Okitsugu Fujiwara

Ambulance deployment analysis: A case study of Bangkok

Abstract Ambulance deployment policies are examined in the case of Bangkok, the capital city of Thailand. The maximum expected coverage location model of Daskin is used to screen the large number of possible alternatives to arrive at ‘good’ solutions. Each of these solutions is then subjected to a detailed analysis by simulation. A new deployment policy is identified which provides current performance levels but with a lesser number of ambulances.

Reliability assessment of water supply systems with storage and distribution networks

The water supply system studied in this paper consists of a water treatment plant, a ground-level storage, a pumping station, and a distribution network in series. Expected served demand is employed to measure reliability taking into account both insufficient heads and flows at individual nodes in the network since it is the most important service level index provided to individual users. A basic method proposed is to assume that the insufficient nodal head reduces the effectiveness of flow supplied at the node and that the authority provides the maximum service to customers so that the real-time pump and network flow operations maximize the effective served system demand. The average value of the maximum effective served system demand relative to the total system demand over all system states is defined as system reliability, and the nodal reliability for each demand node is similarly defined. The Markov chain method introduced by Beim and Hobbs (1988) is employed to describe the evolution of the storage level over time so that the real-time pump and network flow operations can be accurately implemented by solving a nonlinear programming model. Two example systems are presented to demonstrate numerically the advantage of the method proposed in its consideration of the distribution network and nodal reliabilities.

Determining optimal order splitting and reorder level for N-supplier inventory systems

This paper considers multiple-supplier single-item inventory systems, where the item acquisition lead times of suppliers and demand arrival are random, and backorder is allowed. The acquisition takes place when the inventory level depletes to a reorder level, and the order is split among multiple suppliers. The acquisition lead times may have different distributions, the unit purchasing prices from suppliers may be different, and thus the order quantities for different suppliers may be different. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per unit time, consisting of the fixed ordering cost, procurement cost, inventory holding cost and shortage cost, is minimized. We develop a mathematical model describing the system in detail. We also conduct extensive numerical experiments to analyze the advantages and distinct characteristics of multiple-supplier systems.

Reliability improvement for water distribution networks through increasing pipe size

A method of reliability improvement is proposed for water distribution networks. The ratio of expected maximum total water supplied to total water demanded is employed as a measure of reliability. A nonlinear maximum flow model is used to calculate the maximum supply of water under possible link failures and the reliability of the network. Reliability is improved by increasing pipe size. The pipe size increase is determined by considering the ratio of marginal reliability to marginal cost. The method gives a symmetric design when the network is symmetric.

Reliability analysis of water distribution networks in consideration of equity, redistribution, and pressure‐dependent demand

A goal programming model has been developed to analyze the system behavior for the water distribution networks under contingency situations due to failures of pipes and pumps, taking into account three aspects: (1) equity, or sharing inconvenience equally among consumers; (2) redistribution of the network flows to reduce the negative consequences of a failure of one portion on other portions of the network; and (3) consideration of pressure-dependent demand delivery due to insufficient head, namely, if a nodal head falls below a desired level, the flow delivered to that node is reduced. The first priority of the goal program is to maximize the lowest nodal demand supply ratio (or the ratio of actually delivered demand to the required demand at a node). The second priority is to maximize the system demand supply ratio (or the ratio of actually delivered water to the required total system demand). Link flow directions in the model are not fixed but are determined by a set of criteria. The system behaviors with respect to the three aspects of reliability factors are examined through extensive numerical experiments. The impact of equity requirements on redistribution of network flows, link flow directions, nodal demand supply ratio, and system demand supply ratio when failure events become serious is examined in particular detail. It is found that equity requirements can satisfactorily bring about fair sharing of inconvenience among consumers. The model proposed also suggests that network operations should reverse some link flow directions in order to meet equity requirements under severe contingencies.

EOQ models for continuously deteriorating products using linear and exponential penalty costs

Abstract We present EOQ models for perishable products which consider continuous deterioration of the utility of a product and introduce an exponential penalty cost function as a measurement of the utility deterioration. The approach proposed is simple and can be used to obtain easily the closed forms of the economic order quantities, which have not previously been derived. These forms describe the effect of the penalty cost clearly and are a natural extension of economic order quantities for non-perishable products. Our results are shown to be consistent with reported EOQ models with exponential decay but derived more elaborately. Our approach has the added advantage that it can be easily extended to the economic lot scheduling problem for multi-item perishable products.

A reactive dynamic user equilibrium model in network with queues

A discrete time reactive dynamic user equilibrium (DUE) model for network with queues is presented. Based on the point queue model, each link is assumed to have a constant running time and queuing delay caused by link exit capacity. The link performance function and link exit function are given as functions of the arrival rate and the queue length, where the first-in-first-out (FIFO) rule is shown to be satisfied. The DUE problem is then formulated as a variational inequality (VI) problem over a polyhedral set by constructing a new network so that the path enumeration is avoided. Therefore the proposed model is applicable for large-scale networks. The existence of solution for VI problem is proved, and an iteration method is discussed in detail. A static capacity constrained model is employed to initialize the network and avoid the zero-flow network at initial time. Finally, the advantages of the new model and method proposed are tested by numerical examples.

Optimality of Myopic Ordering Policies for Inventory Model with Stochastic Supply

This paper addresses a discrete time inventory model where the maximum amount of supply from which instantaneous replenishment orders can be made is a random variable. Optimal ordering policies are characterized as critical number policies with monotone increasing optimal critical values. A sufficient condition is then presented for myopic ordering policies to be optimal.

An optimal (Q,r) policy for a multipart assembly system under stochastic part procurement lead times

Abstract We consider an EOQ-type model for a simple production system, where a number of parts are acquired to produce a single product and the part procurement lead times are random. Assembly is instantaneous and takes place intermittently in batches but cannot start until all the parts are available. The problem is to simultaneously determine when to order each part and what lot size to produce, namely to determine the reorder point for each part and the assembly lot size, so that the average total cost per unit time, composed of the setup cost, inventory holding costs for the parts and the assembled product, and the shortage cost for the assembled product, is minimized. We then develop a tailormade solution method for this problem to obtain a global optimal solution by taking advantage of the structure of the problem formulation, where the nonlinear programming problem is decomposed into a family of subproblems parametrized by the average assembly delay time. Numerical experiments are then conducted for the case of twopart problems, and some interesting observations are made.

An optimal ordering and issuing policy for a two-stage inventory system for perishable products

This paper considers the problem of ordering and issuing policies arising in controlling finite-life-time fresh-meat-carcass inventories in supermarkets. A supermarket orders a product, which constitutes a set of sub-products of fixed proportion, from a vendor at the beginning of each time cycle. After it is received from the vendor, the product is stored in the cool-room, before being issued to the display shelves. The sub-products then satisfy random customer demand. After passing the life-time, sub-products are salvaged. In this system, the sub-products are issued to the display shelves according to theorder-up-to level policies at the beginning of every period. The decisions to be taken to solve this problem are the product-ordering quantity from the outside vendor and the order-up-to issuing quantities for each sub-product. The objective function to be maximized is the expected profit per unit time, consisting of revenue from sales and salvage, and the cost of ordering, processing (or issuing), inventory holding, emergency issuing, and shortage. In this paper we first develop a mathematical model describing actual operations and then simplify the sub-product runout period so that optimal ordering and issuing policies are easily established. We then carry out extensive numerical experiments for a case of two sub-products in order to ascertain the properties and the behavior of the optimal solutions.