Assortment and inventory decisions with multiple quality levels

We consider the assortment and inventory decisions of a retailer under a locational consumer choice model where products can be differentiated both horizontally (e.g., color of a product) and vertically (e.g., quality of a product). The assortment and quantity decisions affect customer choice and, hence, the demand and sales for each product. In this paper, we investigate two different environments where product availability and assortment affect consumer choice and demand in different ways: make-to-order (MTO) and make-to-stock (MTS). In the MTO environment, customers order and purchase their most preferred product; that is, stockouts do not occur. In the MTS model, customers buy their most preferred product if it is in stock or do not buy if it is out of stock. In both environments we find conditions under which it is optimal to carry assortments of only a single quality level. In the MTS case, we show that an assortment of mixed quality levels can be optimal only within a narrow range of parameters.     

A heuristic for triggering emergency orders in an inventory system

This paper considers a single-echelon inventory system with a warehouse facing compound Poisson customer demand. Normally the warehouse replenishes from an outside supplier according to a continuous review reorder point policy. However, it is also possible to use emergency orders. Such orders incur additional costs but have a much shorter lead time. We consider standard holding and backorder costs as well as ordering costs. A heuristic decision rule for triggering emergency orders is suggested. The decision rule minimizes the expected costs under the assumption that there is only a single possibility for an emergency replenishment, but the rule is used repeatedly as a heuristic. Given a certain reorder point policy for normal replenishments, our decision rule will always reduce the expected costs. A simulation study illustrates that the suggested technique performs well under different conditions.     

Competitive queue policies for differentiated services

We consider the setting of a network providing differentiated services. As is often the case in differentiated services, we assume that the packets are tagged as either being a high priority packet or a low priority packet. Outgoing links in the network are serviced by a single FIFO queue.Our model gives a benefit of α1 to each high priority packet and a benefit of 1 to each low priority packet. A queue policy controls which of the arriving packets are dropped and which enter the queue. Once a packet enters the queue it is eventually sent. The aim of a queue policy is to maximize the sum of the benefits of all the packets it sends.We analyze and compare different queue policies for this problem using the competitive analysis approach, where the benefit of the online policy is compared to the benefit of an optimal offline policy. We derive both upper and lower bounds for the policies we consider. We believe that competitive analysis gives important insight to the performance of these queuing policies.     

Management of the risk of backorders in a MTO–ATO/MTS context under imperfect requirements

Production systems are often classified according to the way production is released, e.g. make-to-stock (MTS), make-to-order (MTO), assembly-to-order (ATO) or engineer-to-order (ETO). The choice of a type of production depends on the decoupling point between customer and supplier. In some supply chains, like in the aeronautical sector, a customer may work according to a MTO process (since his product is highly specific) while his supplier works with a MTS process (since he delivers variants of standards components). This situation sets specific problems that are seldom considered in the literature, especially when collaboration between actors is required for an efficient management of the supply chain, which is the case when uncertainties are present. In this paper, we propose a method based on fuzzy modelling allowing a customer to choose a plan taking into account the uncertainty on his requirements when he works in MTO–ATO while his supplier is in MTS.     

服务水平约束下双需求类静态配给策略

考虑一个周期盘点、无限期、缺货回补、双需求类的库存系统,其中高优先级需求的目标服务水平较高。系统采用基准库存策略补充库存,依据静态配给策略分配库存,即优先满足高优先级需求,仅当持有库存水平不低于固定配给阈值时满足低优先级需求。优化目标是在服务水平约束下最小化期望库存持有量。为提升计算效率,引入“预留库存假设”,即允许通过提高低优先级需求缺货水平的方式补充库存,使得期末持有库存水平不低于本期高优先级需求缺货水平与固定配给阈值之和。基于预留库存假设,给出两类需求服务水平和期望库存持有量的解析表达式,证明上述绩效指标关于控制参数的单调性,刻画满足服务水平约束的控制参数可行域,得到原系统最优控制参数的近似求解算法。算例分析表明,基于预留库存假设的绩效衡量方法和参数求解算法准确性好且计算效率高。     

Optimization of setup times in the furniture industry

The aim of this paper is to develop a scheduling policy oriented towards minimizing setup times in the made-to-order furniture industry. The task is treated as a dynamic job shop scheduling problem, with the exception that customers?? orders collected over a?specified period of time are combined into a?production plan and released together. A?simulation of a production flow based on technological routes of real subassemblies was performed. The proposed method of calculating a setup time eliminates the need to determine machine setup time matrices. Among the tested priority rules the best performance was observed in the case of the hierarchical rule that combines similar setup, the earliest due date and the shortest processing time. This rule allowed the setup time per operation to be reduced by 58?% compared to a combination of the earliest due date with the shortest setup and processing time rule and by over 70?% compared to the single shortest processing time rule.     

Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies

We consider a multi-item inventory system with dependent item demands represented by a multivariate normal distribution and filled under a First-Come-First-Served rule. Each item is managed independently through a periodic review order-up-to policy while all items have the same review cycle. We obtain the joint demand fulfillment probability within a pre-specified time window. We also study the problem of maximizing the joint demand fulfillment probability and discuss a heuristic approach in which equal safety factors (equal fractiles) are specified for all items. Finally we present numerical results and an application with actual data.     

Reinforcement learning for joint pricing,lead-time and scheduling decisions in make-to-order systems

The paper investigates a problem faced by a make-to-order (MTO) firm that has the ability to reject or accept orders, and set prices and lead-times to influence demands. Inventory holding costs for early completed orders, tardiness costs for late delivery orders, order rejection costs, manufacturing variable costs, and fixed costs are considered. In order to maximize the expected profits in an infinite planning horizon with stochastic demands, the firm needs to make decisions from the following aspects: which orders to accept or reject, the trade-off between price and lead-time, and the potential for increased demand against capacity constraints. We model the problem as a Semi-Markov Decision Problem (SMDP) and develop a reinforcement learning (RL) based Q-learning algorithm (QLA) for the problem. In addition, we build a discrete-event simulation model to validate the performance of the QLA, and compare the experimental results with two benchmark policies, the First-Come-First-Serve (FCFS) policy and a threshold heuristic policy. It is shown that the QLA outperforms the existing policies.     

A real-time decision rule for an inventory system with committed service time and emergency orders

In this paper, we study the inventory system of an online retailer with compound Poisson demand. The retailer normally replenishes its inventory according to a continuous review (nQ, R) policy with a constant lead time. Usually demands that cannot be satisfied immediately are backordered. We also assume that the customers will accept a reasonable waiting time after they have placed their orders because of the purchasing convenience of the online system. This means that a sufficiently short waiting time incurs no shortage costs. We call this allowed waiting time “committed service time”. After this committed service time, if the retailer is still in shortage, the customer demand must either be satisfied with an emergency supply that takes no time (which is financially equivalent to a lost sale) or continue to be backordered with a time-dependent backorder cost. The committed service time gives an online retailer a buffer period to handle excess demands. Based on real-time information concerning the outstanding orders of an online retailer and the waiting times of its customers, we provide a decision rule for emergency orders that minimizes the expected costs under the assumption that no further emergency orders will occur. This decision rule is then used repeatedly as a heuristic. Numerical examples are presented to illustrate the model, together with a discussion of the conditions under which the real-time decision rule provides considerable cost savings compared to traditional systems.     

Scheduling policies in the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/1 make-to-stock queue

In this paper, we analyse a production/inventory system modelled as an M/G/1 make-to-stock queue producing different products requiring different and general production times. We study different scheduling policies including the static first-come-first-served, preemptive and non-preemptive priority disciplines. For each static policy, we exploit the distributional Little's law to obtain the steady-state distribution of the number of customers in the system and then find the optimal inventory control policy and the cost. We additionally provide the conditions under which it is optimal to produce a product according to a make-to-order policy. We further extend the application area of a well-known dynamic scheduling heuristic, Myopic(T), for systems with non-exponential service times by permitting preemption. We compare the performance of the preemptive-Myopic(T) heuristic alongside that of the static preemptive-bμ rule against the optimal solution. The numerical study we have conducted demonstrates that the preemptive-Myopic(T) policy is superior between the two and yields costs very close to the optimal.     

Modified base-stock policies for semiconductor production system with dependent yield rates

We consider a two-stage production system faced by semiconductor manufacturing which produces a hierarchy of multiple grades of outputs. In the first stage, a single type of input (wafer) is used to produce multiple types of semi-finished parts with dependent yield rates, and in the second stage, each type of semi-finished parts can be transformed into a corresponding type of final products, or downgraded to a type of lower grade final products. Random customer demands are faced on the final products, and demands of different types of final products are not allowed to be substituted. The advantage of this production system is that it can prevent unhealthy ordering from customers who intentionally send out false demand signals for high grade products and revise the orders to lower grade products when the delivery time is close, which was observed in semiconductor manufacturing. The objective of the study is to plan the quantity of the input at the first stage and the respective downgrade quantities at the second stage so as to meet the required service level at the minimum cost. With some common assumptions, we propose a modified base-stock policy for this two-stage production system and show that the occurrence of nil excess inventory above the base-stock level follows a renewal process. We further extend the modified base-stock policy to a better policy that invokes risk pooling over multiple grade products. The performance of these two polices are evaluated via simulation to provide managerial insights.     

清理策略下有优先权排队的M_2/G_2/1重试排队系统

在有负顾客到达可清空优先权排队中的全部顾客的机制下,研究了M_1,M_2/G_1,G_2/1重试排队系统.假设两类顾客的到达分别服从独立的泊松过程,如服务器忙,优先级高的顾客则排队等候服务,而优先级低的顾客只能进入Orbit中进行重试,直到重试成功.此外,假设负顾客的到达服从Poisson过程,当负顾客到达系统时,若发现服务台忙,将带走正在接受服务的顾客及优先权队列中的顾客.若服务台空闲,则负顾客立即消失,对系统没有任何影响.应用补充变量及母函数法给出了该模型的稳态解的拉氏变换表达式.     

Single vehicle routing problems with a predefined customer sequence, compartmentalized load and stochastic demands

We consider the problem of finding the optimal routing of a single vehicle that delivers K different products to N customers according to a particular customer order. The demands of the customers for each product are assumed to be random variables with known distributions. Each product type is stored in its dedicated compartment in the vehicle. Using a suitable dynamic programming algorithm we find the policy that satisfies the demands of the customers with the minimum total expected cost. We also prove that this policy has a specific threshold-type structure. Furthermore, we investigate a corresponding infinite-time horizon problem in which the service of the customers does not stop when the last customer has been serviced but it continues indefinitely with the same customer order. It is assumed that the demands of the customers at different tours have the same distributions. It is shown that the discounted-cost optimal policy and the average-cost optimal policy have the same threshold-type structure as the optimal policy in the original problem. The theoretical results are illustrated by numerical examples.     

Single machine scheduling with exponential learning functions

In this paper we consider the single machine scheduling problem with exponential learning functions. By the exponential learning functions, we mean that the actual job processing time is a function of the total normal processing times of the jobs already processed. We prove that the shortest processing time (SPT) rule is optimal for the total lateness minimization problem. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms. It also shows that the problems of minimizing the total tardiness and discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.     

Approximation results in parallel machnies stochastic scheduling

We consider scheduling a batch of jobs with stochastic processing times on parallel machines. We derive various new formulae for the expected flowtime and weighted flowtime under general scheduling rules. Smith's Rule, which orders job starts by decreasing ratio of weight to expected processing time provides a natural heuristic for this problem. We obtain a bound on the worst case difference between the expected weighted flow time under Smith's Rule and under an optimal policy. For a wide class of processing time distributions, this bound is of oderO(1) and does not increase with the number of jobs.This research was supported in part by NSF Grant ECS-8712798.     

Dynamic priority rule-based forward-backward heuristic algorithm for resource levelling problem in construction project

Resource levelling aims at minimizing the fluctuation of resource usage, which is accomplished by shifting non-critical activities within their float according to some heuristic rules. Most of these rules adopted a unidirectional scheduling based on a static priority rule. In this paper, we propose a dynamic priority rule-based forward-backward heuristic algorithm (FBHA). The FBHA optimizes resource allocation by shifting non-critical activities within their forward free float (FFF), forward total float (FTF) and backward free float (BFF), successively. A project is divided into several phases during each forward/backward scheduling module. In each phase, the shifting sequence and days of non-critical activities depend on a dynamic priority rule set. The FBHA is integrated into the Microsoft Project 2007 commercial software package to improve the performance of the software and facilitate the project planners. One example is analysed to illustrate the iteration process of the proposed FBHA. Another example with multiple precedence constraints is used to demonstrate the effectiveness of the proposed FBHA in complicated construction projects.     

Tri-directional Scheduling Scheme: Theory and Computation

In this paper we introduce a new scheduling scheme based on so called tri-directional scheduling strategy to solve the well known resource constrained project scheduling problem. In order to demonstrate the effectiveness of tri-directional scheduling scheme, it is incorporated into a priority rule based parallel scheduling scheme. Theoretical and numerical investigations show that the tri-directional scheduling scheme outperforms forward, backward and even bidirectional schemes depending on the problem structure and the priority rule used. Based on empirical evidence, it seems that as the number of activities are increased, the tri-directional scheduling scheme performs better irrespective of the priority rule used. This suggests that tri-directional scheme should also be applied within the category of heuristic methods.     

Queueing analysis on a single-station make-to-stock/make-to-order inventory-production system

We consider a one-station production system that produces standard products for ordinary demands and custom products for specific demands. In this system, the workstation has two manufacturing modes. In mode 1, it produces standard products and, in mode 2, it produces custom products by performing the additional alternating works on one existing finished standard product. Base-stock control policy is applied to control the production of standard products. The fill rate of the ordinary demand and the on-time-delivery-rate of the specific demand are considered as the measures of the qualities of service. By assuming an Markovian system, qualities of service under base-stock policy are obtained; furthermore, the optimal base-stock level can be obtained numerically under the requirements on the qualities of services.     

Optimal size-based opportunistic scheduler for wireless systems

Modern wireless cellular systems are able to utilize the opportunistic scheduling gain originating from the variability in the users’ channel conditions. By favoring users with good instantaneous channel conditions, the service capacity of the system can be increased with the number of users. On the other hand, for service systems with fixed service capacity, the system performance can be optimized by utilizing the size information. Combining the advantages of size-based scheduling with opportunistic scheduling gain has proven to be a challenging task. In this paper, we consider scheduling of data traffic (finite-size elastic flows) in wireless cellular systems. Assuming that the channel conditions for different users are independent and identically distributed, we show how to optimally combine opportunistic and size-based scheduling in the transient setting with all flows available at time 0. More specifically, by utilizing the time scale separation assumption, we develop a recursive algorithm that produces the optimal long-run service rate vectors within the corresponding capacity regions. We also prove that the optimal operating policy applies the SRPT-FM principle, i.e., the shortest flow is served with the highest rate of the optimal rate vector, the second shortest with the second highest rate, etc. Moreover, we determine explicitly how to implement the optimal rate vectors in the actual time slot level opportunistic scheduler. In addition to the transient setting, we explore the dynamic case with randomly arriving flows under illustrative channel scenarios by simulations. Interestingly, the scheduling policy that is optimal for the transient setting can be improved in the dynamic case under high traffic load by applying a rate-based priority scheduler that breaks the ties based on the SRPT principle.     

Modeling and analysis of a supply–assembly–store chain

We consider a supply–assembly–store chain with produce-to-stock strategy, which comprises a set of component suppliers, a mixed-model assembly line with a constantly moving conveyor linking a set of workstations in series, and a set of product storehouses. Each supplier provides components of a specified family, which are assembled at a corresponding workstation. Units belonging to different models of products are sequentially fed onto the conveyor, and pass through the workstations to generate finished products. Each storehouse stores finished products belonging to a specific model for satisfying customer demands. The suppliers deliver components according to a just-in-time supply policy with stochastic leadtimes. Customer demands for a particular model of products arrive at the corresponding storehouse according to a Poisson stream. The paper conducts a modeling and performance analysis in the design stage of the system in the sense of “long-term-behavior”. A rolling technique is constructed for analyzing stationary probability distributions of the numbers of components. A two-dimensional Markov chain with infinite states is introduced for analyzing stationary probability distributions of inventories of finished products. Based on these distributions, performance measures of the system, such as work-in-process of components, inventory amounts of finished products, as well as service levels for customers, can be easily obtained. Managerial insights are obtained from both analytical and numerical results.