On the value of customer information for an independent supplier in a continuous review inventory system

We consider the inventory control problem of an independent supplier in a continuous review system. The supplier faces demand from a single customer who in turn faces Poisson demand and follows a continuous review (R, Q) policy. If no information about the inventory levels at the customer is available, reviews and ordering are usually carried out by the supplier only at points in time when a customer demand occurs. It is common to apply an installation stock reorder point policy. However, as the demand faced by the supplier is not Markovian, this policy can be improved by allowing placement of orders at any point in time. We develop a time delay policy for the supplier, wherein the supplier waits until time t after occurrence of the customer demand to place his next order. If the next customer demand occurs before this time delay, then the supplier places an order immediately. We develop an algorithm to determine the optimal time delay policy. We then evaluate the value of information about the customer’s inventory level. Our numerical study shows that if the supplier were to use the optimal time delay policy instead of the installation stock policy then the value of the customer’s inventory information is not very significant.     

Priority option pricing in an M/M/m queue

We study a system where the service provider offers priority options. We identify the optimal option pricing policy, by deriving the optimal number a customer would buy and the customer’s exercise policy as a function of system congestion, options remaining, time to expiration and possibility of balking.     

Optimising a general repair kit problem with a service constraint

Field services are a particular type of after-sales service performed at the customer’s location where technicians repair malfunctioning machines. The inventory decisions about which spare part types to take to the repair site and in what quantities is called the repair kit problem. This problem is characterized by an order-based performance measure since a customer is only satisfied when all required spare parts are available to fix the machine. As a result, the service level in the decision making process is defined as a job fill rate. In this paper we derive a closed-form expression for the expected service level and total costs for the repair kit problem in a general setting, where multiple units of each part type can be used in a multi-period problem. Such an all-or-nothing strategy is a new characteristic to investigate, but commonly used in practice. Namely, items are only taken from the inventory when all items to perform the repair are available in the right quantity. We develop a new algorithm to determine the contents of the repair kit both for a service and cost model while incorporating this new expression for the job fill rate. We show that the algorithm finds solutions which differ on average 0.2% from optimal costs. We perform a case study to test the performance of the algorithm in practice. Our approach results in service level improvements of more than 30% against similar holding costs.     

Planning and approximation models for delivery route based services with price-sensitive demands

Classical vehicle routing problems typically do not consider the impact of delivery price on the demand for delivery services. Existing models seek the minimum sum of tour lengths in order to serve the demands of a given set of customers. This paper proposes approximation models to estimate the impacts of price on delivery services when demand for delivery service is price dependent. Such models can serve as useful tools in the planning phase for delivery service providers and can assist in understanding the economics of delivery services. These models seek to maximize profit from delivery service, where price determines demand for deliveries as well as the total revenue generated by satisfying demand. We consider a variant of the model in which each customer’s delivery volume is price sensitive, as well as the case in which customer delivery volumes are fixed, but the total number of customers who select the delivery service provider is price sensitive. A third model variant allows the delivery service provider to select a subset of delivery requests at the offered price in order to maximize profit.     

The effects of the availability of waiting-time information on a balking queue

We consider two balking queue models with different types of information about delays. Potential customers arrive according to a Poisson process, and they decide whether to stay or balk based on the available delay information. In the first model, an arriving customer learns a rough range of the current queue length. In the second model, each customer’s service time is the sum of a geometric number of i.i.d. exponential phases, and an arriving customer learns the total number of phases remaining in the system. For each information model, we compare two systems, identical except that one has more precise information. In many cases, better information increases throughput and thus benefits the service provider. But this is not always so. The effect depends on the shape of the distribution describing customers’ sensitivities to delays. We also study the effects of information on performance as seen by customers. Again, more information is often good for customers, but not always.     

The rollon–rolloff waste collection vehicle routing problem with time windows

This study introduces a rollon–rolloff waste collection vehicle routing problem involving large containers that accumulate huge amounts of garbage at construction sites and shopping districts. In this problem, tractors move one container at a time between customer locations, a depot, disposal facilities, and container storage yards. The complicated constraints discussed in this study arise from having multiple disposal facilities, multiple container storage yards, seven service types of customer demands, different time windows for customer demands and facilities, various types and sizes of containers, and the lunch break of tractor drivers. In addition, real-world issues, such as changing service types, multiple demands at a customer’s location, and tractors with different work schedules, are dealt with. This study proposes a large neighborhood search based iterative heuristic approach consisting of several algorithms for the problem. The effectiveness of the proposed methods is demonstrated by computational experiments using benchmark data, some instances of which are derived from real-world problems.     

Scheduling in supply chain environment

Successful companies are those that reach at least the two following objectives: reduce their Work-In-Process (WIP) and respond to customer’s requirements in real time. The approach proposed in this paper allows to reach these goals by controlling the WIP and providing information about the completion times of customer’s demands in real time. The approach we develop in this paper has been integrated in a supply chain environment for flow-shops. This paper extends the approach to assembly systems.     

Modeling churn using customer lifetime value

The definition and modeling of customer loyalty have been central issues in customer relationship management since many years. Recent papers propose solutions to detect customers that are becoming less loyal, also called churners. The churner status is then defined as a function of the volume of commercial transactions. In the context of a Belgian retail financial service company, our first contribution is to redefine the notion of customer loyalty by considering it from a customer-centric viewpoint instead of a product-centric one. We hereby use the customer lifetime value (CLV) defined as the discounted value of future marginal earnings, based on the customer’s activity. Hence, a churner is defined as someone whose CLV, thus the related marginal profit, is decreasing. As a second contribution, the loss incurred by the CLV decrease is used to appraise the cost to misclassify a customer by introducing a new loss function. In the empirical study, we compare the accuracy of various classification techniques commonly used in the domain of churn prediction, including two cost-sensitive classifiers. Our final conclusion is that since profit is what really matters in a commercial environment, standard statistical accuracy measures for prediction need to be revised and a more profit oriented focus may be desirable.     

Mathematical programming models for revenue management under customer choice

We study a network airline revenue management problem with discrete customer choice behavior. We discuss a choice model based on the concept of preference orders, in which customers can be grouped according to a list of options in decreasing order of preference. If a customer’s preferred option is not available, the customer moves to the next choice on the list with some probability. If that option is not available, the customer moves to the third choice on the list with some probability, and so forth until either the customer has no other choice but to leave or his/her request is accepted. Using this choice model as an input, we propose some mathematical programs to determine seat allocations. We also propose a post-optimization heuristic to refine the allocation suggested by the optimization model. Simulation results are presented to illustrate the effectiveness of our method, including comparisons with other models.     

Multi-server queueing systems with cooperation of the servers

In this paper, we consider an N-server queueing model with homogeneous servers in which customers arrive according to a stationary Poisson arrival process. The service times are exponentially distributed. Two new customer’s service disciplines assuming simultaneous service of arriving customer by all currently idle servers are discussed. The steady state analysis of the queue length and sojourn time distribution is performed by means of the matrix analytic methods. Numerical examples, which illustrate advantage of introduced disciplines comparing to the classical one, are presented.     

A study of repairable parts inventory system operating under performance-based contract

Performance-Based Logistics (PBL) is becoming a dominant logistics support strategy, especially in the defense industry. PBL contracts are designed to serve the customer’s key performance measures, while the traditional contracts for after-sales services, such as Fixed-price (FP) and Cost-plus (C+), only provide insurance or incentive. In this research, we develop an inventory model for a repairable parts system operating under a PBL contract. We model the closed-loop inventory system as an M/M/m queue in which component failures are Poisson distributed and the repair times at the service facility are exponential. Our model provides the supplier and the customer increased flexibility in achieving target availability. Analysis of key parameters suggests that to improve the availability of the system with repairable spare parts, the supplier should work to improve the components reliability and efficiency of repair facility, rather than the base stock level, which has minimal impact on system availability.     

The effect of market segmentation with demand leakage between market segments on a firm’s price and inventory decisions

In this paper, we address the simultaneous determination of price and inventory replenishment in a newsvendor setting when the firm faces demand from two or more market segments in which the firm can set different prices. We allow for demand leakage from higher-priced segments to lower-priced segments and assume that unsatisfied demand can be backlogged. We examine the case where the demands occur concurrently without priority and are met from a single inventory. We consider customer’s buy-down behavior explicitly by modeling demand leakage as a function of segment price differentiation, and characterize the structure of optimal inventory and pricing policies.     

When should service firms provide free experience service?

By providing a free experience service, a service firm can attract more uninformed customers. However, it could reversely effect the delay-sensitive, informed customers’ decision. In this paper, we study a priority queueing system with free experience services. We study the customer behavior in equilibrium after we derive the expected customer waiting time. We then construct the service firm’s revenue function and obtain an optimal strategy for the service firm. Our results suggest that when the market size of informed customers is relatively small, the firm should consider providing free experience services for uninformed customers. Conversely, if the demand rate of potential informed customers is quite high, the firm should ignore uninformed customers.     

Price and lead time decisions in dual-channel supply chains

Manufacturers today are increasingly adopting a dual channel to sell their products, i.e., the traditional retail channel and an online direct channel. Empirical studies have shown that service quality (we focus on the delivery lead time of the direct channel) even goes beyond product price as one of the major factors influencing consumer acceptance of the direct channel. Delivery lead time has significant effects on demand, profit, and pricing strategy. However, there is scant literature addressing the decision on the promised delivery lead time of a direct channel and its impact on the manufacturer’s and retailer’s pricing decisions. To fill this gap, we examine the optimal decisions of delivery lead time and prices in a centralized and a decentralized dual-channel supply chain using the two-stage optimization technique and Stackelberg game, and analyze the impacts of delivery lead time and customer acceptance of a direct channel on the manufacturer’s and retailer’s pricing behaviours. We analytically show that delivery lead time strongly influences the manufacturer’s and the retailer’s pricing strategies and profits. Our numerical studies reveal that the difference between the demand transfer ratios in the two channels with respect to delivery lead time and direct sale price, customer acceptance of the direct channel, and product type have great effects on the lead time and pricing decisions.     

Scheduling of inbound and outbound trucks in cross docking systems with temporary storage

Cross docking is a warehouse management concept in which items delivered to a warehouse by inbound trucks are immediately sorted out, reorganized based on customer demands, routed and loaded into outbound trucks for delivery to customers without the items being actually held in inventory at the warehouse. If any item is held in storage, it is usually for a brief period of time that is generally less than 24 hours. This way, the turnaround times for customer orders, inventory management cost, and warehouse space requirements are reduced. One of the objectives for cross docking systems is how well the trucks can be scheduled at the dock and how the items in inbound trucks can be allocated to the outbound trucks to optimize on some measure of system performance. The objective of this research is to find the best truck docking or scheduling sequence for both inbound and outbound trucks to minimize total operation time when a temporary storage buffer to hold items temporarily is located at the shipping dock. The product assignment to trucks and the docking sequences of the inbound and outbound trucks are all determined simultaneously.     

Moderate deviations for a risk model based on the customer-arrival process

In this paper, we investigate the moderate deviations for a customer-arrival-based insurance risk model, in which customer’s actual claim sizes are described as independent and identically distributed heavy-tailed random variables multiplying a shot function, and the model can be treated as a Poisson shot noise process.     

Transient analysis of a queue with system disasters and customer impatience

A single server queue with Poisson arrivals and exponential service times is studied. The system suffers disastrous breakdowns at an exponential rate, resulting in the loss of all running and waiting customers. When the system is down, it undergoes a repair mechanism where the repair time follows an exponential distribution. During the repair time any new arrival is allowed to join the system, but the customers become impatient when the server is not available for a long time. In essence, each customer, upon arrival, activates an individual timer, which again follows an exponential distribution with parameter ξ. If the system is not repaired before the customer’s timer expires, the customer abandons the queue and never returns. The time-dependent system size probabilities are presented using generating functions and continued fractions.     

Individual customer’s behaviour in networks with state-dependent arrival rates

We consider Jackson networks with state-dependent arrival and service rates which show product form or nearly product form steady-states and come up with examples of load-dependent admission control. For these networks we prove an arrival theorem for external as well as for internal arrivals. In case of open tandem systems with state-independent service rates we compute the joint distribution of the sojourn times of a customer in the nodes and the distribution of the customer’s end-to-end-delay. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal retailer’s replenishment decisions in the EPQ model under two levels of trade credit policy

The main purpose of this paper is to investigate the optimal retailer’s replenishment decisions under two levels of trade credit policy within the economic production quantity (EPQ) framework. We assume that the supplier would offer the retailer a delay period and the retailer also adopts the trade credit policy to stimulate his/her customer demand to develop the retailer’s replenishment model under the replenishment rate is finite. Furthermore, we assume that the retailer’s trade credit period offered by supplier M is not shorter than the customer’s trade credit period offered by retailer N (M ? N). Since the retailer cannot earn any interest in this situation, M < N.     

An integrated production and inventory model to dampen upstream demand variability in the supply chain

We consider a two-echelon supply chain: a single retailer holds a finished goods inventory to meet an i.i.d. customer demand, and a single manufacturer produces the retailer’s replenishment orders on a make-to-order basis. In this setting the retailer’s order decision has a direct impact on the manufacturer’s production. It is a well known phenomenon that inventory control policies at the retailer level often propagate customer demand variability towards the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). The manufacturer, however, prefers to smooth production, and thus he prefers a smooth order pattern from the retailer. At first sight a decrease in order variability comes at the cost of an increased variance of the retailer’s inventory levels, inflating the retailer’s safety stock requirements. However, integrating the impact of the retailer’s order decision on the manufacturer’s production leads to new insights. A smooth order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer’s safety stock. We show that by including the impact of the order decision on lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels. This leads to a situation where both parties are better off.