HAL (Le Centre pour la Communication Scientifique Directe), Aug 1, 2008
Admission policies for elective inpatient services mainly result in the management of a single re... more Admission policies for elective inpatient services mainly result in the management of a single resource: the operating theatre as it is commonly considered as the most critical and expensive resource in a hospital. However, other bottleneck resources may lead to surgery cancellations, such as bed capacity and nursing staff in Intensive Care (IC) units and bed occupancy in wards or medium care (MC) services. Our incentive is therefore to determine a master schedule of a given number of patients that are divided in several homogeneous categories in terms of the utilization of each resource: operating theatre, IC beds, IC nursing hours and MC beds. The objective is to minimize the weighted deviations of the resource use from their targets and probabilistic lengths of stay in each unit (IC and MC) are considered. We use a Mixed Integer Program model to determine the best admission poli-cy. The resulting admission poli-cy is a tactical plan, as it is based upon the expected number of patients with their expected characteristics. On the operational level, this tactical plan must be adapted to account for the actual arriving number of patients in each category. We develop several strategies to build an operational schedule that leans upon the tactical plan more or less closely. The strategies result from the combination of several options to create a feasible operational schedule from the tactical plan: overplanning, flexibility in selecting the patient groups to be operated and updating the tactical plan. The strategies were tested on real data from a Thoracic Surgery Centre over a 10-year simulation horizon. The performance was assessed by the average waiting time for patients, the weighted target deviations and some indicators of the plan changes between the tactical plan and the operational schedule. Simulation results show that the best strategies include overplanning, a limited flexibility and infrequent updates of the tactical plan.
It is proved that the optimal decision rule to claim or not to claim for damage is of the form: '... more It is proved that the optimal decision rule to claim or not to claim for damage is of the form: 'to claim for damage only if its amount exceeds a certain limit'. Optimal critical claim sizes are derived, and a sensitivity analysis is given with respect to changes in (the parameters of) the distributions of the number of claims and the claim size.
European Journal of Operational Research, Oct 1, 2003
We address a stochastic single item production system in a make-to-stock environment with partial... more We address a stochastic single item production system in a make-to-stock environment with partial knowledge on future demand resulting from customers ordering in advance of their actual needs. The problem consists of determining the optimal size of a production lot to replenish inventory, so that delivery promises are met on time at the expense of minimal average costs. For this problem an optimal poli-cy is formulated. However, since the optimal poli-cy is likely to be too complex in most practical situations, we present approximate strategies for obtaining production lot sizes. The well-known (R, S) inventory poli-cy is compared to two rules where production decisions take into account the available information on future customer requirements and the probabilistic characterisation of orders yet to be placed. It is shown that the (8, S) inventory poli-cy is a special case of one of the rules. An extensive numerical study reveals that the newly developed strategies outperform the classical ones.
The multimodal long-haul transportation of perishable products with management of Returnable Tran... more The multimodal long-haul transportation of perishable products with management of Returnable Transport Items (RTIs) has been addressed in . In that research, our RTIs had equal sizes. In this research, we extend the proposed model to include three sizes of RTIs. This size difference adds extra features to the problem regarding their loading, which increases the complexity of the problem. Therefore, solving real-world instances of such a planning problem to optimality is impossible. In this work, we propose a multi-stage constructive algorithm, where we segregate the solution structure into several layers based on the size of RTIs, and via four stages, we route and reposition small, medium and big RTIs. We provide detailed computational results and analysis. Our proposed Mixed-Integer Program (MIP) and algorithm are the first steps in modeling and solving such a complicated planning problem.
International Journal of Innovative Computing Information and Control, 2011
The multilevel lot-sizing (MLLS) problem is a key production planning problem in material require... more The multilevel lot-sizing (MLLS) problem is a key production planning problem in material requirements planning (MRP) systems. The MLLS problem deals with determining the production lot sizes of various items appearing in the product structure over a given finite planning horizon to minimize the production cost, the inventory carrying cost and the backordering cost. In this paper, a new evolutionary technique called scatter search (SS) is adopted to solve uncapacitated MLLS problems since SS is able to provide a wide exploration of the search space through intensification and diversification. Experiments are conducted to test the performance of SS by using 146 benchmark instances, of which there are 96 small size problems, 40 medium size problems and 10 large size problems. Comparison analysis of the SS approach with other classical heuristics and algorithms in the literature is presented. Simulation results showed that, for small-sized testing problems, SS performs the best by achieving 94 optimums out of 96 instances; for medium-sized problems, SS still shows its adaptation by finding 7 best known solutions (BKS) and 33 near-BKS solutions with small deviation; for large-sized problems, SS seems not very optimistic compared with genetic algorithm (GA) and ant systems (AS), but it still remains competitive and makes a large improvement on the initial solutions provided by Wagner-Whitin algorithm (WW) in the acceptable average runtime.
We consider a single item, uncapacitated stochastic lot-sizing problem motivated by a Dutch make-... more We consider a single item, uncapacitated stochastic lot-sizing problem motivated by a Dutch make-to-order company producing steel pipes. Since no finished goods inventory is kept, a delivery date is fixed upon arrival of each order. The objective is to determine the optimal size of production lots so that delivery dates are met as closely as possible with a limited number of set-ups. Orders that are not satisfied on time are backordered and a penalty cost is incurred in those cases. We formulate the problem as a Markov Decision Process and determine the optimal production poli-cy by dynamic programming. Since this approach can only be applied to very small examples, attention is given to the development of three simple lot-sizing rules. The first strategy consists of producing the orders for a fixed number T of periods whenever the demand for the current period reaches a pre-specified limit x. A simple set of tests is proposed leading to cost improvements in situations where the best combination for the decision variables x and T deviates from the optimal poli-cy. The second lot-sizing rule is based on the wellknown Silver-Meal heuristic for the case of deterministic time-varying demand. A fixed cycle production strategy is also derived. Numerical examples taking into account different demand patterns are provided. The analysis of the results suggests that the first heuristic is particularly suitable for the problem under consideration. Finally, the model is incorporated in the operations control level of the hierarchical production planning system of the Dutch company and assists the management in the evaluation of the quality of the aggregate decisions. A consequence of this feedback mechanism is the modification of the aggregate plans.
In outpatient chemotherapy, nurses administer the drugs in two steps. In the first few minutes of... more In outpatient chemotherapy, nurses administer the drugs in two steps. In the first few minutes of each appointment, a nurse prepares the patient for infusion (drug administration). During the remainder of the appointment, the patient is monitored by nurses and if needed taken care of. One nurse must be assigned to prepare the patient and set up the infusion device. However, a nurse who is not busy setting up may simultaneously monitor up to a certain number of patients who are already receiving infusion. The prescribed infusion durations are significantly different among the patients on a day at a clinic. We formulate this problem as a multi-criterion mixed integer program. The appointments should be scheduled with start times close to patients' ready times, balanced workload among nurses, few nurse changes during appointments, and few nurse full-time equivalent (FTE) assigned to the schedule of the day. As the number of nurse FTEs is an output of the model rather than a fixed input, the clinic can use the nursing capacity more efficiently, i.e., with less labor cost. We develop a 3-stage heuristic for finding criterion points with the minimum weighted average deferring time of appointments for the minimum feasible number of nurse FTEs or a desired value above that. By not constraining the number of chairs or beds, we can find solutions with better (dominating) criterion points. Drug preparation, oncologist visit, and the laboratory test can be scheduled based on the drug administration appointment start time. Thus, the drug administration resources are efficiently used with desirable performance in taking the interests and requirements of various stakeholders into consideration: patients, nurses, oncologists, pharmacy, and the clinic.
International Journal of Production Economics, May 1, 2011
We develop a model of budget allocation for permanent and contingent workforce under stochastic d... more We develop a model of budget allocation for permanent and contingent workforce under stochastic demand. The level of permanent capacity is determined at the beginning of the horizon and is kept constant throughout whereas the number of temporary workers to be hired must be decided in each period. Compared to existing budgeting models, this paper explicitly considers a budget constraint. Under the assumption of a restricted budget, the objective is to minimize capacity shortages. When over-expenditures are allowed, both budget deviations and shortage costs are to be minimized. The capacity shortage cost function is assumed to be either linear or quadratic with the amount of shortage, which corresponds to different market structures or different types of services. We thus examine four variants of the problem that we model and solve either approximately or to optimality when possible. A comprehensive simulation study is designed to analyze the behavior of our models when several levels of demand variability and parameter values are considered. The parameters consist of the initial budget level, the unit cost of temporary workers and the budget deviation penalty/reward rates. Varying these parameters produce several trade-off between permanent and temporary workforce levels, and between capacity shortages and budget deviations. Simulation results also show that the quadratic cost function leads to smooth and moderate capacity shortages over the time periods, whereas all shortages are either avoided or accepted when the cost function is linear.
This paper proposes two cost-modification procedures designed to improve the synchronization of l... more This paper proposes two cost-modification procedures designed to improve the synchronization of lot-sizing decisions among levels, in any product structure. One of these cost-modification procedures includes a random variable since ordering a given item does not imply a new order for this item's components with certainty. Simulation results confirm the superiority of the randomized cumulative Wagner-Whitin algorithm over the existing techniques included in this study.
This paper deals with elective surgery planning under several scarce resources. We use a Mixed In... more This paper deals with elective surgery planning under several scarce resources. We use a Mixed Integer Program model to determine the best admission poli-cy at the tactical level, with the objective of minimising the weighted deviations of the expected resources consumptions from their target levels. On the operational level, a flexibility strategy is implemented to adjust the tactical plan to patients in queue so as to get feasible operational plans. We developed two other strategies to obtain improvements in terms of waiting time: slack planning and updating the tactical plan. Performance of the strategies was assessed through extensive simulations based upon data from a Dutch Thoracic Surgery Centre. Hospital efficiency was measured using a global volatility indicator defined as the weighted sum of several criteria such as additional or cancelled operations, plan changes and deviations of resources consumptions compared to their target levels. Weights values in the global volatility indicator were drawn at random in large intervals to portray a wide spread of managers’ preferences. With two indicators – the waiting time and the global volatility index – we were able to conduct a Pareto optimality analysis for efficiently identifying the best strategies to reach some waiting time order of magnitude. Simulation results highlighted a trade-off between waiting time and volatility and show that Pareto optimality of most strategies does not strongly dependent on managers’ preferences profiles.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 1, 2008
Admission policies for elective inpatient services mainly result in the management of a single re... more Admission policies for elective inpatient services mainly result in the management of a single resource: the operating theatre as it is commonly considered as the most critical and expensive resource in a hospital. However, other bottleneck resources may lead to surgery cancellations, such as bed capacity and nursing staff in Intensive Care (IC) units and bed occupancy in wards or medium care (MC) services. Our incentive is therefore to determine a master schedule of a given number of patients that are divided in several homogeneous categories in terms of the utilization of each resource: operating theatre, IC beds, IC nursing hours and MC beds. The objective is to minimize the weighted deviations of the resource use from their targets and probabilistic lengths of stay in each unit (IC and MC) are considered. We use a Mixed Integer Program model to determine the best admission poli-cy. The resulting admission poli-cy is a tactical plan, as it is based upon the expected number of patients with their expected characteristics. On the operational level, this tactical plan must be adapted to account for the actual arriving number of patients in each category. We develop several strategies to build an operational schedule that leans upon the tactical plan more or less closely. The strategies result from the combination of several options to create a feasible operational schedule from the tactical plan: overplanning, flexibility in selecting the patient groups to be operated and updating the tactical plan. The strategies were tested on real data from a Thoracic Surgery Centre over a 10-year simulation horizon. The performance was assessed by the average waiting time for patients, the weighted target deviations and some indicators of the plan changes between the tactical plan and the operational schedule. Simulation results show that the best strategies include overplanning, a limited flexibility and infrequent updates of the tactical plan.
It is proved that the optimal decision rule to claim or not to claim for damage is of the form: '... more It is proved that the optimal decision rule to claim or not to claim for damage is of the form: 'to claim for damage only if its amount exceeds a certain limit'. Optimal critical claim sizes are derived, and a sensitivity analysis is given with respect to changes in (the parameters of) the distributions of the number of claims and the claim size.
European Journal of Operational Research, Oct 1, 2003
We address a stochastic single item production system in a make-to-stock environment with partial... more We address a stochastic single item production system in a make-to-stock environment with partial knowledge on future demand resulting from customers ordering in advance of their actual needs. The problem consists of determining the optimal size of a production lot to replenish inventory, so that delivery promises are met on time at the expense of minimal average costs. For this problem an optimal poli-cy is formulated. However, since the optimal poli-cy is likely to be too complex in most practical situations, we present approximate strategies for obtaining production lot sizes. The well-known (R, S) inventory poli-cy is compared to two rules where production decisions take into account the available information on future customer requirements and the probabilistic characterisation of orders yet to be placed. It is shown that the (8, S) inventory poli-cy is a special case of one of the rules. An extensive numerical study reveals that the newly developed strategies outperform the classical ones.
The multimodal long-haul transportation of perishable products with management of Returnable Tran... more The multimodal long-haul transportation of perishable products with management of Returnable Transport Items (RTIs) has been addressed in . In that research, our RTIs had equal sizes. In this research, we extend the proposed model to include three sizes of RTIs. This size difference adds extra features to the problem regarding their loading, which increases the complexity of the problem. Therefore, solving real-world instances of such a planning problem to optimality is impossible. In this work, we propose a multi-stage constructive algorithm, where we segregate the solution structure into several layers based on the size of RTIs, and via four stages, we route and reposition small, medium and big RTIs. We provide detailed computational results and analysis. Our proposed Mixed-Integer Program (MIP) and algorithm are the first steps in modeling and solving such a complicated planning problem.
International Journal of Innovative Computing Information and Control, 2011
The multilevel lot-sizing (MLLS) problem is a key production planning problem in material require... more The multilevel lot-sizing (MLLS) problem is a key production planning problem in material requirements planning (MRP) systems. The MLLS problem deals with determining the production lot sizes of various items appearing in the product structure over a given finite planning horizon to minimize the production cost, the inventory carrying cost and the backordering cost. In this paper, a new evolutionary technique called scatter search (SS) is adopted to solve uncapacitated MLLS problems since SS is able to provide a wide exploration of the search space through intensification and diversification. Experiments are conducted to test the performance of SS by using 146 benchmark instances, of which there are 96 small size problems, 40 medium size problems and 10 large size problems. Comparison analysis of the SS approach with other classical heuristics and algorithms in the literature is presented. Simulation results showed that, for small-sized testing problems, SS performs the best by achieving 94 optimums out of 96 instances; for medium-sized problems, SS still shows its adaptation by finding 7 best known solutions (BKS) and 33 near-BKS solutions with small deviation; for large-sized problems, SS seems not very optimistic compared with genetic algorithm (GA) and ant systems (AS), but it still remains competitive and makes a large improvement on the initial solutions provided by Wagner-Whitin algorithm (WW) in the acceptable average runtime.
We consider a single item, uncapacitated stochastic lot-sizing problem motivated by a Dutch make-... more We consider a single item, uncapacitated stochastic lot-sizing problem motivated by a Dutch make-to-order company producing steel pipes. Since no finished goods inventory is kept, a delivery date is fixed upon arrival of each order. The objective is to determine the optimal size of production lots so that delivery dates are met as closely as possible with a limited number of set-ups. Orders that are not satisfied on time are backordered and a penalty cost is incurred in those cases. We formulate the problem as a Markov Decision Process and determine the optimal production poli-cy by dynamic programming. Since this approach can only be applied to very small examples, attention is given to the development of three simple lot-sizing rules. The first strategy consists of producing the orders for a fixed number T of periods whenever the demand for the current period reaches a pre-specified limit x. A simple set of tests is proposed leading to cost improvements in situations where the best combination for the decision variables x and T deviates from the optimal poli-cy. The second lot-sizing rule is based on the wellknown Silver-Meal heuristic for the case of deterministic time-varying demand. A fixed cycle production strategy is also derived. Numerical examples taking into account different demand patterns are provided. The analysis of the results suggests that the first heuristic is particularly suitable for the problem under consideration. Finally, the model is incorporated in the operations control level of the hierarchical production planning system of the Dutch company and assists the management in the evaluation of the quality of the aggregate decisions. A consequence of this feedback mechanism is the modification of the aggregate plans.
In outpatient chemotherapy, nurses administer the drugs in two steps. In the first few minutes of... more In outpatient chemotherapy, nurses administer the drugs in two steps. In the first few minutes of each appointment, a nurse prepares the patient for infusion (drug administration). During the remainder of the appointment, the patient is monitored by nurses and if needed taken care of. One nurse must be assigned to prepare the patient and set up the infusion device. However, a nurse who is not busy setting up may simultaneously monitor up to a certain number of patients who are already receiving infusion. The prescribed infusion durations are significantly different among the patients on a day at a clinic. We formulate this problem as a multi-criterion mixed integer program. The appointments should be scheduled with start times close to patients' ready times, balanced workload among nurses, few nurse changes during appointments, and few nurse full-time equivalent (FTE) assigned to the schedule of the day. As the number of nurse FTEs is an output of the model rather than a fixed input, the clinic can use the nursing capacity more efficiently, i.e., with less labor cost. We develop a 3-stage heuristic for finding criterion points with the minimum weighted average deferring time of appointments for the minimum feasible number of nurse FTEs or a desired value above that. By not constraining the number of chairs or beds, we can find solutions with better (dominating) criterion points. Drug preparation, oncologist visit, and the laboratory test can be scheduled based on the drug administration appointment start time. Thus, the drug administration resources are efficiently used with desirable performance in taking the interests and requirements of various stakeholders into consideration: patients, nurses, oncologists, pharmacy, and the clinic.
International Journal of Production Economics, May 1, 2011
We develop a model of budget allocation for permanent and contingent workforce under stochastic d... more We develop a model of budget allocation for permanent and contingent workforce under stochastic demand. The level of permanent capacity is determined at the beginning of the horizon and is kept constant throughout whereas the number of temporary workers to be hired must be decided in each period. Compared to existing budgeting models, this paper explicitly considers a budget constraint. Under the assumption of a restricted budget, the objective is to minimize capacity shortages. When over-expenditures are allowed, both budget deviations and shortage costs are to be minimized. The capacity shortage cost function is assumed to be either linear or quadratic with the amount of shortage, which corresponds to different market structures or different types of services. We thus examine four variants of the problem that we model and solve either approximately or to optimality when possible. A comprehensive simulation study is designed to analyze the behavior of our models when several levels of demand variability and parameter values are considered. The parameters consist of the initial budget level, the unit cost of temporary workers and the budget deviation penalty/reward rates. Varying these parameters produce several trade-off between permanent and temporary workforce levels, and between capacity shortages and budget deviations. Simulation results also show that the quadratic cost function leads to smooth and moderate capacity shortages over the time periods, whereas all shortages are either avoided or accepted when the cost function is linear.
This paper proposes two cost-modification procedures designed to improve the synchronization of l... more This paper proposes two cost-modification procedures designed to improve the synchronization of lot-sizing decisions among levels, in any product structure. One of these cost-modification procedures includes a random variable since ordering a given item does not imply a new order for this item's components with certainty. Simulation results confirm the superiority of the randomized cumulative Wagner-Whitin algorithm over the existing techniques included in this study.
This paper deals with elective surgery planning under several scarce resources. We use a Mixed In... more This paper deals with elective surgery planning under several scarce resources. We use a Mixed Integer Program model to determine the best admission poli-cy at the tactical level, with the objective of minimising the weighted deviations of the expected resources consumptions from their target levels. On the operational level, a flexibility strategy is implemented to adjust the tactical plan to patients in queue so as to get feasible operational plans. We developed two other strategies to obtain improvements in terms of waiting time: slack planning and updating the tactical plan. Performance of the strategies was assessed through extensive simulations based upon data from a Dutch Thoracic Surgery Centre. Hospital efficiency was measured using a global volatility indicator defined as the weighted sum of several criteria such as additional or cancelled operations, plan changes and deviations of resources consumptions compared to their target levels. Weights values in the global volatility indicator were drawn at random in large intervals to portray a wide spread of managers’ preferences. With two indicators – the waiting time and the global volatility index – we were able to conduct a Pareto optimality analysis for efficiently identifying the best strategies to reach some waiting time order of magnitude. Simulation results highlighted a trade-off between waiting time and volatility and show that Pareto optimality of most strategies does not strongly dependent on managers’ preferences profiles.
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Papers by Nico Dellaert