Example Models

@RISK Models

xls Aggregate Planning

Minimum Edition: @RISK Industrial. This model plans production over the next six months in the face of uncertain demand. The company produces three products, and these products compete for labor hours. Each month there are 800 regular-time hours available, and up to 150 overtime hours can be used. The hours used must then be allocated to the three products. Each product has its own production rate (items per labor hour).

xls Building Onshore versus Offshore

Minimum Edition: @RISK Industrial. The purpose of this model is to provide a comparison between building an onshore plant in the U.S. and building an offshore plant in China. The model is for a company based in the U.S. with sales in the U.S. However, despite transportation costs, there might be benefits to building in China. The model includes uncertainty in the exchange rate, weekly demand, and amounts of extra weekly capacity available. The future exchange rates are based on fitting historical exchange rates with @RISK's Time Series Fit tool.

xls Capacity Decision with Time Series

Minimum Edition: @RISK Industrial. A manufacturing company that is building a new production facility for the next 15 years must decide how much capacity to build now in the face of future demand uncertainty, where demand in excess of capacity is lost. Future demands are forecast by using @RISK's Time Series Fit tool on historical demand data. There is also uncertainty in the plant cost, the unit production cost, and the unit operating cost.

xls Comparison of Ordering Policies

Minimum Edition: @RISK Industrial. A company faces infrequent and uncertain demands for a high-priced product. The company orders the product from a supplier, and there is an uncertain lead time from when an order is placed until it arrives. The company wants an ordering policy that keeps average inventory low but also keeps stockouts low. The model compares a standard ordering policy to a more anticipatory policy.

xls Hospital Capacity

The purpose of this model is to see how many hospitals are required to accommodate all patients in various scenarios. The model assumes that patients are assigned to hospitals in a particular order: hospital 1, then hospital 2, and so on. There is uncertainty in the numbers of available beds at the hospitals.

xls Line Balancing

Minimum Edition: @RISK Industrial. This is a simplified model of a multistage manufacturing process. Each stage has a number of identical machines, and each machine can produce a random number of items in a fixed period of time. Each stage feeds the next stage. However, any stage from stage 2 on can produce only as many items as it receives, even it has the potential to produce more. The problem is to determine the number of machines at each stage to maximize mean profit, which is the revenue from selling all items produced during the period minus the operating costs of the machines.

xls Managing Supplier Inventory, Production

Minimum Edition: @RISK Industrial. This is a supply chain model of the relationship between a manufacturer and its supplier, modeled from the point of view of the supplier. The manufacturer produces several products with random daily demands. These products require several components from the supplier. The supplier produces these components and stores them at the manufacturer's site so that they are on hand when needed. In turn, the components requires several subcomponents. These subcomponents are stored at the supplier's location for use in the components. Production of components and subcomponents is driven by two sets of decision variables, triggers and batch sizes, and the model explores the effects of these.

xls Multiserver Queue 1 - Customer Service

This example illustrates a general multiserver queueing system. Customers arrive at random times. If at least one of the servers is idle, an arrival goes directly into service. But if all servers are busy, the arrival joins the end of a queue, from which customers are served in first-come-first-served order.

xls Multiserver Queue 2 - Ambulance Service

This example adapts the general multiserver queueing system to a city's ambulance service. The ambulances are the "servers," and a customer "arrival" corresponds to a call for an ambulance from some location. If at least one ambulance is not currently busy, it responds immediately to the call for service. Otherwise this call waits, in first-come-first served order, for the next available ambulance. In addition to the usual queueing outputs, the model keeps track of waiting and ambulance costs per day. The number of ambulances can be increased or decreased to explore the trade-off between ambulances and waiting time.

xls Newsvendor Model with Demand Diversion

Minimum Edition: @RISK Industrial. This model illustrates the newsvendor ordering model in a multiple-product setting with the possibility of demand diversion. This means that if supply of product A, say, is not sufficient to satisfy demand for product A, some customers (but not all of them) who wanted product A but couldn't get it are willing to purchase another product instead.

xls Supply Chain Disruptions

This model illustrates how disruptions at suppliers, such as weather, strikes, or others, can affect a supply chain, and how such disruptions can be mitigated. The model has two suppliers and two manufacturers. Normally, each supplier supplies a single manufacturer. However, there are occasional disruptions at the suppliers, and each disruption can last a random number of weeks. If an order is placed during a disruption period, this order is ignored by the supplier, resulting in an increased chance of stockouts at the manufacturer. The model explores the mitigation strategy where the manufacturers can "share" suppliers.

xls Work Allocation to Products

Minimum Edition: @RISK Industrial. This model finds optimal allocations of work hours in several work centers toward production of several SKUs in a specific month. There are four sources of uncertainty: monthly demands for the SKUs, available work hours per day at the work centers, productivities of the work centers for each of the SKUs, and profit margins for each of the SKUs produced at each of the work centers.

xls Worker Scheduling

Minimum Edition: @RISK Industrial. A company is open from 7AM until 11PM each day of the week. Each of its workers must work 5 consecutive days, and each day worked, he/she must work 4 consecutive hours, then have an hour off, and then work 4 more consecutive hours. The model assumes that the hourly schedule for a given worker is the same each day worked. The problem is basically to hire as few workers as possible, and to schedule them appropriately, so that there are enough on hand to meet the daily/hourly requirements.




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