Manufacturing delivery performance for supply chain management

This paper considers single-stage make-to-order production systems. We focus on (1) modeling the appropriate expected costs under a variety of modeling assumptions and (2) characterizing the optimal policies. Our approach to solving the problem is to derive the distribution of actual completion times of the process for individual orders and to compare it to the corresponding quoted due dates in order to obtain the expected total costs. We then show the convexity of the objective cost function for determining the decision variable(s), the planned customer order leadtime.     

Evaluation of three production planning procedures for the use of recipe flexibility

Process industries often obtain their raw materials from mining or agricultural industries. These raw materials usually have variations in quality, which often lead to variations in the recipes used for manufacturing a product. Another reason for varying the recipe is to minimize production costs by using the cheapest materials that still lead to a satisfactory quality in the product. A third reason for using recipe flexibility is that it may occur that at the time of production not all materials for the standard recipe are available. In earlier research we showed under what conditions the use of this type of recipe flexibility should be preferred to the use of high materials stock to avoid materials shortages. We also showed that the use of recipe flexibility to account for material shortages can be justified if the material replenishment leadtime is long, the demand uncertainty is high and the required service level is high. In this paper we assume that these conditions are satisfied and we investigate three different production planning procedures that make use of recipe flexibility to cope with the uncertainty in demand and supply. We assume that the customer order leadtime is much smaller than the material replenishment leadtime, and therefore demand uncertainty is high. The optimal procedure optimizes material use over a planning horizon equal to the material replenishment leadtime, taking into account the customers orders and knowledge of the distribution function of future demand. The deterministic procedure also optimizes the material use over the material replenishment leadtime, but it assumes a deterministic demand level for unknown orders. The simplest, myopic procedure optimizes material use over only the accepted customer orders. These three procedures are investigated via an experimental design of computer simulations of an elementary small scale model of the production planning situation. The results show that the optimal procedure outperforms the other two procedures. Furthermore, for a realistic cost structure in feed industry under certain circumstances the use of the optimal procedure may lead to a 4% increase in profit. However, this improvement must be weighted against the cost incurred by the operational use of this complex procedure. Based on these considerations and the numerical results in this paper, we may expect that for some situations in practice the use of the simplest myopic procedure, optimizing material use only over the available customer orders, will be justified from an overall cost point of view.     

An appointment-based service center with guaranteed service

Customers are scheduled to arrive at periodic scheduling intervals to receive service from a single server system. A customer must start receiving service within a given departure interval; if this is not the case, the system will pay a penalty and/or transfer the customer to another facility at the system's cost. A complete transient and steady-state analysis of the system is given, the optimal scheduling and departure intervals are determined, and the virtual work in the system is analyzed.     

A matching approach for replenishing rectangular stock sizes

Consider a replenishment problem in which several different rectangular sizes of material are stocked. Customers order rectangles of the material, but the rectangles ordered have a range on specified width as well as on specified length. To satisfy the customer requirements, the stock material can be cut once longitudinally in order to satisfy two customer requirements or not cut at all, that is, an entire stock piece of material is used to satisfy one customer requirement. If an exact match is impossible in the current planning period, the unused material must be returned to stock— an expensive and undesirable situation. In this paper, a nonbipartite weighted matching problem formulation will be given for determining the replenishment requirements of rectangular stock sizes. Then, a hybrid solution approach, capable of solving real applications (typically up to 3000 nodes) efficiently, will be discussed. This solution was implemented in September 1998 and has operated successfully since then.     

Dynamic scheduling of a single-server two-class queue with constant retrial policy

We analyze the non-preemptive assignment of a single server to two infinite-capacity retrial queues. Customers arrive at both queues according to Poisson processes. They are served on first-come-first-served basis following a cost-optimal routing policy. The customer at the head of a queue generates a Poisson stream of repeated requests for service, that is, we have a constant retrial policy. All service times are exponential, with rates depending on the queues. The costs to be minimized consist of costs per unit time that a customer spends in the system. In case of a scheduling problem that arise when no new customers arrive an explicit condition for server allocation to the first or the second queue is given. The condition presented covers all possible parameter choices. For scheduling that also considers new arrivals, we present the conditions under which server assignment to either queue 1 or queue 2 is cost-optimal.     

Waiting Time Distributions in the Preemptive Accumulating Priority Queue

We consider a queueing system in which a single server attends to N priority classes of customers. Upon arrival to the system, a customer begins to accumulate priority linearly at a rate which is distinct to the class to which it belongs. Customers with greater accumulated priority levels are given preferential treatment in the sense that at every service selection instant, the customer with the greatest accumulated priority level is selected next for servicing. Furthermore, the system is preemptive so that the servicing of a customer is interrupted for customers with greater accumulated priority levels. The main objective of the paper is to characterize the waiting time distributions of each class. Numerical examples are also provided which exemplify the true benefit of incorporating an accumulating prioritization structure, namely the ability to control waiting times.     

A heuristic method for dispatching repair men

A company has to provide service to its customers. A service consists of a visit to the customer plus the spending of some given time at the scene. The future customer demand is not known but the probability distribution for the demand may be known. When a customer call comes in, the company must immediately specify a time window within which the start of service will be provided. The problem is for a fixed service level to determine an optimal strategy of route design and time window setting so that the total distance travelled is minimized over the time horizon given. A heuristic method BARTOC (Booking Algorithm for Routing and Timing Of Customers) to solve the problem mentioned above is suggested. BARTOC is based on a cluster-first route-second approach. Some computational results are presented. The results indicate that BARTOC produces high quality solutions.Peter Matthiesen, Inc.Dano Chemo, Inc.     

Setting Planned Leadtimes in Capacity Requirements Planning

This paper deals with the problem of determining planned leadtimes in a periodic loading system, such as ‘Material Requirements Planning.’ A method for determining planned leadtime for an individual job, based upon the operation time for the job, is presented from the standpoint that the planned leadtime should be determined under a management policy, taking a trade off between work-in-process quantities and capacity requirements variations into consideration. The proposed method, which is derived with Lagrange's method of indeterminate coefficients, can minimize capacity requirements variations under a given average loading time, under general operation time distributions.     

Expected waiting times in polling systems under priority disciplines

In this paper, we analyse a service system which consists of several queues (stations) polled by a single server in a cyclic order with arbitrary switchover times. Customers from several priority classes arrive into each of the queues according to independent Poisson processes and require arbitrarily distributed service times. We consider the system under various priority service disciplines: head-of-the-line priority limited to one and semi-exhaustive, head-of-the-line priority limited to one with background customers, and global priority limited to one. For the first two disciplines we derive a pseudo conservation law. For the third discipline, we show how to obtain the expected waiting time of a customer from any given priority class. For the last discipline we find the expected waiting time of a customer from the highest priority class. The principal tool for our analysis is the stochastic decomposition law for a single server system with vacations.     

The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service

Customers arriving according to a Markovian arrival process are served at a single server facility. Waiting customers generate priority at a constant rate γ$\gamma$; such a customer waits in a waiting space of capacity 1 if this waiting space is not already occupied by a priority generated customer; else it leaves the system. A customer in service will be completely served before the priority generated customer is taken for service (non-preemptive service discipline). Only one priority generated customer can wait at a time and a customer generating into priority at that time will have to leave the system in search of emergency service elsewhere. The service times of ordinary and priority generated customers follow PH-distributions. The matrix analytic method is used to compute the steady state distribution. Performance measures such as the probability of n consecutive services of priority generated customers, the probability of the same for ordinary customers, and the mean waiting time of a tagged customer are found by approximating them by their corresponding values in a truncated system. All these results are supported numerically.     

Analysis of queueing systems with customer interjections

In this paper we study queueing systems with customer interjections. Customers are distinguished into normal customers and interjecting customers. All customers join a single queue waiting for service. A normal customer joins the queue at the end and an interjecting customer tries to cut in the queue. The waiting times of normal customers and interjecting customers are studied. Two parameters are introduced to describe the interjection behavior: the percentage of customers interjecting and the tolerance level of interjection by individual customers. The relationship between the two parameters and the mean and variance of waiting times is characterized analytically and numerically.     

Bivariate Forecasting with a Variable Leadtime

The assumption of a constant leadtime between a forecast variable and a leading indicator is difficult to support in a number of forecasting contexts, especially in relationships between economic variables. The forecasting method described uses a leading indicator and has the capability to handle varying leadtimes between the forecast variable and the leading indicator. This is achieved by modelling the behaviour of the leadtime as a Markov chain. The method is shown to be effective at detecting and reacting to changes in the leadtime by using simulated series, the only situation where the leadtime is known, and demonstrated on other series.     

A tabu search algorithm for the single vehicle routing allocation problem

In the single vehicle routing allocation problem (SVRAP) we have a single vehicle, together with a set of customers, and the problem is one of deciding a route for the vehicle (starting and ending at given locations) such that it visits some of the customers. Customers not visited by the vehicle can either be allocated to a customer on the vehicle route, or they can be isolated. The objective is to minimize a weighted sum of routing, allocation and isolation costs. One special case of the general SVRAP is the median cycle problem, also known as the ring star problem, where no isolated vertices are allowed. Other special cases include the covering tour problem, the covering salesman problem and the shortest covering path problem. In this paper, we present a tabu search algorithm for the SVRAP. Our tabu search algorithm includes aspiration, path relinking and frequency-based diversification. Computational results are presented for test problems used previously in the literature and our algorithm is compared with the results obtained by other researchers. We also report results for much larger problems than have been considered by others.     

Modeling customer impatience in a newsboy problem with time-sensitive shortages

Customers across all stages of the supply chain often respond negatively to inventory shortages. One approach to modeling customer responses to shortages in the inventory control literature is time-dependent partial backlogging. Partial backlogging refers to the case in which a customer will backorder shortages with some probability, or will otherwise solicit the supplier’s competitors to fulfill outstanding shortages. If the backorder rate (i.e., the probability that a customer elects to backorder shortages) is assumed to be dependent on the supplier’s backorder replenishment lead-time, then shortages are said to be represented as time-dependent partial backlogging. This paper explores various backorder rate functions in a single period stochastic inventory problem in an effort to characterize a diversity of customer responses to shortages. We use concepts from utility theory to formally classify customers in terms of their willingness to wait for the supplier to replenish shortages. Under mild assumptions, we verify the existence of a unique optimal solution that corresponds to each customer type. Sensitivity analysis experiments are conducted in order to compare the optimal actions associated with each customer type under a variety of conditions. Additionally, we introduce the notion of expected value of customer patience information (EVCPI), and then conduct additional sensitivity analyses to determine the most and least opportune conditions for distinguishing between customer behaviors.     

Customer equilibrium and optimal strategies in Markovian queues in series

We consider series of M/M/m queues with strategic customer behavior. Customers arrive to the first queue and decide whether to enter the system or balk and, if they enter, up to which queue to proceed before departing. Each customer makes an independent decision, with the objective of maximizing her total net benefit, which is equal to the value of service minus a cost due to expected delay. We formulate the customer decision as a game and identify the unique symmetric Nash equilibrium strategy, which is expressed in a backward recursive form. We also analyze the problem of maximizing the total customer welfare and establish the relationship between the equilibrium and the welfare maximizing strategies.     

Linking the individual forgetting context with customer capital from a seller's perspective

Customer capital is a result of interaction between an organization and its customers. Customers change their characteristics, including addresses, behaviour and preferences; but as the customer requirements change, basic beliefs or processes that is, things that individuals take for granted at an implicit and an explicit level of knowledge, must also change. This paper aims to identify the role of an individual forgetting context on customer capital in today's organization through an empirical study of 229 sellers (front-line contact people) in the Spanish optometry industry. Two structural equation models have been used, resulting in the conclusion that before obtaining an up-to-date memory, it is necessary to identify new ways of doing and interpreting things, which in turn result in a shift in relations that favour the customers.     

MAP/(PH/PH)/c Queue with Self-Generation of Priorities and Non-Preemptive Service

Abstract

Customers arriving according to a Markovian arrival process are served at a c server facility. Waiting customers generate into priority while waiting in the system (self-generation of priorities), at a constant rate γ; such a customer is immediately taken for service, if at least one of the servers is free. Else it waits at a waiting space of capacity c exclusively for priority generated customers, provided there is vacancy. A customer in service is not preempted to accommodate a priority generated customer. The service times of ordinary and priority generated customers follow distinct PH-distributions. It is proved that the system is always stable. We provide a numerical procedure to compute the optimal number of servers to be employed to minimize the loss to the system. Several performance measures are evaluated.     

Analysis of Multi-Product Kanban Systems with State-Dependent Setups and Lost Sales

We propose a decomposition-based approximation method that generates fairly accurate estimates for steady-state performance measures of a kanban-controlled production system. The manufacturing facility of this system can process items of several different products. Setup and processing times are assumed to be exponentially distributed. Customers arrive according to mutually independent Poisson processes. A customer whose demand cannot be met from stock leaves the system and satisfies his demand elsewhere (lost sales). The manufacturing facility processes items of a product until a target inventory level given by the number of kanbans has been reached. Then the manufacturing facility is set up for the next product according to a fixed setup sequence if the next product's inventory level is below target. Otherwise, this product is skipped (cyclic-exhaustive processing with state-dependent setups). The manufacturing facility idles when the inventory levels of all products are at their target levels.     

N-策略休假排队系统中异质信息顾客策略分析

本文研究N-策略休假M/M/1排队系统中的异质信息顾客策略和社会最优收益。来到系统的顾客分为两类,第一类顾客有系统信息,加入系统前知道服务员的状态和系统中顾客数;第二类顾客没有系统信息,加入系统前既不知道服务员的状态,也不知道系统中顾客数。利用粒子群优化算法,分析了两类顾客的最优策略行为和最优社会收益。结果表明,最优社会收益随着转换门限N的增大而减小,随着v和系统负载p的增大而增大。并且,第一类顾客的比例越大,社会收益越大。     

Light traffic in a cellular system with mobile subscribers and its applications

This paper is concerned with a cellular system with mobile subscribers (customers). This system consists of a cell, called the tagged cell, and its adjacent cells. Each cell has some finite number of channels. The sojourn times of customers in the tagged cell have an exponential distribution. Customers in the adjacent cells move to the tagged cell according to a Poisson process whose rate depends on the number of customers in the tagged cell. Each customer without call in progress generates his call according to an exponential distribution and the channel holding times of calls at each cell have a common exponential distribution. We first show that under some restriction, the light traffic limit for the stationary state distribution in the tagged cell is given by a mixture of a Poisson and binominal distributions. Based on the limit, we develop formulae for evaluating the hand-off and blocking probabilities and the mean number of busy channels in the tagged cell. Several numerical examples are presented that demonstrate the practical usefulness of the formulae.