Shaul P. Ladany

Optimal cruise-liner passenger cabin pricing policy

Abstract The first attempt, in any marketing environment, to consider the optimal number of market segments, as well as the corresponding prices, is performed here in conjunction with cruise liners. The optimal market segmentation pricing strategy for passenger cabins on cruise-liners is investigated under the assumption of an aggregate linear demand function, and for four different situations: (a) single price market, (b) optimal segmentation of the Unused capacity of a single-price-market, (c) optimal segmentation of all cabins, and (d) optimal segmentation allowing for infiltration from higher-priced to adjacent lower-priced segments. A numerical example is provided for each case.

NETWORK MODELS FOR SEAT ALLOCATION ON FLIGHTS

This paper examines the problem of proper (optimal) control over the seat allocation on flights. Given a heterogeneous fleet of aircraft types, multi-leg flights, a number of different passenger categories, and cancelations, an airlines objective is to devise an effective system which aids in setting the seat allocation targets for each category of passengers on each flight. This issue is analyzed by a number of authors in the context of economic, simulation based, probabilistic, and mathematical programming studies. We present an attempt to address this problem from the systems prospective emphasizing characteristics such as: passenger cancelations, multi-leg flights, and rolling tactical planning time horizon. Starting from a very simple network flow models for a single flight with a number of intermediate stops, a number of progressively complex models are presented. The airline flights and the seat allocation system are represented as a generalized network flow model (with gains/losses on arcs) with the objective of flow maximization (profit maximization). This modelling approach does not claim to replace the seat allocation approaches presented in Alstrup et al. (1985), Mayer (1976), Richter (1982), Simpson (1985a), and Wang (1983), but rather construct seat allocations utilizing some of those referenced schemes in a parameter setting mode for a large network model. The objective of this paper is not to report on computational experiments, but to present a modeling approach which seems to be promising, if somewhat speculative.

A discounted machine-replacement model with an expected future technological breakthrough

A machine-replacement problem is analyzed in a technological-development environment, in which a new-type machine (built by a new technology) may appear in the future. The solution of the replacement problem depends on purchasing, operating, and resale costs, and on the probability distribution of the market debut of the new technology, and it indicates whether to replace the existing machine now with an available similar type of machine, or to continue to operate the existing machine for at least one more period. A dynamic discounted cost model is presented, and a method is suggested for finding the optimal age for replacement of an existing machine (under rather general conditions of a technological environment). A solution procedure and a numerical example are given.

Optimal seat allocation for flights with one intermediate stop

Abstract During the time prior to departure of a flight with an intermediate stop decisions must be made concerning the allocation of reserved seats to passengers requesting space on the full or partial spans of the flight. The paper presents a model for finding the maximum allowable allocation of seats on the various spans at each time prior to departure such that a maximum expected contribution to profit for the flight is obtained. The model utilizes the time distribution of reservations and cancellations for both spans. Consideration is given to the effects of waitlists, standbys and overbookings. A Bayesian reassessment of probabilities is incorporated in a sequential decision procedure. A computer program was written to perform the calculations, and the results of a short sample problem which was run to test the validity of the model are presented.

The one-period bus touring problem: Solved by an effective heuristic for the orienteering tour problem and improvement algorithm

Abstract The one-period bus touring problem – also referred to as simply the bus touring problem (BTP) – objective is to maximize the total attractiveness of the tour by selecting a subset of sites to be visited and scenic routes to be traveled – both having associated non-negative attractivity values – given the geographic frame considerations and constraints on touring time, cost and/or total distance. The integer linear-programming model developed to derive an optimal bus touring solution for the BTP is not practical for such a NP-complete problem. A similar NP-hard problem is the orienteering tour problem (OTP) in which the identical start and end point is specified along with other locations having associated scores. Competitors seek to visit in a fixed amount of time, a subset of locations in order to maximize the total score. This paper presents a transformation from the BTP to the OTP and illustrates the use of an effective heuristic for the OTP together with an improvement process, aimed at generating a fast near-optimal BTP solution. The results of 11 bus touring problems are presented.

Optimal routing of a single vehicle with loading and unloading constraints

A real-life situation in which a trucker has to collect a cargo of similar size from n different customers spread out in a given region and to deliver them to n locations spread out in another far-away region has been formulated as a route-design problem for a single vehicle. The minimal total time of loading, shipping and unloading is considered for different reshuffling methods, and the optimal method is determined. A solution procedure by enumeration is suggested to solve an actual small size problem, and an illustration is provided. (Author/TRRL)

Profit Maximizing Warranty Period with Sales Expressed by a Demand Function

The problem of determining the optimal warranty period, assumed to coincide with the manufacturers lower specification limit for the lifetime of the product, is addressed. It is assumed that the quantity sold depends via a Cobb–Douglas-type demand function on the sale price and on the warranty period, and that both the cost incurred for a non-conforming item and the sale price increase with the warranty period. A general solution is derived using Response Modeling Methodology (RMM) and a new approximation for the standard normal cumulative distribution function. The general solution is compared with the exact optimal solutions derived under various distributional scenarios. Relative to the exact optimal solutions, RMM-based solutions are accurate to at least the first three significant digits. Some exact results are derived for the uniform and the exponential distributions. Copyright

Efficient Sampling by Artificial Attributes

Hypotheses about the fraction of items in a lot possessing a “specification attribute” X < L can be tested by generally sampling the variable X or directly sampling the attribute of interest. When the process variance is known, it is often more efficient to test against “compressed limits” for one or more “artificial” attributes X < La , X < Lb etc. This study discusses the efficient choice of one or two compressed limits. General guidelines for this choice are suggested, and then evaluated under many hypothetical test specifications. One compressed limit offered ~40% – 97% savings over direct attribute sampling; two limits allowed about 20% further savings.

Optimal Scheduling Of Ocean Cruises

AbstractA company leasing a luxury ocean liner for Christmas cruises from southern Florida is confronted with the problem of deciding upon the type of cruises to be offered. The decision variables include the routings, the durations, the departure dates, and the fare schedules of the cruises. The problem was solved in two stages. The first stage involved the estimation of the demand curve for various itineraries and fares using regression analysis. In the second stage, a Dynamic Programming model was formulated to maximize the net profit for the season by establishing the required optimal values of the decision variables. The approach was applied to a case involving cruises to the Bahamas, Jamaica, and Puerto Rico.

Bayesian dynamic operating rules for optimal hotel reservations

SummaryDuring the time prior to rent of rooms in a hotel, decisions have to be made concernin the allocation of the rooms to customers requesting single-bed or double-bed rooms. The paper presents a model for finding the maximum allowable number of bookings of customers requesting single and double-bed rooms at each time prior to rent such that a maximum expected contribution to profit for the rental day is obtained.The model utilizes the time distribution of reservations and cancellations for both room sizes. Consideration is given to the effects of late unbooked arrivals, waitlists, standbys and overbookings. A Bayesian reassessment of probabilities is incorporated in a sequential decision procedure. The model is extendable to handle requests for periods longer than a single night, for group requests of various room types, and for different combinations of them. A numerical example is provided.ZusammenfassungWährend des Vorbuchungszeitraumes von Hotelzimmern müssen Entscheidungen über die Zimmerzuteilung je nach Kundenwunsch getroffen werden. Der Aufsatz beschreibt ein Modell für das Auffinden der maximal möglichen Anzahl von Buchungen für Ein- und Zweibettzimmer zu jedem Vorbestellungszeitpunkt. Hierdurch kann der Gesamtertrag je Miettag maximiert werden.Das Modell macht sich die Zeitverteilung von Reservierung und Stornierung für beide Zimmergrößen zunutze. Berücksichtigt werden spätere, nicht gebuchte Ankünfte, Wartelisten, länger als geplante Aufenthalte und Überbuchungen. Das Modell basiert auf einem mehrstufigen Entscheidungsprozeß. Es kann für längere Zeiträume, Gruppenanfragen sowie Kombinationen davon ausgebaut werden. Das praktische Vorgehen wird an einem numerischen Beispiel dargestellt.