Israel David

How far should JIT vendor–buyer relationships go?

Abstract In pull production management systems such as JIT, deliveries must be made on an as-needed basis only, and production begins only when requested. It is supposed to match customer demand, i.e., producing only enough to replenish what the customer has used or sold. In this work, we argue that there should be a certain degree of independence between successive links of the supply chain, to allow flexibility in production management in individual links. We attempt to identify the degree of independence and level of flexibility in terms of lot sizing and delivery scheduling in a single-vendor–single-buyer system. Toward this aim, appropriate two-sided vendor–buyer inventory–production models are formulated, some interesting conclusions from their analysis are drawn, and a numerical study, which compares relevant policies, is discussed. It shows that imposing a lot-for-lot production on the JIT supplier is strikingly un-economical. On the other hand, delivery on demand can be met without intervening in the suppliers operations, and where deviation from the optimal of the resulting joint total costs is tolerable.

Sequential Assignment Match Processes with Arrivals of Candidates and Offers

An infinite random stream of ordered pairs arrives sequentially in discrete time. A pair consists of a “candidate” and an “offer,” each of which is either of type I (with probability p ) or of type II (with probability q = 1 – p ). Offers are to be assigned to candidates, yielding a reward R > 0 if they match in type, or a smaller reward 0 ≤ r ≤ R if not. An arriving candidate resides in the system until it is assigned, whereas an arriving offer is either assigned immediately to one of the waiting candidates or lost forever. We show that the optimal long-term average reward is R , independent of the population proportion p and the “second prize” r , and that the optimal average reward policy is to assign only a match. Optimal policies for discounted and finite horizon models are also derived.

An Inventory Model with Exogenous Failures

This note introduces a model where inventory is repeatedly wiped out due to exogenous failure processes. The difference between this model and perishable inventory models is pinpointed by two sample examples. Relevant applications are also mentioned.

A dynamic-programming approach to continuous-review obsolescent inventory problems

Inventory models of modern production and service operations should take into consideration possible exogenous failures or the abrupt decline of demand resulting from obsolescence. This article analyzes continuous-review versions of the classical obsolescence problem in inventory theory. We assume a deterministic demand model and general continuous random times to obsolescence (“failure”). Using continuous dynamic programming, we investigate structural properties of the problem and propose explicit and workable solution techniques. These techniques apply to two fairly wide (and sometimes overlapping) classes of failure distributions: those which are increasing in failure rate and those which have finite support. Consequently, several specific failure processes in continuous time are given exact solutions.

A Sequential Assignment Match Process with General Renewal Arrival Times

This work studies sequential assignment match processes, in which random offers arrive sequentially according to a renewal process, and when an offer arrives it must be assigned to one of given waiting candidates or rejected. Each candidate as well as each offer is characterized by an attribute. If the offer is assigned to a candidate that it matches, a reward R is received; if it is assigned to a candidate that it does not match, a reward r ≤ R is received; and if it is rejected, there is no reward. There is an arbitrary discount function, which corresponds to the process terminating after a random lifetime. Using continuoustime dynamic programming, we show that if this lifetime is decreasing in failure rate and candidates have distinct attributes, then the policy that maximizes total expected discounted reward is of a very simple form that is easily determined from the optimal single-candidate policy. If the lifetime is increasing in failure rate, the optimal policy can be recursively determined: a solution algorithm is presented that involves scalar rather than functional equations. The model originated in the study of optimal donor-recipient assignment in live-organ transplants. Some other applications are mentioned as well.

An efficient heuristic for a partially observable Markov decision process of machine replacement

There is, so far, only limited practical experience applying solution schemes for real-life partially observable Markov decision processes (POMDPs). In this work we address the special-case POMDP associated with the famous machine-replacement problem. The machine deteriorates down a series of states according to known transition probabilities. A state is identified by a probability of producing a defective item. Only a sample of the produced items is observable at each stage, in which it is to be decided whether to replace the machine or not. We suggest a very simple heuristic decision-rule that can easily handle replacement-type problems of large size and which is based on the Howard solution of the fully observable version of the problem. By a simulation experimental design we compare the performance of this heuristic relative to the generic POMDP solution algorithm which has been proposed by Lovejoy.

A new algorithm for the multi-item exponentially discounted optimal selection problem

Abstract We approach the classical problem of optimal selection, where n identical units have to be sold to bidders who come in an infinite stream, and it has to be decided which bids to accept and when. Optimal strategies are defined so as to maximize the expected total discounted revenue from the n units. The present work assumes that bids are i.i.d. and that they arrive according to a general renewal process. Observing that the optimal policy may be determined using a series of threshold values which are sorted by the values of a discrete approximation of the bid-distribution, and that in the case of exponential discounting these threshold values are easily calculable, we propose an appropriate solution algorithm. The algorithm provides the value of the problem as well.

Lanchester modeling and the biblical account of the battles of gibeah

A very basic Lanchester model is given to fit the story in Judges 20 about the “War at Gibeah.” The narrative, as is usual in the Bible, is very elliptic with regard to technical details. The model presented in this article can aid one to more fully understand the story, particularly the role played by the famed slingers of the tribe of Benjamin.

Explicit results for a class of asset-selling problems

We consider the following optimal selection problem: There are n identical assets which are to be sold, one at a time, to coming bidders. The bids are i.i.d. where there are only two possible bid-values, with known probabilities. The stream of bidders constitutes a general renewal process, and rewards are continuously discounted at a constant rate. The objective is to maximize the total expected discounted revenue from the sale of the n assets. The optimal policy here is stationary, where the decision in question is only whether to accept a low bid or not; the answer is affirmative depending on a critical number n∗ of remaining assets. In this paper we derive an explicit formula for n∗, being a function of the Laplace transform of the renewal distribution evaluated at the discount rate, the probability for a low bid, and the ratio between the two bid-values. We also specify the pertinent value functions. Applications of the model are discussed in detail, and extensions are made to include holding costs and to allow for optimal pricing.

On Conducting Simultaneous Versus Sequential Engineering Activities in Risky R&D

We consider development projects in which the activities can be classified in two types: uncertainty resolving RD and routine technical investments which aim at improving the profitability of the project once the discovery has been made. The advantage of initiating routine preparatory activities prior to the achievement of a technological breakthrough in such projects, sometimes termed as ‘concurrent engineering’, is analyzed within a suitable dynamic optimization framework. The optimal double expenditure policy is compared with the conservative delayed investment policy, under which all the routine engineering activities are delayed until the risky R&D efforts culminate in a breakthrough. A criterion for the optimality of the latter policy is developed on the basis of the probability distribution of the discovery date. The application of the criterion is illustrated for a variety of specifications regarding the uncertainty associated with the R&D process. We find that simultaneous investment is the optimal policy for a large class of probability distributions. However, if the conditional probability of immediate discovery is always below some critical value, it is optimal to delay the preparatory activities until the discovery.