policies that are often assumed in the literature. Furthermore, we study several model extensions which fit in the same modeling framework.

Stock optimization for service differentiated demands with fill rate and waiting time requirements

We develop a computationally efficient optimization procedure to optimize stock and rationing levels for a model consisting of a single product with two priority–demand classes, given by mutually independent, stationary, Poisson demand processes. Each priority class has its own service levels requirements, defined by the class-specific fill rate and expected waiting-time levels. Order lead times are independent and identically distributed random variables. This is the first study in this setting to consider both waiting-time constraints along with fill rate requirements.

Shipment consolidation with two demand classes: Rationing the dispatch capacity

We analyze the problem faced by a logistics provider that dispatches shipment orders (parcels or larger packages) of two order classes, viz. expedited and regular. Shipment orders arrive according to a compound Poisson process for each class. Upon an arrival, the logistics provider may continue consolidating arriving orders by paying a holding cost. Alternatively, the provider may dispatch, at a fixed cost, a vehicle containing (a portion of) the load consolidated so far. In addition, the provider must specify the composition of each dispatch by allocating (rationing) the volume of the vehicle between expedited and regular shipment orders. We model this problem as a continuous-time Markov Decision Process and minimize the expected discounted total cost. We prove the existence of quantity-based optimal threshold policies under particular conditions. We also structurally analyze the thresholds of these optimal policies. Based on these structural properties, we develop an efficient solution approach for large problem instances which are difficult to solve using the conventional policy-iteration method. For two real-life applications, we show that the quantity-based threshold policies derived using the proposed approach outperform the time policies used in practice.

On the effect of inventory policies on distribution network design with several demand classes

This paper studies the effect of several inventory policies on the design of a distribution network for fast-moving items able to provide differentiated service levels in terms of product availability for several demand classes. We consider the distribution network design problem when the global round-up, single class allocation, local separate stock, local round-up, and critical level inventory policies are used. We show how to formulate these problems as conic quadratic mixed-integer problems and prove that the critical level policy provides the lowest cost distribution network design. Further results and a computational study show how these different models compare in practice.

The Joint Stock and Capacity Rationings of a Make-To-Stock System with Flexible Demand

This paper studies the joint stock and production capacity rationing polices for a make-to-stock system with two partially substitutable products manufactured at two factories, respectively. Customers are classified into three types with each type further segmented into multiple classes. Type I and Type II customers are selective and accept their favorite products only. Type III accepts either of the two products and hence its demand is regarded as the flexible demand. The management has to decide whether to run or stop production and whether the various classes of demand for each type of customers have to be satisfied from available inventory or not — in which case demand is lost — in order to minimize the firm’s inventory and production costs. We formulate the problem as a make-to-stock queue system and characterize the optimal joint stock and production rationing policies as monotone switching curves. Numerical examples are given to illustrate the optimal policies and demonstrate the value of flexible demand. Moreover, we develop a simple heuristic policy and compare the costs associated with the optimal and heuristic policies for different parameters.

Analysis of Two-Echelon Inventory System with Two Demand Classes with Partial Backlogging

This paper deals with a continuous review two-echelon inventory system with two demand classes. Two echelon inventory systems consist of one retailer (lower echelon) and one distributor (upper echelon) handling a single finished product. The demand at retailer is of two types. The First type of demand is usual single unit and the second type is of bulk or packet demand. The arrival distribution for single and packet demands are assumed to be independent Poisson with rates λ1(>0) and λd (>0) respectively. The operating policy at the lower echelon for the (s, S) that is whenever the inventory level drops to ‘s’ on order for Q = (S-s) items is placed, the ordered items are received after a random time which is distributed as exponential with rate µ>0. We assume that the demands occurring during the stock-out period are lost. The retailer replenishes the stock from the distributor which adopts (0, M) policy. The objective is to minimize the anticipated total cost rate by simultaneously optimizing the inventory level. The joint probability disruption of the inventory levels at retailer and the distributor are obtained in the steady state case. Various system performance measures are derived and the long run total expected inventory cost rate is calculated. Several instances of numerical examples, which provide insight into the behavior of the system, are presented.

An investigation into e-commerce service chain model algorithm

On the basis of the traditional fixed-fee contract, three specific contract forms' models (single contract, menu contract and confused contract) are discussed in service supply chain with effort-sensitive demand and asymmetric information. Under the service supply chain management, there is a class of demands with effort-sensitive members and asymmetric information. While efforts of service supply chain members have impact on market demand, the members can have more choices in pursuing profit maximisation in terms of price, volume and effort level. Under such circumstances, there is one more route to realise service supply chain coordination, namely choosing the suitable effort level in the scope of service effort to realise the balance between pricing and effort level on the basis of negotiated price, volume and effort level. Solutions of the three contract models are optimised and analysed. The solutions' effect and meaning are pointed out for the service supply chain contract forms.

An investigation into e-commerce service chain model algorithm

On the basis of the traditional fixed-fee contract, three specific contract forms' models (single contract, menu contract and confused contract) are discussed in service supply chain with effort-sensitive demand and asymmetric information. Under the service supply chain management, there is a class of demands with effort-sensitive members and asymmetric information. While efforts of service supply chain members have impact on market demand, the members can have more choices in pursuing profit maximisation in terms of price, volume and effort level. Under such circumstances, there is one more route to realise service supply chain coordination, namely choosing the suitable effort level in the scope of service effort to realise the balance between pricing and effort level on the basis of negotiated price, volume and effort level. Solutions of the three contract models are optimised and analysed. The solutions' effect and meaning are pointed out for the service supply chain contract forms.

Water availability and state of water resources within water-economic basins in Kazakhstan

Water is one of the most important natural resources. The water availability and scarcity depend on various natural and anthropogenic factors. Based on generalization and analyses of the numerous cartographic materials, and long-term runoff data, the water-economic basins (WEBs) in Kazakhstan were classified in order to identify the basin affected by human activities the most, to show the dynamics of river runoff within Kazakhstan, as well as to estimate the demand for water resources in the WEBs. Additionally, the water availability in the WEBs was determined by share (%) of water resources (rivers, lakes, water reservoirs). The Zhaiyk-Caspian WEB has the highest share (94%) of river water. By water resource (43.8 km3), the Ertis WEB is the most water-rich basin. A significant anthropogenic transformation was observed in the Aral-Syrdarya and Esil WEBs. Both basins are characterized by a deteriorated water quality. Due to natural factors and human activities, the total runoff decreased by 39.4 km3/year (23 km3/year is transboundary and local runoff is 16.5 km3/year) since 1965. Water consumption has decreased to 57% due to reduction of irrigation areas and industrial activities. However, the water consumption has increased by 1.33 and 1.25 km3/year in communal services and other needs due to the population growth. The water demand in Zhaiyk-Caspian WEB is very high and estimated in crisis degree (fourth class). The Balkash-Alakol WEB is characterized by a critical degree of water demand and belongs to the third class of water demand.

Transshipment policies for systems with multiple retailers and two demand classes

Many retailers discriminate among their customers based on their value to the firm. Instead of losing a customer due to this discrimination or lack of inventory, a retailer might prefer to place a transshipment request with other retailers to satisfy the customer’s demand. The system as a whole can benefit from this type of transshipments. In this paper, we study a problem of a centrally controlled system with multiple retailers. Each retailer serves two types of customers: high priority and low priority. Each retailer employs a rationing policy with a rationing level k in the context of a continuous-review (r, Q) inventory replenishment model. The overall policy is referred to as an (r, k, Q) policy. Retailers can transship items from either other retailers or a more expensive central depot. We propose an enumeration-based approximation to find the cost-minimizing policy parameters for the individual retailers and an approximation procedure to solve the combined rationing and transshipment problem. The latter relies on adjusting the demand arrival rates and the unit transshipment costs for both types of customers at all retailers. An extensive numerical study highlights the impact of transshipments on the retailers’ rationing policies. Without transshipment opportunities among each other, retailers set their policy parameters so that the resulting service levels are high for both types of customers. Allowing transshipments results in more aggressive rationing policies, and retailers with aggressive rationing policies benefit from the transshipments the most.

Integrated multi-site aggregate production-pricing planning in a two-echelon supply chain with multiple demand classes

• Studying an aggregate production-pricing problem with multiple demand classes. • Developing a new demand response function with cannibalization. • Determining optimal price gaps in multi-channel retailing. • Involving a convexification strategy based on convex hulls in the solution algorithm. • Investigating sensitivity of objective function to leakage rates. This paper proposes a production and differential pricing decision model in a two-echelon supply chain that involves a demand from two or more market segments. In this framework, the retailer is allowed to set different prices during the planning horizon. While integrated production-marketing management has been a key research issue in supply chain management for a long time, little attention has been given to set prices and marketing expenditures in integrated multi-site (parallel) manufacturing systems and multiple demand classes. Generally, the presence of multiple demand classes induced by different market segments may impose demand leakage and then change production plan and ordering policies throughout the supply chain system. To tackle this problem, this paper develops a novel approach in order to provide an optimal aggregate production and marketing plan by interconnecting the sales channels of the retailer and demand. A non-linear model is established to determine optimal price differentiation, marketing expenditures and production plans of manufacturing sites in a multi-period, multi-product and multi-sale channels production planning problem by maximizing total profit of the supply chain. To handle the model and obtain solutions, we propose an efficient analytical model based upon convex hulls. Finally, we apply the proposed procedure to a clothing company in order to show usefulness and significance of the model and solution method.

An empirical investigation on the antecedents of the bullwhip effect: Evidence from the spare parts industry

Supply chain effectiveness and costs are affected by the demand variability, especially in the upstream echelons. The propagation of demand variability moving upstream in the supply chain has been widely studied in the literature and it is known as the Bullwhip Effect phenomenon. In this paper, the bullwhip effect in a European automotive spare parts chain is identified, with the aim of shedding some light on how demand variability propagates in different groups of products. We considered more than 30,000 products, characterised by different technical characteristics, demand classes and planning parameters.The results showed that the considered supply chain is affected by the bullwhip effect. Additional analyses suggested that the bullwhip effect is larger for fast moving products rather than for slow movers. Hence, dealers tends to decouple supply and demand and, when they are given incentives to forward-buy, they may prefer to forward-buy fast moving items. Moreover, as the dealers tend to exploit the promotional benefits by forward-buying in the final period of promotions, frequent switches from promotional to non promotional periods tend to increase the propagation of the demand variability.

On the decomposition property for a dynamic inventory rationing problem with multiple demand classes and backorder

In this paper, we study a dynamic inventory rationing problem of a single item with multiple demand classes and backorder. Demand classes are differentiated by their unit backlogging costs. The corresponding dynamic programming problem is multidimensional and computationally challenging. With a novel state transformation, we find that the optimal policy can be described by a nested base stock policy. In particular, we can decompose the value function as the sum of single-variable convex functions. This property breaks the curse of dimensionality and significantly reduces computational effort in computing optimal policies. Our approach allows us to extend the results to systems with ordering, exogenous supply, priority upgrading.