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John Muckstadt

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Papers by John Muckstadt

A Multi-Echelon, Multi-Item Inventory Model for Service Parts Management with Generalized Service Level Constraints

In the realm of service parts management, customer relationships are often established through se... more In the realm of service parts management, customer relationships are often established through service agreements that extend over a period of months or years. These agreements typically apply to a product (or group of products) that the customer has purchased, and specify the type of service that will be provided, as well as the timing with which the service will take place. In the case of a customer that operates in multiple locations, service agreements may apply to several products across several locations. In this paper we describe a continuous review inventory model for a multi-item, multi-echelon distribution system for service parts in which service level constraints exist for general groups of items across multiple locations and distribution channels. In addition to instantaneous service level constraints, a special class of time-based service level constraints are also considered, in which the specified service times coincide with transport times from replenishment sites within the distribution network. We derive exact fill rate expressions for each item's distribution channel and describe a solution approach for determining target inventory levels that meet all service level constraints at minimum investment.

A review of the stochastic lot scheduling problem

International Journal of Production Economics, 1999

This paper surveys the current research literature on the stochastic lot scheduling problem which... more This paper surveys the current research literature on the stochastic lot scheduling problem which deals with scheduling production of multiple products with random demand on a single facility with limited production capacity and signi"cant change-overs between products. The deterministic version of this problem has received signi"cant coverage in the literature; however, the stochastic problem has been addressed only recently. Furthermore, a range of distinctly di!erent analytical methods have been applied to this problem. This paper provides a unifying framework for discussing these approaches and o!ers some explanation and clari"cation of the di!erent analytical methods for this problem. After discussing some of the modeling and managerial implications of this problem, a detailed review of both continuous and discrete time control strategies is given, and areas for further research are outlined.

Optimal Stocking in Reparable Parts Networks with Repair Capacity and Inventory Pooling

This paper addresses a tactical planning problem for a three-echelon, reparable-parts service net... more This paper addresses a tactical planning problem for a three-echelon, reparable-parts service network characterized by a capacitated repair facility and local opportunities for inventory pooling. The problem is to find the optimal total system stock. The model proposed is appropriate for high-cost, high-criticality, low-demand-rate parts for which transport times are short and for which optimization-based stock allocation is performed in the distribution system. The model includes parameters that characterize design and management decisions in the resupply system. The model can be solved in time that is nlog(n) in the number of part number-location combinations, making it a practical technique for large-scale inventory problems. One implication of this approach is to emphasize the importance of optimization-based stock allocation and repair priority routines in inventory management execution systems.

Dynamic Lot Sizing with Deterministic Demand

Springer eBooks, Oct 27, 2009

To this point we have examined environments in which demand was assumed to occur at a known, cons... more To this point we have examined environments in which demand was assumed to occur at a known, constant rate over an infinite horizon.We now turn our attention to developing a finite-horizon, discrete-time model with deterministic but non-stationary demand for a single product at a single stage. In a finite-horizon discrete-time model, as the name suggests, the length of the planning horizon is finite and the order placement decisions are made at discrete intervals of time. Inventory is reviewed only at the beginning of a period, hence we can call this model a periodic review model. Backorders are not permitted. There are three types of costs considered in this environment, the fixed ordering cost, the variable procurement cost (or payment to the supplier) and the hol ding cost. If there were no fixed cost, it would be optimal to place an order in every period. The fixed cost provides an economic incentive to combine several periods’ demands into a single order. The variable procurement cost is also incurred only when an order is placed. The magnitude of this cost is proportional to the order quantity. Unlike the fixed and variable costs of order placement, the holding cost is not incurred when an order is placed. The holding cost is charged every period in proportion to the amount of on-hand inventory at a period’s end.

Inventories Are Everywhere

Springer series in operations research, Oct 27, 2009

This morning I began the day by pouring a glass of orange juice from a half gallon container, fil... more This morning I began the day by pouring a glass of orange juice from a half gallon container, filling a bowl with cereal, which was stored in a large box in a kitchen cabinet, taking a banana from a bunch sitting on our kitchen countertop along with many other items, slicing the banana onto the cereal, pouring milk into the bowl from a gallon container, and then sitting at a table to enjoy my breakfast. There are six chairs at my breakfast table, but, of course, I occupy only one. When taking the cereal from the cabinet, I had to choose from six different cereals we have stocked. I could have selected either low or high pulp content orange juice, since we stock both types; I could have chosen either 1% or skim milk to place on my cereal. The kitchen remains full of food items and food preparation materials that will be used at some later time. The remainder of my house contains many other types of items sitting idly, waiting to be used at a future time. My Jaguar convertible will not be used today. It is raining, so I will take the Dodge minivan to the office.

Power-of-Two Policies

Springer series in operations research, Oct 27, 2009

We will extend the results of the last chapter in three ways. First, we will consider multistage ... more We will extend the results of the last chapter in three ways. First, we will consider multistage systems. These systems are characterized by multiple locations where inventory management decisions have to be made. Recall that in the last chapter, there was only a single stage, that is, the ordering and inventory management decisions involved only one location. Second, we will work with the reorder interval as the decision variable over which cost is optimized instead of the order quantity. We continue to assume that demand occurs at a deterministic and stationary rate. Thus, once we know the reorder interval, we can easily determine the corresponding order quantity. Therefore, the two decision variables are equivalent; our preference for the reorder interval is due to practical reasons, as we explain below. Third, instead of determining the optimal solution, we will develop algorithms that determine reorder intervals that are easier to use in practice but are not necessarily optimal. However, we will establish that the worst possible cost will not be higher than the optimal cost by more than 6%. These inventory management policies that we will develop are referred to as power-of-two (PO2) policies.

Single-Period Models

Springer series in operations research, Oct 27, 2009

The models and environments discussed in the preceeding chapters have all been based on the premi... more The models and environments discussed in the preceeding chapters have all been based on the premise that the demand process is deterministic. In most real situations, this assumption is violated. Our goal in this, and in subsequent chapters, is to consider uncertainty directly in the decision models. In this chapter we will study the most basic models in which demand is described by a random variable. These models pertain to situations in which only a single procurement decision is made, and the effect of that decision is felt over a single period of finite duration. These models are often called one-shot or newsvendor models.

A Tactical Planning Model for Managing Recoverable Items in Multi-Echelon Systems

Springer series in operations research, Oct 27, 2009

ABSTRACT

Optimal Policy for Database Batch Operations: Backup, Check-Pointing, and Batch Update

The effects of load smoothing on inventory levels in a capacitated production and inventory system

Stochastic Analysis of Cyclic Schedules

Operations Research, Oct 1, 1993

Principles of Inventory Management

Springer series in operations research, 2010

Managing inventories in multi-echelon on-line retail fulfillment system with different response lead time demands

When designing and operating an order fulfillment system for an on-line retailer, many factors mu... more When designing and operating an order fulfillment system for an on-line retailer, many factors must be taken into account. In this paper, we study a multi-echlon on-line fulfillment system with different response lead time demands. We present a delayed allocation system, which is called the primary warehouse system (PWS). In this system, inventories to satisfy different response lead time demands are managed differently. Since there are many millions of items managed in the system, determining stock levels quickly is a necessity. The focus of this paper is on planning inventory levels. Specifically, our goals are to describe a model for setting stock levels for each item, to present a computationally tractable method for determining their values, and to provide numerical results that illustrate the applications of the model to the on-line retailer's environment.

A comparison of alternative kanban control mechanisms. I. Background and structural results

Iie Transactions, Apr 1, 1995

The design of inventory control policies for serial systems is a topic currently being explored b... more The design of inventory control policies for serial systems is a topic currently being explored by a number of researchers. Our goal -in two papers - is to synthesize and extend some of these efforts. We consider, simultaneously, four sources of variability in production lines - processing time variability, machine breakdowns, rework and yield loss - and show some similarities

Production Control of Cyclic Schedules with Demand and Process Variability

Production and Operations Management, Jan 5, 2009

An Application of Lagrangian Relaxation to Scheduling in Power-Generation Systems

Operations Research, Jun 1, 1977

Two major decisions are made when scheduling the operations of a fossil-fuel power-generating sys... more Two major decisions are made when scheduling the operations of a fossil-fuel power-generating system over a short time horizon. The “unit commitment” decision indicates what generating units are to be in use at each point in time. The “economic dispatch” decision is the allocation of system demand among the generating units in operation at any point in time. Both these decisions must be considered to achieve a least-cost schedule over the short time horizon. In this paper we present a mixed integer programming model for the short time horizon power-scheduling problem. The objective of the model is to minimize the sum of the unit commitment and economic dispatch costs subject to demand, reserve, and generator capacity and generator schedule constraints. A branch-and-bound algorithm is proposed using a Lagrangian method to decompose the problem into single generator problems. A sub gradient method is used to select the Lagrange multipliers that maximize the lower bound produced by the relaxation. We present computational results that indicate the technique is capable of solving large problems to within acceptable error tolerances.

Reorder Point, Lot Size Models: The Continuous Review Case

Springer eBooks, Oct 27, 2009

When there is a significant fixed cost incurred when placing an order with a supplier, it is no l... more When there is a significant fixed cost incurred when placing an order with a supplier, it is no longer beneficial to order each time a demand occurs. In Chapter 2 we examined the impact of fixed costs on ordering quantities when the demand processes were known with certainty. Now we will study situations in which significant fixed ordering costs are incurred and the demand process is assumed to be a stationary stochastic process. Furthermore, we will assume a transaction reporting system exists. That is, we assume that we monitor the inventory levels continuously through time, and place an order for a quantity of stock, called the lot size, at a point in time so as to minimize the average annual cost of operations.

Lot Sizing Models: The Periodic Review Case

Springer series in operations research, Oct 27, 2009

We now turn our attention to managing inventory in a periodic review setting in which there are f... more We now turn our attention to managing inventory in a periodic review setting in which there are fixed costs incurred when placing orders. Thus we are examining the same type of problem presented in the previous chapter, but doing so now in a periodic review rather than a continuous review operational environment. As was the case in our study of continuous review systems, owing to the presence of these fixed ordering costs, it may no longer be economical to place an order in each period of the planning horizon. The fixed cost requires that the order be large enough to justify incurring this cost. This leads to a policy in which there are two critical numbers: the reorder point and the order-up-to level. This is the (s,S) policy introduced in the preceding chapter. When this policy is followed, an order is placed if and only if the inventory position at the beginning of a period is less than or equal to the reorder point. If an order is placed, then the size of the order will be such that the inventory position after placing the order will be equal to the order-up-to level. This means that the size of the order has to be at least the difference between the order-up-to level and the reorder point.

Optimal policy for batch operations

Many database maintenance operations are performed periodically in batches, even in realtime syst... more Many database maintenance operations are performed periodically in batches, even in realtime systems. The purpose of this paper is to present a general model for determining the optimal frequency of these batch operations. Specifically, optimal backup, checkpointing, batch updating, and reorganization policies are derived. The approach used exploits inventory parallels by seeking the optimal number of items-rather than a time interval-to trigger a batch. The Renewal Reward Theorem is used to find the average long run costs for backup, recovery, and item storage, per unit time, which is then minimized to find the optimal backup policy. This approach permits far less restrictive assumptions about the update arrival process than did previous models, as well as inclusion of storage costs for the updates. The optimal checkpointing, batch updating, and reorganization policies are shown to be special cases of this optimal backup policy. The derivation of previous results as special cases of this model, and an example, demonstrate the generality of the methodology developed.

Background Concepts: An Introduction to the (s − 1, s) Policy under Poisson Demand

Springer series in operations research, Oct 27, 2009

In the previous chapter we studied order-up-to policies when time was divided into periods. We wi... more In the previous chapter we studied order-up-to policies when time was divided into periods. We will now discuss the implications of following a similar policy, called an (s–1, s) inventory policy. In this chapter we assume inventories are reviewed continuously in time. Recall that the stock level, s, measures the amount of inventory on hand plus on order minus backorders, that is, the stock level represents the inventory position for a particular location. In certain situations, we will refer to the on-order quantity as the “in resupply” quantity. This “in resupply” terminology is often used in military and aviation applications in which items fail and are repaired or are procured from an external source. When an (s–1, s) policy is followed in continuous review environments, an order is placed immediately whenever a demand occurs for one or more units of an item. The order quantity matches the size of the demand exactly. Hence, the inventory position is constant in the case where the demand process and costs are stationary over an infinite planning horizon, which is the one we will examine in some detail in this chapter.

A Multi-Echelon, Multi-Item Inventory Model for Service Parts Management with Generalized Service Level Constraints

In the realm of service parts management, customer relationships are often established through se... more In the realm of service parts management, customer relationships are often established through service agreements that extend over a period of months or years. These agreements typically apply to a product (or group of products) that the customer has purchased, and specify the type of service that will be provided, as well as the timing with which the service will take place. In the case of a customer that operates in multiple locations, service agreements may apply to several products across several locations. In this paper we describe a continuous review inventory model for a multi-item, multi-echelon distribution system for service parts in which service level constraints exist for general groups of items across multiple locations and distribution channels. In addition to instantaneous service level constraints, a special class of time-based service level constraints are also considered, in which the specified service times coincide with transport times from replenishment sites within the distribution network. We derive exact fill rate expressions for each item's distribution channel and describe a solution approach for determining target inventory levels that meet all service level constraints at minimum investment.

A review of the stochastic lot scheduling problem

International Journal of Production Economics, 1999

This paper surveys the current research literature on the stochastic lot scheduling problem which... more This paper surveys the current research literature on the stochastic lot scheduling problem which deals with scheduling production of multiple products with random demand on a single facility with limited production capacity and signi"cant change-overs between products. The deterministic version of this problem has received signi"cant coverage in the literature; however, the stochastic problem has been addressed only recently. Furthermore, a range of distinctly di!erent analytical methods have been applied to this problem. This paper provides a unifying framework for discussing these approaches and o!ers some explanation and clari"cation of the di!erent analytical methods for this problem. After discussing some of the modeling and managerial implications of this problem, a detailed review of both continuous and discrete time control strategies is given, and areas for further research are outlined.

Optimal Stocking in Reparable Parts Networks with Repair Capacity and Inventory Pooling

This paper addresses a tactical planning problem for a three-echelon, reparable-parts service net... more This paper addresses a tactical planning problem for a three-echelon, reparable-parts service network characterized by a capacitated repair facility and local opportunities for inventory pooling. The problem is to find the optimal total system stock. The model proposed is appropriate for high-cost, high-criticality, low-demand-rate parts for which transport times are short and for which optimization-based stock allocation is performed in the distribution system. The model includes parameters that characterize design and management decisions in the resupply system. The model can be solved in time that is nlog(n) in the number of part number-location combinations, making it a practical technique for large-scale inventory problems. One implication of this approach is to emphasize the importance of optimization-based stock allocation and repair priority routines in inventory management execution systems.

Dynamic Lot Sizing with Deterministic Demand

Springer eBooks, Oct 27, 2009

To this point we have examined environments in which demand was assumed to occur at a known, cons... more To this point we have examined environments in which demand was assumed to occur at a known, constant rate over an infinite horizon.We now turn our attention to developing a finite-horizon, discrete-time model with deterministic but non-stationary demand for a single product at a single stage. In a finite-horizon discrete-time model, as the name suggests, the length of the planning horizon is finite and the order placement decisions are made at discrete intervals of time. Inventory is reviewed only at the beginning of a period, hence we can call this model a periodic review model. Backorders are not permitted. There are three types of costs considered in this environment, the fixed ordering cost, the variable procurement cost (or payment to the supplier) and the hol ding cost. If there were no fixed cost, it would be optimal to place an order in every period. The fixed cost provides an economic incentive to combine several periods’ demands into a single order. The variable procurement cost is also incurred only when an order is placed. The magnitude of this cost is proportional to the order quantity. Unlike the fixed and variable costs of order placement, the holding cost is not incurred when an order is placed. The holding cost is charged every period in proportion to the amount of on-hand inventory at a period’s end.

Inventories Are Everywhere

Springer series in operations research, Oct 27, 2009

This morning I began the day by pouring a glass of orange juice from a half gallon container, fil... more This morning I began the day by pouring a glass of orange juice from a half gallon container, filling a bowl with cereal, which was stored in a large box in a kitchen cabinet, taking a banana from a bunch sitting on our kitchen countertop along with many other items, slicing the banana onto the cereal, pouring milk into the bowl from a gallon container, and then sitting at a table to enjoy my breakfast. There are six chairs at my breakfast table, but, of course, I occupy only one. When taking the cereal from the cabinet, I had to choose from six different cereals we have stocked. I could have selected either low or high pulp content orange juice, since we stock both types; I could have chosen either 1% or skim milk to place on my cereal. The kitchen remains full of food items and food preparation materials that will be used at some later time. The remainder of my house contains many other types of items sitting idly, waiting to be used at a future time. My Jaguar convertible will not be used today. It is raining, so I will take the Dodge minivan to the office.

Power-of-Two Policies

Springer series in operations research, Oct 27, 2009

We will extend the results of the last chapter in three ways. First, we will consider multistage ... more We will extend the results of the last chapter in three ways. First, we will consider multistage systems. These systems are characterized by multiple locations where inventory management decisions have to be made. Recall that in the last chapter, there was only a single stage, that is, the ordering and inventory management decisions involved only one location. Second, we will work with the reorder interval as the decision variable over which cost is optimized instead of the order quantity. We continue to assume that demand occurs at a deterministic and stationary rate. Thus, once we know the reorder interval, we can easily determine the corresponding order quantity. Therefore, the two decision variables are equivalent; our preference for the reorder interval is due to practical reasons, as we explain below. Third, instead of determining the optimal solution, we will develop algorithms that determine reorder intervals that are easier to use in practice but are not necessarily optimal. However, we will establish that the worst possible cost will not be higher than the optimal cost by more than 6%. These inventory management policies that we will develop are referred to as power-of-two (PO2) policies.

Single-Period Models

Springer series in operations research, Oct 27, 2009

The models and environments discussed in the preceeding chapters have all been based on the premi... more The models and environments discussed in the preceeding chapters have all been based on the premise that the demand process is deterministic. In most real situations, this assumption is violated. Our goal in this, and in subsequent chapters, is to consider uncertainty directly in the decision models. In this chapter we will study the most basic models in which demand is described by a random variable. These models pertain to situations in which only a single procurement decision is made, and the effect of that decision is felt over a single period of finite duration. These models are often called one-shot or newsvendor models.

A Tactical Planning Model for Managing Recoverable Items in Multi-Echelon Systems

Springer series in operations research, Oct 27, 2009

ABSTRACT

Optimal Policy for Database Batch Operations: Backup, Check-Pointing, and Batch Update

The effects of load smoothing on inventory levels in a capacitated production and inventory system

Stochastic Analysis of Cyclic Schedules

Operations Research, Oct 1, 1993

Principles of Inventory Management

Springer series in operations research, 2010

Managing inventories in multi-echelon on-line retail fulfillment system with different response lead time demands

When designing and operating an order fulfillment system for an on-line retailer, many factors mu... more When designing and operating an order fulfillment system for an on-line retailer, many factors must be taken into account. In this paper, we study a multi-echlon on-line fulfillment system with different response lead time demands. We present a delayed allocation system, which is called the primary warehouse system (PWS). In this system, inventories to satisfy different response lead time demands are managed differently. Since there are many millions of items managed in the system, determining stock levels quickly is a necessity. The focus of this paper is on planning inventory levels. Specifically, our goals are to describe a model for setting stock levels for each item, to present a computationally tractable method for determining their values, and to provide numerical results that illustrate the applications of the model to the on-line retailer's environment.

A comparison of alternative kanban control mechanisms. I. Background and structural results

Iie Transactions, Apr 1, 1995

The design of inventory control policies for serial systems is a topic currently being explored b... more The design of inventory control policies for serial systems is a topic currently being explored by a number of researchers. Our goal -in two papers - is to synthesize and extend some of these efforts. We consider, simultaneously, four sources of variability in production lines - processing time variability, machine breakdowns, rework and yield loss - and show some similarities

Production Control of Cyclic Schedules with Demand and Process Variability

Production and Operations Management, Jan 5, 2009

An Application of Lagrangian Relaxation to Scheduling in Power-Generation Systems

Operations Research, Jun 1, 1977

Two major decisions are made when scheduling the operations of a fossil-fuel power-generating sys... more Two major decisions are made when scheduling the operations of a fossil-fuel power-generating system over a short time horizon. The “unit commitment” decision indicates what generating units are to be in use at each point in time. The “economic dispatch” decision is the allocation of system demand among the generating units in operation at any point in time. Both these decisions must be considered to achieve a least-cost schedule over the short time horizon. In this paper we present a mixed integer programming model for the short time horizon power-scheduling problem. The objective of the model is to minimize the sum of the unit commitment and economic dispatch costs subject to demand, reserve, and generator capacity and generator schedule constraints. A branch-and-bound algorithm is proposed using a Lagrangian method to decompose the problem into single generator problems. A sub gradient method is used to select the Lagrange multipliers that maximize the lower bound produced by the relaxation. We present computational results that indicate the technique is capable of solving large problems to within acceptable error tolerances.

Reorder Point, Lot Size Models: The Continuous Review Case

Springer eBooks, Oct 27, 2009

When there is a significant fixed cost incurred when placing an order with a supplier, it is no l... more When there is a significant fixed cost incurred when placing an order with a supplier, it is no longer beneficial to order each time a demand occurs. In Chapter 2 we examined the impact of fixed costs on ordering quantities when the demand processes were known with certainty. Now we will study situations in which significant fixed ordering costs are incurred and the demand process is assumed to be a stationary stochastic process. Furthermore, we will assume a transaction reporting system exists. That is, we assume that we monitor the inventory levels continuously through time, and place an order for a quantity of stock, called the lot size, at a point in time so as to minimize the average annual cost of operations.

Lot Sizing Models: The Periodic Review Case

Springer series in operations research, Oct 27, 2009

We now turn our attention to managing inventory in a periodic review setting in which there are f... more We now turn our attention to managing inventory in a periodic review setting in which there are fixed costs incurred when placing orders. Thus we are examining the same type of problem presented in the previous chapter, but doing so now in a periodic review rather than a continuous review operational environment. As was the case in our study of continuous review systems, owing to the presence of these fixed ordering costs, it may no longer be economical to place an order in each period of the planning horizon. The fixed cost requires that the order be large enough to justify incurring this cost. This leads to a policy in which there are two critical numbers: the reorder point and the order-up-to level. This is the (s,S) policy introduced in the preceding chapter. When this policy is followed, an order is placed if and only if the inventory position at the beginning of a period is less than or equal to the reorder point. If an order is placed, then the size of the order will be such that the inventory position after placing the order will be equal to the order-up-to level. This means that the size of the order has to be at least the difference between the order-up-to level and the reorder point.

Optimal policy for batch operations

Many database maintenance operations are performed periodically in batches, even in realtime syst... more Many database maintenance operations are performed periodically in batches, even in realtime systems. The purpose of this paper is to present a general model for determining the optimal frequency of these batch operations. Specifically, optimal backup, checkpointing, batch updating, and reorganization policies are derived. The approach used exploits inventory parallels by seeking the optimal number of items-rather than a time interval-to trigger a batch. The Renewal Reward Theorem is used to find the average long run costs for backup, recovery, and item storage, per unit time, which is then minimized to find the optimal backup policy. This approach permits far less restrictive assumptions about the update arrival process than did previous models, as well as inclusion of storage costs for the updates. The optimal checkpointing, batch updating, and reorganization policies are shown to be special cases of this optimal backup policy. The derivation of previous results as special cases of this model, and an example, demonstrate the generality of the methodology developed.

Background Concepts: An Introduction to the (s − 1, s) Policy under Poisson Demand

Springer series in operations research, Oct 27, 2009

In the previous chapter we studied order-up-to policies when time was divided into periods. We wi... more In the previous chapter we studied order-up-to policies when time was divided into periods. We will now discuss the implications of following a similar policy, called an (s–1, s) inventory policy. In this chapter we assume inventories are reviewed continuously in time. Recall that the stock level, s, measures the amount of inventory on hand plus on order minus backorders, that is, the stock level represents the inventory position for a particular location. In certain situations, we will refer to the on-order quantity as the “in resupply” quantity. This “in resupply” terminology is often used in military and aviation applications in which items fail and are repaired or are procured from an external source. When an (s–1, s) policy is followed in continuous review environments, an order is placed immediately whenever a demand occurs for one or more units of an item. The order quantity matches the size of the demand exactly. Hence, the inventory position is constant in the case where the demand process and costs are stationary over an infinite planning horizon, which is the one we will examine in some detail in this chapter.