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## Interactive bicriterion decision support for a large scale industrial scheduling system

### Annals of Operations Research (2015-04-01) 227: 45-61 , April 01, 2015

In this paper we develop an interactive decision analysis approach to treat a large scale bicriterion integer programming problem, addressing a real world assembly line scheduling problem of a manufacturing company. This company receives periodically a set of orders for the production of specific items (jobs) through a number of specialised production (assembly) lines. The paper presents a non compensatory approach based on an interactive implementation of the *ε*-constraint method that enables the decision maker to achieve a satisfactory goal for each objective separately. In fact, the method generates and evaluates a large number of non dominated solutions that constitute a representative sample of the criteria ranges. The experience with a specific numerical example shows the efficiency and usefulness of the proposed model in solving large scale bicriterion industrial integer programming problems, highlighting at the same time the modelling limitations.

## Research on permutation flow shop scheduling problems with general position-dependent learning effects

### Annals of Operations Research (2013-12-01) 211: 473-480 , December 01, 2013

Machine learning exists in many realistic scheduling situations. This study focuses on permutation flow shop scheduling problems, where the actual processing time of a job is defined by a general non-increasing function of its scheduled position, i.e., general position-dependent learning effects. The objective functions are to minimize the total completion time, the makespan, the total weighted completion time, and the total weighted discounted completion time, respectively. To solve these problems, we present approximation algorithms based on the optimal permutations for the corresponding single machine scheduling problems and analyze their worst-case error bound.

## Joint pricing and inventory control for additive demand models with reference effects

### Annals of Operations Research (2015-03-01) 226: 255-276 , March 01, 2015

We study a periodic review joint inventory and pricing problem of a single item with stochastic demand subject to reference effects. The random demand is contingent on the current price and the reference price that acts a benchmark against which customers compare the price of a product. Randomness is introduced with an additive random term. The customers perceive the difference between the price and the reference price as a loss or a gain. Hence, they have different attitudes towards them, such as loss aversion, loss neutrality or loss seeking. We model the problem using safety stock as the decision variable and show that the problem can be decomposed into two subproblems for all demand models under mild conditions. Using the decomposition, we show that a steady state solution exists for the infinite horizon problem and we characterize the steady state solution. Defining the modified revenue as revenue less the production cost, we show that a state-dependent order-up-to policy is optimal for concave demand models with concave modified revenue functions and provide example demand models with absolute difference reference effects and loss-averse customers. We also show that the optimal inventory level increases with the reference price. All of our results hold for finite and infinite horizon problems.

## A multiscale decision theory analysis for revenue sharing in three-stage supply chains

### Annals of Operations Research (2015-03-01) 226: 277-300 , March 01, 2015

Revenue sharing is an effective mechanism for coordinating decisions in a supply chain. For a three-stage supply chain, we explore how revenue-based incentives can be used by the stage 1 supply chain agent (retailer) to motivate cooperative behavior from its two upstream partners with conflicting interests. To illustrate our analysis, we provide a food supply chain example, with retailer, processor and farmer. Compared to the frequently studied two-stage problem, a three-stage supply chain leads to a more complex decision and incentive problem. To model and solve this more complex problem, we apply multiscale decision theory (MSDT), a novel approach for multi-level system analysis. MSDT enables us to account for uncertainties at all stages of the supply chain, not just at the final stage, and to derive analytic solutions. Results show and quantify the extent to which contracting and information sharing facilitate chain-wide cooperation. Further, it determines optimal decisions and incentives for agents at each stage. This paper is the first to apply MSDT to supply chains and contributes to its theory by advancing MSDT modeling and analysis capabilities. The modeling and solution approach can be applied to decision and inventive problems in other multi-level enterprise systems.

## Combining optimization with simulation to obtain credible models for intensive care units

### Annals of Operations Research (2014-10-01) 221: 255-271 , October 01, 2014

In this paper we develop a simulation model to study bed occupancy levels in an Intensive Care Unit (ICU). The main contributions of this study are: (1) A proposal for generalized regression models to fully capture the high variability of patients’ length of stay; (2) Proof that a simulation model that does not incorporate the management decisions by clinical staff cannot be considered valid; (3) The development of a mathematical model to represent these management decisions, and (4) A proposal for a method combining optimization with simulation to estimate the model parameters.

This provides a valid simulation model that includes the physician management of an ICU. Validation is accomplished by comparing distribution patterns in daily bed occupancy records against simulated bed occupancy data.

The methodology is tested using data provided by the Hospital of Navarre in Spain.

## Advanced basis construction in linear programming

### Annals of Operations Research (1986-05-01) 5: 413-424 , May 01, 1986

This paper considers basis construction in a linear program when the number of activities with basic status is not equal to the number of rows in the particular scenario. This arises when starting with an ‘advanced basis’, obtained from a solution to another scenario. The goal here is to provide a triangular-seeking algorithm that takes advantage of structural properties during the construction of a basis agenda. For completeness, some facts, which are known but have not been published, are given about choosing an advanced basis and about spikes.

## A generalized coupon collecting model as a parsimonious optimal stochastic assignment model

### Annals of Operations Research (2013-09-01) 208: 133-146 , September 01, 2013

There is a given set of *n* boxes, numbered 1 thru *n*. Coupons are collected one at a time. Each coupon has a binary vector *x*_{1},…,*x*_{n} attached to it, with the interpretation being that the coupon is eligible to be put in box *i* if *x*_{i}=1,*i*=1…,*n*. After a coupon is collected, it is put in a box for which it is eligible. Assuming the successive coupon vectors are independent and identically distributed from a specified joint distribution, the initial problem of interest is to decide where to put successive coupons so as to stochastically minimize *N*, the number of coupons needed until all boxes have at least one coupon. When the coupon vector *X*_{1},…,*X*_{n} is a vector of independent random variables, we show, if *P*(*X*_{i}=1) is nondecreasing in *i*, that the policy *π* that always puts an arriving coupon in the smallest numbered empty box for which it is eligible is optimal. Efficient simulation procedures for estimating *P*_{π}(*N*>*r*) and *E*_{π}[*N*] are presented; and analytic bounds are determined in the independent case. We also consider the problem where rearrangements are allowed.

## A parameterized hessian quadratic programming problem

### Annals of Operations Research (1986-05-01) 5: 373-394 , May 01, 1986

We present a general active set algorithm for the solution of a convex quadratic programming problem having a parametrized Hessian matrix. The parametric Hessian matrix is a positive semidefinite Hessian matrix plus a real parameter multiplying a symmetric matrix of rank one or two. The algorithm solves the problem for all parameter values in the open interval upon which the parametric Hessian is positive semidefinite. The algorithm is general in that any of several existing quadratic programming algorithms can be extended in a straightforward manner for the solution of the parametric Hessian problem.

## Supply chain networks with global outsourcing and quick-response production under demand and cost uncertainty

### Annals of Operations Research (2013-09-01) 208: 251-289 , September 01, 2013

This paper develops a modeling and computational framework for supply chain networks with global outsourcing and quick-response production under demand and cost uncertainty. Our model considers multiple off-shore suppliers, multiple manufacturers, and multiple demand markets. Using variational inequality theory, we formulate the governing equilibrium conditions of the competing decision-makers (the manufacturers) who are faced with two-stage stochastic programming problems but who also have to cooperate with the other decision-makers (the off-shore suppliers). Our theoretical and analytical results shed light on the value of outsourcing from novel real option perspectives. Moreover, our simulation studies reveal important managerial insights regarding how demand and cost uncertainty affects the profits, the risks, as well as the global outsourcing and quick-production decisions of supply chain firms under competition.

## Flexible hiring in a make to order system with parallel processing units

### Annals of Operations Research (2013-10-01) 209: 159-178 , October 01, 2013

In this paper, we study a make-to-order production system with parallel, identical processing units. Each order needs to be satisfied on a single processing unit that is run by a crew. The inter-arrival time and the service time for each order are random variables. The system operates under a lead time performance constraint, which demands the completion of each order within a pre-determined lead time with a certain probability. The minimum number of processing units needed to satisfy this constraint is determined at the tactical level. Our research focuses on the cost savings that can be realized with the use of flexible crews via contractual hiring agreements with an External Labor Supply Agency (ELSA). The ELSA can periodically provide an agreed number of crews. The cost incurred for a flexible crew is higher than that for a permanent crew, and is decreasing in the period length. We model and analyze this system using the transient behavior analysis of multi-server queues and propose several empirically testable functions for the cost of flexible crews. In our computational study, we demonstrate possible cost savings of 2-level, threshold type hiring policies, relative to the fixed capacity system, under 9 scenarios with three demand-to-processing rate ratios and three lead time performance constraints, each of which reflects a different level of ambition. We observe that the maximum savings occur when the cost of a flexible crew is same as that of a permanent crew, and range from 29.38% to 50.56%. However, as the flexible crews become more expensive, the system may choose to employ permanent crews only. We observe that cost savings consist of two parts: savings due to the cancellation of the sclerosis of capacity discreteness, and savings due to the use of workload information in hiring actions. The latter part is higher for more ambitious lead time performance constraints, and for higher mean processing times. Finally, when there is an additional cost for transacting an agreement with the ELSA, we observe that the capacity flexibility option loses its charm, especially if the transaction cost is higher than the cost of a permanent crew.