Routing and scheduling of vehicles and crews: The state of the art

The single-period problem (SPP), also known as the newsboy or news-vendor problem, is to find the order quantity which maximizes the expected profit in a single period probabilistic demand framework. Interest in the SPP remains unabated and many extensions to it have been proposed in the last decade. These extensions include dealing with different objectives and utility functions, different supplier pricing policies, different news-vendor pricing policies and discounting structures, different states of information about demand, constrained multi-products, multiple-products with substitution, random yields, and multi-location models. This paper builds a taxonomy of the SPP literature and delineates the contribution of the different SPP extensions. This paper also suggests some future directions for research.

The single-period (news-vendor) problem: literature review and suggestions for future research

Traditionally, fashion products have incurred high losses due to stockouts and inventory obsolence because long lead times coupled with a concentrated selling season force all or at least most production to be committed before demand information is available. Under a Quick Response system, lead times are shortened sufficiently to allow a greater portion of production to be scheduled in response to initial demand. We model and analyze the decisions required under Quick Response and give a method for estimating the demand probability distributions needed in our model. We applied these procedures with a major fashion skiwear firm and found that cost relative to the current informal response system was reduced by enough to increase profits by 60%. Relative to the cost that would have been incurred if no response were used, optimized response reduces cost by enough to roughly quadruple profits.

https://www.jstor.org/stable/pdfplus/171907.pdf

Reducing the Cost of Demand Uncertainty Through Accurate Response to Early Sales

Production scheduling can be defined as the allocation of available production resources over time to best satisfy some set of criteria. Typically, the scheduling problem involves a set of tasks to be performed, and the criteria may involve both tradeoffs between early and late completion of a task, and between holding inventory for the task and frequent production changeovers. The intent of this paper is to present a broad classification for various scheduling problems, to review important theoretical developments for these problem classes, and to contrast the currently available theory with the practice of production scheduling. This paper will highlight problem areas for which there is both a significant discrepancy between practice and theory, and for which the practice corresponds closely to the theory.

A Review of Production Scheduling

The literature on maintenance models is surveyed. The focus is on work appearing since the 1965 survey "Maintenance Policies for Stochastically Failing Equipment: A Survey" by John McCall and the 1965 book", "The Mathematical Theory of Reliability", by Richard Barlow and Frank Proschan. The survey includes models which involve an optimal decision to procure, inspect, and repair and/or replace a unit subject to deterioration in service.

A survey of maintenance models: The control and surveillance of deteriorating systems

We consider the situation of a family of items sharing a common supplier or common production facility. There is a major setup header cost to make a replenishment of the family and a minor line cost for each item included in the replenishment. In such a setting it makes sense to coordinate replenishments of the various items of a family. Under the assumption of deterministic demand, several authors have suggested iterative solutions which are not necessarily guaranteed to be optimal, yet are not easy to implement. We present an alternative procedure which is extremely simple to use, yet appears to have rather small cost penalties in relation to the earlier more sophisticated methods.

A Simple Method of Determining Order Quantities in Joint Replenishments Under Deterministic Demand

We consider the situation of a deterministic demand pattern having a linear trend. The problem is to select the timing and sizes of replenishments so as to keep the total of replenishment and carrying costs as low as possible. An earlier developed heuristic for the general case of a deterministic, time-varying, demand pattern is specialized to the case of a linear trend. The simple decision rule is shown to lead to small cost penalties in two examples that have been exactly analyzed in an earlier article in this journal.

A Simple Inventory Replenishment Decision Rule for a Linear Trend in Demand

We consider the situation of a single item having a deterministic, time-varying demand pattern. Production lot sizes, so as to minimize the total of setup and carrying costs, are to be determined subject to production capacity restrictions that can vary with time. Two important theorems concerning properties of the optimal solution are exploited in developing a tree search algorithm. In addition, other properties are utilized to reduce the amount of search necessary. Results of extensive tests are presented and discussed.

An Algorithm for the Dynamic Lot-Size Problem with Time-Varying Production Capacity Constraints

In this paper the economic order quantity formulation is extended to include the case where the quantity received from the supplier does not necessarily match the quantity requisitioned. The best o...

Establishing The Order Quantity When The Amount Received Is Uncertain

A style goods item has a finite selling period during which the sales rate varies in a seasonal and, to some extent, predictable fashion. There are only a limited number of opportunities to purchase or manufacture the style goods item, and the cost, in general, will depend on the time at which the item is obtained. The unit revenue achieved from sales of the item also varies during the selling season, and, in particular, reaches an appreciably lower terminal salvage value. Previous work on this class of problem has assumed one of the following: (a) There is a known deterministic sales rate during the season. (b) The sales are generated by a stochastic process having exactly known probabilities. Both of these formulations of the problem overlook what we believe to be an essential feature—that initially we have a great uncertainty concerning the sales potential of the item but have an opportunity to develop a better forecast as actual sales become known. The model discussed in this paper treats the sales po...

Edward A. Silver

Papers

A Simple Method of Determining Order Quantities in Joint Replenishments Under Deterministic Demand

A Simple Inventory Replenishment Decision Rule for a Linear Trend in Demand

An Algorithm for the Dynamic Lot-Size Problem with Time-Varying Production Capacity Constraints

Establishing The Order Quantity When The Amount Received Is Uncertain

A Bayesian Analysis of the Style Goods Inventory Problem