Considering stochastic lead times in a manufacturing/remanufacturing system with deterministic demands and returns

In this paper we study a manufacturing/remanufacturing system with stochastic lead times and a constant demand. We base our approach on previous research in which we have developed models to describe an inventory system with stochastic lead times. In this paper, we first adopt this method to manufacturing/remanufacturing situations, where there are essentially two supply sources for replenishing serviceable inventory. We then provide a solution procedure when a cycle ordering policy is used. Secondly, we investigate the possibility to use a dual sourcing ordering policy in which each order is split between a manufacturing and a remanufacturing process. Finally, we compare the two ordering policies and illustrate how the lead-time patterns influence the economic consequences.     

Optimal inventory and pricing policies for remanufacturable leased products

In this paper we consider a company which leases new products and also sells remanufactured versions of the new product that become available at the end of their lease periods. When the amount of end-of-lease items in stock is not sufficient to meet the demand for remanufactured products, the firm may purchase additional cores from a third-party supplier. We develop a dynamic programming formulation for determining the optimal price of remanufactured products, and optimal payment structure for the leased products. Our objective is to maximize the discounted system-wide profit over a finite horizon. The profit function consists of revenues that are obtained from remanufactured product sales and leasing, remanufacturing and manufacturing costs, inventory holding and shortage costs. We consider a consumer choice based demand model for mapping a potential customer into one of the product segments (a remanufactured product customer or a customer for a leased product with a particular lease period) for a given price/lease payment vector. We explore several properties of the discounted profit function and provide insight on the behavior of pricing and inventory policies. We also investigate the effect of key product characteristics such as deterioration in age, cost of shortage in remanufacturable product inventory, and key market characteristics such as relative willingness-to-pay for buying a remanufactured product and relative willingness-to-pay for leasing a new product on optimal pricing policies through a computational study.     

An investigation of setup instability in non-stationary stochastic inventory systems

In stochastic inventory systems unfolding uncertainties in demand lead to the revision of earlier replenishment plans which in turn results in an instability or so-called system nervousness. In this paper, we provide the grounds for measuring system nervousness in non-stationary demand environments, and gauge the stability and the cost performances of (R,S) and (s,S) inventory policies. Our results reveal that, both the stability and the cost performance of inventory policies are affected by the demand pattern as well as the cost parameters, and the (R,S) policy has the potential to replace the cost-optimal (s,S) policy for systems with limited flexibility.     

Price elasticity of demand for broadband: Evidence from Latin America and the Caribbean

In this study the authors analyze fixed broadband retail prices in Latin America and the Caribbean (LAC), and provide estimates about the effect of price changes on broadband adoption. The analysis is based on a survey of plans and tariffs conducted by the authors during Q2 2010. Their results suggest that fixed broadband services in LAC are generally expensive and of poor quality when benchmarked against Organisation for Economic Co-operation and Development (OECD) countries, although there is significant variance between markets in the region. In order to isolate the effect of prices on broadband adoption they use an instrumental-variable approach. Their findings show that broadband demand is relatively elastic to price in LAC but not in the OECD. They estimate that an average price reduction of 10% would result in an increase of almost 22% in the penetration rate in LAC, equivalent to almost 8.5 million additional broadband connections. Several policy implications result from these findings. First, national broadband policies in LAC should pay a closer attention to a deficit of competition in fixed broadband services, as households and firms face high prices for poor quality services, thus deterring adoption. Second, while their findings generally suggest that price reductions could significantly increase penetration, they elasticity estimates reveal that price effects might not be sufficient to achieve the penetration goals set in national broadband plans. This validates the need for complementary policy strategies that affect other determinants of broadband demand. The example of Brazil is used to illustrate this finding.     

Simulation-based optimisation of multi-echelon inventory systems

Multi-location inventory models are one of the most widely investigated fields in mathematical inventory theory, but the analytically tractable models suffer from various restrictive assumptions. To overcome these restrictions simulation can be used. However, simulation is not an optimisation approach. Therefore, we propose the simulation optimisation approach where a simulator is combined with an appropriate optimisation tool.In the present paper, we show that simulation optimisation successfully can be applied to define optimal policies in very general multi-echelon inventory systems. A numerical example shows the usability of our approach.     

Distribution contracts to support optimal inventory holdings under demand uncertainty

When suppliers produce products for which demand is uncertain, they face a problem of inducing downstream distributors to stock inventory levels that the suppliers prefer. This paper considers a wide array of alternative supply contracts, each of which consists of a mixture of constant per-unit wholesale prices, buy-back arrangements, and post sale payments contingent on sales made, such as revenue sharing or buybacks. We show that linear supply contracts specifying any combination of two of these three instruments can implement the vertical integrated outcome for a monopoly, thereby generating the supplier's preferred inventory configuration and price distribution. We extend our results to differentiated product oligopoly, demonstrating that each supplier obtains its preferred inventory configuration and price distribution, given the choices of its rival. Distributors choose optimal inventories from the suppliers' standpoint, even if suppliers do not know the distribution of demand uncertainty, and, given the perfect competition among distributors, all profits in the supply chain are captured by suppliers. Thus, suppliers are able to deal with demand uncertainty with remarkably little information about demand, and without the need to control dealer actions in detail. In particular, suppliers need not specify either dealer inventories or resale prices, but instead encourage distributors to order based on information in their possession and to set prices that generate desirable resale price dispersion.     

Integrated inventory models with controllable lead time and backorder discount considerations

Many companies use time as a means of differentiating themselves in the marketplace. In many literatures, the controllable lead time is regarded as a decision variable and decomposed into several components, each having a crashing cost function for the respective reduced lead time. When an item is out of stock, the loyal, patient and captive customers will wait until the outstanding orders arrive and are served from them. To compensate for the inconvenience of backordering and to secure orders, the supplier may offer a price discount on the stockout item. In this paper, an integrated inventory system in which shortage is allowed and both lead time and backordering are negotiable is investigated. The lead time crashing cost is represented as a function of reduced lead time and the quantities in the orders. There are two inventory models proposed in the paper, one with normally distributed demand, and another with generally distributed demand.     

Optimal production–inventory strategies for a HMMS-type reverse logistics system

The aim of the paper is to find optimal inventory policies in a reverse logistics system with special structure. It is assumed that demand is a known continuous function in a given planning horizon and return rate of used items is a given function. There is a constant delay between the using and return process. We investigate two stores. The demand is satisfied from the first store, where the manufactured and remanufactured items are stored. The returned products are collected in the second store and then remanufactured or disposed. The costs of this system consist of the quadratic holding costs for these two stores and the quadratic manufacturing, remanufacturing and disposal costs.The model is represented as an optimal control problem with two state variables (inventory status in the first and second store) and with three control variables (rate of manufacturing, remanufacturing and disposal). The objective is to minimize the sum of the quadratic deviation from described inventory levels in stores and from described manufacturing, remanufacturing and disposal rates. In this form, the model can be considered as a generalization of the well-known Holt et al. (Planning Production, Inventories, and Work Forces, Prentice-Hall, Englewood Cliffs, NJ, 1960) model with two warehouses. After solving the problem, we give some numerical examples to represent the optimal path in dependence of the demand rates.     

Concurrent pricing and lot sizing for make-to-order contract production

This paper develops a model for the simultaneous (i.e. concurrent) determination of the inventory and pricing policies of a supplier, which produces and supplies a product to a buyer, on the basis of a contractual agreement, calling for the delivery of a specific quantity periodically. Assuming that the customer is rational, i.e. it follows its own optimal purchasing policy, the objective of the supplier is to determine the product's selling price, in conjunction with an appropriate production/inventory policy, so that a predetermined gross profit level is achieved. It is further assumed that the supplier's production batch size is an integer multiple of the buyer's order quantity. In formulating a mathematical model of this situation, the interactions between the product's price, the buyer's economic order quantity and the supplier's selling price, costs and profit are taken into account. For solving this model, a simple iterative algorithm is proposed, which is illustrated through a numerical example. Sensitivity analysis performed on the model demonstrates that it is relatively robust and quite insensitive to errors in estimating the buyer's ordering to carrying cost ratio on the part of the producer.     

Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand

In this paper, a joint pricing and inventory control for non-instantaneous deteriorating items is developed. We adopt a price and time dependent demand function. Shortages is allowed and partially backlogged. The major objective is to determine the optimal selling price, the optimal replenishment schedule and the optimal order quantity simultaneously such that, the total profit is maximized. We first show that for any given selling price, optimal replenishment schedule exists and unique. Then, we show that the total profit is a concave function of price. Next, we present a simple algorithm to find the optimal solution. Finally, we solve a numerical example to illustrate the solution procedure and the algorithm.     

Joint pricing and procurement of fashion products in the existence of clearance markets

This paper focuses on the joint pricing and procurement of fashion products in the existence of clearance markets. It is assumed that the expected regular season demand is a linear decreasing function of the price and the end of period excess inventory is sold at a known discounted price in a clearance market where the demand is a random variable that follows a general distribution. It is shown that the expected profit function is unimodal and the optimal procurement quantity and price can be found from the first order conditions. Existence of a clearance market increases the profit, price, and the procurement quantity. In order to prove this, the optimal procurement and pricing policy of a price-setting retailer who does not have a clearance market is provided. As opposed to the literature, it is shown that the expected profit function of this problem is unimodal as well. A numerical study demonstrating the magnitude of the increase in profit, procurement quantity, and price is reported.     

A robustness study of a multi-echelon inventory model via simulation

This paper examines the robustness of a standard model of multi-echelon inventory systems, specifically the models discussed in Axsäter (Oper. Res. 48(5) (2000) 686). A simulation model was developed to explore the model's ability to predict system performance for a two-echelon one-warehouse, multiple retailer system using (R,Q) inventory policies under conditions that violate the model's fundamental modeling assumptions. In particular, the impact of non-stationary demand on this stationary demand inventory model was examined. The model performs well at the low demand and large retailer order batch size situations, but our testing of the model indicated that care must be taken when applying this model to situations that violate its fundamental assumption. These results should help practitioners to better understand the assumptions of these models and to determine when or when not to apply these models in practice.     

Optimal ordering policies in response to a discount offer

Sometimes supplier offers a temporary price discount to increase cash flow or decrease the inventory level of certain items. Thus, the manufacturer may be able to improve the effectiveness of his inventory system by ordering a special quantity at this sale period. In this paper, economic order quantity (EOQ) models with a discounted price are developed to obtain the optimal ordering policy during the sale period for five different cases: (a) coincidence of sale period with replenishment time, (b) non-coincidence of sale period with replenishment time, (c) sale period is longer than a cycle, (d) discounted price as a function of the special ordering quantity, and (e) incremental discount. Each case has its own characteristics of the sale period and the discounted price. The objective is to take the maximum possible advantage from the discounted price by ordering a special quantity during the sale period. The optimal ordering policy is obtained by maximizing the difference between the two costs: Regular EOQ cost and special quantity cost during the sale period. Moreover, a comparison of different discount scenarios is developed to sense the effect of different parameters on the ordering policies. The annual gain obtained is linearly related to the discount and the on-hand remnant inventory. Numerical analyses are provided to illustrate and testify the values of the optimal special quantity. The analysis showed an impressive improvement in the effectiveness of the inventory system when a special order is placed during the sale period. The optimal special quantity is driven for each case to visualize real-life problems. Sensitivity analysis is also initiated to study the change in the total savings with respect to the variation of the special optimal quantity.     

Revenue Sharing and Vertical Control in the Video Rental Industry

Revenue sharing contracts, in which retailers pay a royalty on sales to their suppliers, are now widely used in the video rental industry. We show that revenue sharing is valuable in vertically separated industries in which demand is either stochastic (unpredictable) or variable (e.g., systematically declining), downstream inventory is chosen before demand is realized and downstream firms engage in intrabrand competition. Unlike two-part tariffs, revenue sharing achieves the first best outcome by softening retail price competition without distorting retailers' inventory decisions. Our theories are also consistent with trends in prices and availability following retailers' adoption of revenue sharing contracts.     

Lot sizes in a capacity constrained facility—a simulation study of stationary stochastic demand

This paper considers the scheduling of several different items on a single machine, in literature known as the economic lot scheduling problem, ELSP. One of the characteristics of this problem is that the demand rate is deterministic and constant. However, in a practical situation demand usually varies. In this paper we examine if a deterministic model can be used if demand is stationary stochastic. A dynamic programming approach from Bomberger (Manage. Sci. 12(11) (1966) 778) and a heuristic method from Segerstedt (Int. J. Production Econom. 59(1–3) (1999) 469) are used to calculate lot sizes for four items. The production of these items is simulated with different variations in demand rates. Our conclusion is that a deterministic model of this kind can be used in a practical situation where the demand rate is stationary stochastic, but the models must be complemented by a decision rule; which item to produce and when to produce it. In our tests the heuristic method and the dynamic programming approach perform rather similarly with respect to costs and inventory levels, but the dynamic programming approach results in more backorders when there is small variation in demand rates. This study indicates that the model used for determination of lot sizes is of less importance than the decision rule used for identification of the item to produce and when to produce it.     

Integer-ratio policies for distribution/inventory systems

We study a multistage distribution/inventory system with a central warehouse and N retailers. Customer demand arrives at each retailer at a constant rate. The retailers replenish their inventories from the warehouse, which in turn orders from an outside supplier. It is assumed that shortages are not allowed and lead times are negligible. The goal is to determine policies which minimize the overall cost in the system, that is, the sum of the costs at each facility consisting of a fixed charge per order and a holding unit cost. We propose a heuristic procedure to compute near-optimal policies. Computational results on several randomly generated problems are reported.     

Dynamic Pricing,Advance Sales and Aggregate Demand Learning in Airlines

This paper uses a unique U.S. airlines panel data set to study empirically the dynamic pricing of inventories with uncertain demand over a finite horizon. I estimate a dynamic pricing equation and a dynamic demand equation that jointly characterize the adjustment process between prices and sales as the flight date nears. I find that the price increases as the inventory decreases, and decreases as there is less time to sell. Consistent with aggregate demand learning and price adjustment, demand shocks have a positive and much larger effect on prices than the positive effect of anticipated sales.     

An organizational perspective on inventory control: Theory and a case study

Inventory control is a well-covered area in literature. Nowadays, many concepts and techniques are available for effectively controlling inventories. Eminent examples are stochastic models to determine order quantities, techniques for forecasting demand and different kinds of ABC analysis. Remarkably enough, the theoretical backgrounds of these concepts and techniques show a great deal of similarity: they all stem from the field of operations management and operations research. Despite the value of the available concepts, such a one-sided approach has its limitations in practice. In this article it is argued that it is important to take a broader view when dealing with practical inventory control problems. First of all, an organizational perspective on inventory control is developed. The main idea behind this perspective is the importance of the organizational context of inventories. This means that in addition to the traditional points for attention, such as order quantities and replenishment strategies, other aspects need attention as well. They are, for example, the allocation of responsibilities and authorities regarding inventory management, the quality of inventory information and the relevant decision-making processes. These contextual factors as well as the traditional factors are mapped out and integrated into a framework to be used in solving practical inventory control problems. One of the main features of the framework is that it is useful in both analyzing and redesigning an inventory situation. Secondly, this article describes the results of a case study regarding the application of the organizational perspective to a practical inventory control problem. The central issue of the case study is the spare parts inventory of a missionary aviation organization in Africa. The case study shows that the organizational perspective on inventory control is very helpful in dealing with inventory control problems. It is illustrated that taking into account the organizational context of inventories, especially the responsibilities and authorities of the persons concerned, is a necessity to accurately understand inventory control problems. In addition, it is illustrated that the organizational perspective leads to a more appropriate redesign.     

The uniform distribution as a first practical approach to new product inventory management

It is common sense that the premises usually considered in inventory models have little applicability to new product inventory management. This paper develops a first practical approach to deal with this issue: the solution to the (Q, r) inventory model for uniform demand forecasts and lead-times. Based on the fact that the uniform distribution is defined by two parameters that are easy to estimate—maximum and minimum—this paper shows that such a premise may comprise a helpful and accurate decision support tool for managers until they begin to learn about the distribution characteristics of the demand during the lead-time.     

A new look at residential electricity demand using household expenditure data

Many electricity demand estimates have been obtained based on the assumption that consumers optimize with respect to known marginal prices, but increasing empirical evidence suggests that consumers are more likely to respond to average prices. Under this assumption, this paper develops a new strategy based on Generalized Method of Moments to estimate household electricity demand. Our demand estimation approach uses publicly available expenditure data and utility-level consumption data from several major U.S. cities, complementing studies that use individual billing data which are richer yet often proprietary. We estimate the price elasticity near − 0.50, which is at the upper end (in magnitude) among the estimates from previous studies. This could have important implications for policy analysis such as those on climate policies that may affect electricity prices.