Case-Mix Planning Problem and Resource Allocation in Hospitals

Issues and Challenges

Aiming at maximising resource efficiency, case-mix planning determines optimal number of patients from each pathology group that can be treated at hospitals. The study focuses on issues and challenges on assignment of operating rooms to surgeon groups, allocation of beds under constraints like patient and surgeon's preference, workforce capacity, etc.

Hospitals all around the world are facing increasing pressure in cost reduction. Besides, shortages of physicians, nurses and other hospital resources further magnify the problem. Such issues can be solved by the efficient and effective allocation and utilisation of the available resources and the decision of an appropriate case mix. Case mix planning problem decides the number of patients to be treated over a planning horizon from each pathology group. Operations research tools and techniques are recommended for solving challenging case-mix planning problems.

Due to advancement in technology and demographical changes, hospitals all around the world are facing increasing economic pressure. Besides, limited number of physicians, nurses and other resources make the situation challenging to manage. Such problem can be solved by the efficient and effective allocation and utilisation of the available resources and the decision of an appropriate case mix. In case-mix, patients requiring similar type of diagnostic tests, treatment procedures and resources are grouped together and treated accordingly in a particular hospital. Specifically, the Case Mix Planning (CMP) problem decides the number of patients to be treated over a planning horizon from each pathology group (Mc Rae et al., 2019). With the aim to maximise the resource utilisation, the CMP problem determines an optimal case-mix pattern to generate maximum revenue of hospitals. Determination of assignment of operating rooms to surgeon groups, allocation of beds and annual number of patients of each type treated at the hospital taking into consideration the surgery demand, operating room capacity constraints, workforce capacity constraints (anaethetists, nursing staff), patient preference constraints, surgeons preference constraints, material requirement constraints, availability of intensive care unit and recovery beds is the objective of a hospital case mix and resource allocation problem.

CMP problem is exceedingly pertinent for hospitals which follow reimbursement mechanism according to Diagnosis-Related Groups (DRGs). DRGs groups patients based on their clinical conditions.

CMP in hospitals is a critical decision variable incorporated within the resource allocation problem in order to distinguish the various pathologies or patient groups. The patients in each group share similar resources and return equivalent profit. It is a way to define hospital’s production system and is a major cause in cost differing among patients. The various types of patients in a hospital grouped according to the indicators like the rate of consumption of resources, is a tool for managing and planning healthcare services. The CMP of a hospital depends onthe way the hospital resources are allocated. For example, scheduling of the operating room, management of waiting lines and queues, allocation of physicians and nurses, promotional activities, etc. Generally, CMP decisions are revised by the hospital administration every year. Existing literature on CMP focuses on (i) exploring economies of scale and scope (McRae et al., 2019) and (ii) CMP under uncertainty (Freeman et al., 2017; McRae and Brunner, 2019).

Issues and Challenges

Increasing pressure in cost reduction are forcing hospitals to surge their revenues, while minimising the operating costs; however, without compromising with the patient service level. Balancing satisfactory patient care and the providing variety of services in lower cost is a challenge. Identifying a case mix plan is even challenged by the uncertainties prevailing in hospitals, such as uncertain patient arrivals, emergency patients, uncertain surgery time, length of stay of patients, and limited capacity in hospitals.

An issue with the conventionalmode of hospital reimbursement, i.e. fee-for-service, where the hospital charges a payer (for example, insurance provider). However, there is a conflict that fee-for-service may result in oversupply of treatments and also lacks minimisation of wasteful use of surgical supplies as the payer pays for all items used, irrespective of the actual necessity. This may result in rise in healthcare costs.

Apart from that, while identifying the optimal case mix, the question of how to decide the best allocation of resources to various departments, sub-specialties, wards, and physician groups, based on the hospital setting. However, the issue is that patients are expected to be heterogeneous with respect to medical condition and resource use.

Moreover, the optimal case mix depends on the demand of scheduled and emergency patients. Decisions regarding managing scheduled patients and emergency patients are different. Subsequently, emergency patient demand effects the capacity of resources available for scheduled patients rather than being a primary part of case mix planning. Besides, the decision to what amount bottleneck resources is allocated is a vital managerial decision.

For CMP, it is essential to consider along with the expected resource requirements, the variability. For example, in case high variability in operating timerequirementsfor a particular surgery, extra time is required resulting in overtime of medical personnel or frequent rescheduling; however, in case of predictable and standardised surgical procedures, a department need not face such situations.

In a hospital, CMP is the central issue during negotiations between hospital administration and insurance companies. CMP implementation includes resource allocation, admission planning, appointment schedules, and management of waiting lines. For example, patients from specific pathological group may be prioritised by reserving a higher share of resources.

In certain hospitals, there exists a minimum patient volume restriction for a specific pathology group. For example, in a hospital, liver transplantation is allowed if the expected patient volume for this type of surgery was larger than say, twenty.The availability of resources is also an essential factor. For instance, shortages of available nurses are correlated with increasing patient mortality. Hence, to satisfy patients and provide them adequate treatment and caret, there should be a match between the available resources and the target case mix.

Case mix often requires reallocation of the available resources like medical staff, and other physical resources to match the new case mix (Dexter et al., 2005; Gupta, 2007). The level to which patients requiring same type of diagnostic testsmay be treated in other department depends on the current hospital settings. Moreover,it is often possible for only a particular section of patients may be treated in other department (Ma and Demeulemeester, 2013; Harper, 2002). For example, patients with heart attack or accidents should be admitted to the nearest hospital to avoid any fatal consequences due to delay, irrespective of the whether the hospital and set of departments in the hospital is offering related services. Generally, certain hospital resources, like medical personnel, operating room, etc. are allocated for a medium to long-term basis to various sub-specialties in a hospital. Hence, the redistribution of a few cardiology department ward beds to the pulmonary ward may incur additional costs. In case there is no extra cost incurred, therequired resources could be redistributed, and the only issue would be to determine the optimal required resources. Besides, at times it is also suggested to increase the available resources. For example, hiring qualified medical personnel or includingnew operating theatres. However, it needs to be planned well in advance. For minor fluctuations in demand, overtime by the medical personnel is recommended.

Efficient and effective decision support tools for developing and evaluating the case mix strategies is required in hospitals with limited resources and highly variable demand for hospital services. Various other sources for uncertainties are the time taken in an operating theatre for a surgery, length of stay of patients in a particular hospital care unit, etc.

Besides, there also exists uncertainties in the resources utilisation and resource capacity (McRae and Brunner, 2019).Uncertainties and variabilities in resource capacity may initiate from various sources. One of the important factor concerns the human labor. Uncertainties in the capacity of resources, such as operating theatres, intensive care units or ward capacity initiates from the randomness or stochasticity in the medical staffing levels due to various reasons like absenteeism of the staff, delays of the first surgery in an operating theatre, etc. Hospital resources are maintained for both emergency and scheduled patients. The available resource capacity for scheduled patients is the total resource capacity available minus the resource capacity required by the emergency patients.

Solution Approaches

Case-mix problems can be deterministic (known and constant patient demand) or stochastic (random patient demand). One way to incorporate the uncertainties prevailing in the hospital settings is to consider the patient demand, resource requirements, etc. as random variables following a particular probability distribution pattern with mean and variance. The variance of the sum of resource requirements over all patients in hospital departments is the linear combination of patient volumes. However, the aggregate mean and aggregate variance only offer anapproximate estimate of the uncertainty of resource requirements. Data on bedoccupancy with the associated resource utilisation, treatment variabilities, and operational inefficiencies may help in case mix decision planning. In case the hospital is constantly operating at a loss, the management should reorganise its departments.

From the analysis of various existing research, operations research tools and techniques, such as mathematical programming (mixed-integer programming) and simulation are identified as the modelling and solution approaches for CMP problems. The optimal case mix in terms of the optimal number of patient volumes in each pathology group, the optimal number of operating rooms, optimal number of medical personnel, etc. are determined solving the case mix planning problem by mathematical programming optimisation techniques. Simulation models like discrete event simulation helps to evaluate the performance of the case mix planning problem by considering the real complexities prevailing in a hospital setting.

Concluding, CMP is a significant tool for hospital operationalplanning with the objective of effective and efficient planning of resources and fulfilment of patient demand.


1.    McRae, S. and Brunner, J. O. (2019), Assessing the impact of uncertainty and the level of aggregation in case mix planning, Omega.
2.    Dexter, F., Ledolter, J., Wachtel, R. E. (2005). Tactical decision making for selective expansion of operating room resources incorporating financial criteria and uncertainty in subspecialties’ future workloads. Anesthesia and Analgesia, 100(5):1425–1432.
3.    Gupta, D. (2007). Surgical suites’ operations management. Production and Operations Management, 16 (6):689–700.
4.    Ma, G, Demeulemeester, E. (2013). A multilevel integrative approach to hospital case mix and capacity planning. Computers and Operations Research, 40 (9):2198–207.
5.    Harper, P. R. (2002). A framework for operational modelling of hospital resources.Health Care Management Science, 5(3):165–73.
6.    Freeman, N, Zhao, M, Melouk, S. (2018). An iterative approach for case mix planning under uncertainty, Omega, 76, 160-173.
7.    McRae, S., Brunner, J. O., Bard, J. F. (2019). Analyzing economies of scale and scope in hospitals by use of case mix planning, Health Care Management Science,


Esha Saha

More about Author

Esha Saha is currently an Assistant Professor at Rajagiri Business School, India. She is pursuing her PhD from IIT Kharagpur, India. She received her Master of Technology from NIT Calicut and Bachelor of Technology from West Bengal University of Technology. Her research interests include operations, stochastic modelling, and healthcare systems.