Service Characteristics 1. Service Mechanism or Process: For each category of customer it is necessary to describe the service process. This is usually expressed as a probability distribution for service times; for example, service times might be normally distributed or uniformly distributed. At the least, we need to state the average time it takes for a server to serve a customer and the variance or standard deviation of the service time. We decline ? = average service rate possible per server in customers/unit time so 1/? is the average service time.
2. Queue Discipline When customers are in the queue, the system must have operating rules that determine which customer to serve next; these rules are called the queue discipline. Frequently, we assume that the queue discipline is first-come-first-served (FCFS) System Configuration 1. Number, Type, and Configuration of Servers Number of servers in the system. Everything being equal, the more servers available, the less waiting time. Type of servers used. We may choose between two types of machines, or combinations of people and machines, that have different average service rates and different variances in service times.
Queuing analysis can help us determine whether a faster or less variable server is worth extra cost. The configuration of servers. For example, should the system have dedicated servers only certain customers can use certain servers. 2. Queue Capacity Another design variable is the maximum number of customers that can be put in the queue before additional customers must be turned away. For example, a normal telephone has a queue capacity of zero.
When the phone is being used (a caller is being served), additional incoming calls cannot enter the queue; they receive a busy signal and are turned away. Phone systems can, however, be designed so that incoming calls are put on hold in a queue. 3. Number of Queues Whether each server has its own queue or all servers share a single queue can affect not only the average waiting time, Btu also the distribution and equity of waiting times as will be shown later. Steady state: When the rate of departures from the system equals the rate of arrivals.
This implies that any start-up or shutdown (called transient) effects are eliminated. For example, when a bank opens in the morning all servers are available, so the amount of waiting in the queue is reduced, but there will also be some time lag until customers begin to leave the system. Utilization factor measures how much of the queuing system capacity is actually utilized serving customers. The simplest queuing system that includes randomness is the M/M/I system. It is based on the following assumptions.
1. Arrivals are generated by a Poisson process 2. Service times are exponentially distributed 3. There is one server 4. Any queue discipline can be used 5.
Queue capacity is infinite 6. The customer population is homogenous and infinite in size 7. Customers are well behaved; no balking or reneging occurs. Benefits of pooling servers into one system If customers ore homogeneous (with respect to their service time distributions), then there will be less customer waiting on average if servers are pooled into one queuing system, rather than having a separate one-server system for each population of customers. The Number of Queues for multiserver systems Using a single waiting line for several servers is usually more efficient, and it is perceived by customers as being more equitable than having separate waiting lines for each server.
Even when a single queue is practical, it may not be most efficient, especially when the customers and servers are people. There are at least four factors that in some cases may make separate waiting lines for each server preferable to a single queue. 1. With separate queues, servers are sometimes able to serve to two customers at once 2. The time it takes for a customer to move from a common queue to the server may be longer than with individual queues for each server.
3. Servers sometimes work faster when they have their own queue, the customers in their queue are their customers and they are sensitive to the waiting incurred, whereas with a single queue the customer-server relationship is depersonalized until service begins and there is less sense of an obligation to serve customers quickly. 4. With separate queues, customers can choose their server. In some situations, servers can provide both faster and better-quality service to customers they have served before on a regular basis.
Some customers prefer using the same server for this reason, and customer satisfaction should certainly be of primary importance in service systems. Separate queues also make it possible to implement certain delay avoidance tactics. For example, requiring customers to use only cash in an express line at the grocery store means that the customers can obtain the benefits of a shorter wait only if they do something that also saves service time, which can translate into better service for everyone. Finally, separate queues are sometimes necessary to implement other service improvement tactics. For example, when the population of customers is heterogeneous (customers require different types or amounts of service with substantially different average service times), it can be advantageous to have separate servers and queues for each type of customer.
Independent demand models are applicable to items, such as tools sold by a hardware store or common components used by a manufacturer, whose demand or usage rate can be treated in isolation from the demand for other items. Dependent demand such as tires or transmissions used by an auto manufacturer, which depend directly on production of finished automobiles. Reasons for holding inventories Any materials that are held for future use can be considered inventories. There are at least four reasons to hold inventories: 1. To increase operating efficiency 2.
To provide a quick response to customers 3. To provide safety against normal business uncertainties 4. To take advantage of unusual price opportunities or to protect against irregular business risks. Economic efficiency Inventories can improve operating efficiency in several ways. 1.
Spreading the fixed costs of Procurement or Setups If there is a fixed setup cost to produce a product, then the more units produced per production run the lower the setup cost per unit. 2. Decoupling of Production In-process inventories make it possible to decouple one production stage from another, allowing grater scheduling and staffing flexibility. For example, if in-process inventories exist between stages, production at stage B could be stopped for a while without forcing stages A and C to stop. Although it is desirable to keep inventories of semifinished goods as low as possible, even JIT production systems allow for minimal amounts of inventories between stages.
3. Smoothing an Stabilizing Production If demand for a product is seasonal, it is often less expensive to maintain a constant level of production and employment levels to match demand. During period of low demand production exceeds demand and inventories of the product increase, then during period of high demands, these inventories are depleted. Quick customer response 1. By maintaining inventories of its final products, a company can respond immediately to customer demands, thereby providing more competitive service.
2. Raw material and in-process inventories can also be used to shorten the response time to customers. If raw materials or partially finished products are already available, a company can begin production to fill an order faster than if it had to acquire the raw materials. Risk reduction and safety Inventories play a major role in risk reduction for organizations 1. Uncertainties in the supply system.
Inventories of raw materials can protect a company against late inventories, allowing the production process to operate until inventories are replenished. 2. Decoupling production stages. Inventories of semifinished products allow firms to decouple production stages. This not only allows production of other stages to continue while one stage stops for a product changeover or planned maintenance; it also protects against unplanned stoppages such as machine failures or employee absences. 3.
Unexpected Surges in Demand. Inventories of final products can satisfy unexpected surges in demand. Inventories also put the company in a better competitive position, allowing it to supply new customers quickly when competitors are out of stock. Exploiting or protecting against unusual events Three types of inventories: 1. Speculative inventories are sometimes held to protect against unusual events or to take advantage of unusual opportunities. 2. Inventories held primarily to achieve economic efficiency normally increase and decrease in a planned cycle and are called cycling inventories. 3.
In contrast, inventories that are held to protect the organization against normal business uncertainties and risks are called safety stocks. Inventory-related costs Three primary costs influence the inventory policy: holding costs, ordering or setup costs, and stockout or shortage costs. The holding cost is the cost of actually keeping items in inventory. The primary components of this cost are (1) the opportunity cost of capital, (2) taxes and insurance, (3) breakage, spoilage, pilferage, and obsolescence, and (4) handling and storing. Ordering or setup costs. It is important to note that Co should include only fixed costs (independent of order size) that are directly attributable to ordering or producing the product, general overhead cost such as corporate office expenses or maintenance should not be included.
We consider fixed costs because the best number of units to order or produce at a time is function of the fixed cost of acquisition. The larger the order size or production lot size, the lower the fixed ordering or setup costs per nit because the fixed cost is spread over a larger number of units. Shortage or stockout costs. When customers wish to buy a product and it is not available, the supplier incurs a cost, which might include not only lost profit but also lost future profits if the customer changes suppliers. Likewise, if a company runs out of a raw material, it may have to stop its production system, idling workers and possibly causing shortages of the final product. These costs are called stockout or shortage costs.
Sometimes it is accepted practice in an industry to accept orders for future rather than immediate delivery. This is called backordering. Backordering is similar to having a negative inventory level and may involve a cost per unit time, usually due to loss of goodwill. Hidden costs. Inventories also carry many hidden costs. Companies keep extra raw materials on hand to protect themselves against unreliable deliveries by suppliers.
They maintain substantial in-process inventories to keep some activities operating when machines break or workers fail to show for work. They overproduce products in the expectation that some will be defective. Not only do excessive inventories hide production problems, they often amplify them. Independent versus dependent demand. In contrast to dependent demand items, which occur almost exclusively in manufacturing systems, independent demand items occur extensively in both manufacturing and service systems.
Inventory review policies. A fundamental aspect of an inventory policy is deciding whether the inventory position (the number of units in inventory plus those on order) will be reviewed on a continuous or periodic basis. The organization reviews (counts) the inventory for the product and places orders at fixed time intervals. The amount ordered each time may vary according to the inventory position and the expected demand. A major disadvantage of this system is that between reviews the inventory can become dangerously low without the companys knowledge until the next review occurs.
Continuous (or perpetual) review policies have become widespread. Continuous review systems involve less risk (and require less inventory) because the company always knows its current inventory position: as soon as inventories drop to a predetermined level, called the reorder point (RP), the company can place an order for some fixed amount. One way of differentiating the two systems is that periodic review systems typically have variable order quantities but fixed time intervals between order, whereas continuous reviews systems have fixed order quantities but variable time intervals between orders. Basic economic order quantity (EOQ) model The assumptions of the basic EOQ model are as follows: 1. The demand for or usage of the item is relatively constant over time at a rate of D units per unit time.
2. The items cost (price), p, is independent of the quantity ordered; that is, there are no quantity discounts. 3. There is a fixed cost, Co, for executing an order that is independent of the quantity ordered, Q. 4.
The holding cost for inventories is proportional to the quantity stored; that is the holding cost per unit per unit time, Ch, is independent of the inventory level. 5. No shortages are allowed; all demand must be satisfied when requested. 6. The lead-time (LT) for deliveries, which is the time from when an order is placed until it is delivered, is known with certainty and is constant.
7. All items ordered are delivered at the same time; there are no split deliveries. Reorder Point, RP, should be set equal to the number of units used during the lead time, called the demand during lead time (DDLT). RP= DDLT = D x LT Computing the optimal order quantity. To determine the optimal order quantity, we begin by expressing the firms total material cost (TMC) for the product during a unit of time (e.g., a year) as a function of the order quantity Q. Because shortages are not allowed, there appear to be three components to the material cost function: ordering costs, holding costs, and variable item costs.
Ordering cost per unit time = Co (D/Q) Holding cost per unit time = Ch (Q/2) TMC = Co (D/Q) + Ch(Q/2) + pD But the item cost is not a function of the order quantity there are no quantity discounts so the amount spent on the items per unit time, pD, is a constant. Therefore, the value of Q that minimizes equation is the value that minimizes the sum of the ordering ad holding costs, called the total stocking cost (TSC) The economic production lot-size model A problem frequently encountered by manufacturers is to determine how many units of a product or a component to produce during a production run. This quantity is called the production lot size. The problem of determining the optimal lot size, called the economic lot size (ELS), is similar to the economic order quantity problems, with only minor differences. ABC Classification of items and the pareto principle In the nineteenth century, the Italian economist Vilfredo Pareto discovered empirically that wealth is maldistributed: for example, 80% of a nations wealth is typically owned by less than 20% of the population (and therefore, less than 20% of the nations wealth is owned by 80% of the population).
This concept of maldistribution, called the Pareto principle. ABC classification scheme = a way to set priorities on the amount of attention to devote to the inventories of various items. Items are divided into three categories according to their impact on the organization. Causes of Inaccuracy. An open stockroom makes it easy for people to remove items from inventory without recording the withdrawal; even when the item is used for legitimate purposes, a discrepancy results.
Other causes include the following: 1. Orders are recorded as received when they have not been or vice versa 2. The number or type of items received in a delivery do not match what was ordered, and the difference is not recognized 3. Items withdrawn form inventory may later be returned but not recorded (e.g. a mechanic may withdraw two sizes of a part to fix a machine and then return the one that does not fit) 4. Items may be stored in the wrong place even though they exist, they are not of use because they cant be found.
These and other types of errors can be costly, and they present opportunities for improvement. An alternate approach is to use cycle counting of inventories. With this method all items are counted on a rotating basis. For example, each month 1/12th of the companys items may be physically counted. This reduces disruptions and even makes it possible to have permanent staff devoted to physical counting and reconciliation of inventory records. Cycle counting also makes it easier to develop counting strategies that give differential attention to items according to their importance.
Cycle counting can also be made more efficient by selecting items to count during a cycle using the following guidelines. 1. Count items when inventory records show a small quantity in stock, thereby reducing the number of objects to count. 2. Count items when inventory record show a positive level but a stockout is reported 3. Count items after an unusually large amount of inventory activity (receipts and withdrawals) for that item. The two bin system For small items, a simple way of identifying when the reorder point has been reached is to use a two-bin system for storage.
In this system, units of a product are literally stored in two bins; the first bin hold a number of units equal to the reorder point quantity, and the second bin holds the remainder. Items are withdrawn form the second bin, this is a signal to place an order; until delivery is received, items are drawn from the first bin. In recent years, companies have found that there are substantial benefits from establishing a long-term sole-supplier (sole-sourcing) relationship with vendors. By offering a supplier all of the customers purchases of an item for the next three to five years, the customer can insist on guarantees of reliable delivery, high quality, stab le or decreasing prices, and a share in productivity improvements. In many situations, using a sole-supplier (sole-sourcing) method can reduce costs and enhance product innovation; the main problem is the risk of a supply interruption. Buying recycled and recyclable materials can be profitable as well as environmentally sound.
A popular method that uses to schedule production and purchasing of dependent demand items is material requirements planning (MRP) MRP is a computer based information system for scheduling production and purchases of dependent demand items. It uses information about end product demands, product structure and component requirements, production and purchase lead times, and current inventory levels to develop cost-effective production and purchasing schedules. MRP inputs. An MRP system requires four specific types of information: a schedule of requirements (or planned production) for each end product. A list of all components of the product according to the products hierarchical structure, expected lead times for producing or purchasing all components and materials, and information about current inventory levels.
This information is maintained in three standard data files: the master schedule file, the bill-of-materials file, and the inventory record file. These files are used not only by the MRP system but also for product design, personnel scheduling, purchasing, shipping, and accounting activities. The master schedule file contains the master production schedule for each product. The master production schedule (MPS) for a product specifies how much of the end product is needed or is to be produced and when. The MPS is derived from the aggregate production plan based on demand forecasts, customer orders, and capacity limitations.
The MPS is divided into time period called time buckets. These time buckets a …