Qnt 561 week 3

Expansion Strategy and Establishing a Re-Order Point

Expansion Strategy and Establishing a Re-Order Point

Bell Computer Company

Medium scale and large scale are the two expansion options for the Bell Computer Company. The demand can be high, medium, or high and 0.2, 0.3, and 0.5 probability for both medium scale expansion and large scale expansion. Profits in the case of high, medium and low demand for medium scale expansion are $200,000, $150,000 and $200,000. Profits in the case of high, medium and low for large scale expansion are $300,000, $100,000 and $0. Choosing the large scale expansion or medium scale expansion is the issue plaguing management. In the case of medium and low demand, large scale expansion will produce lower profits than medium scale expansion but large scale expansion has the potential to generate higher profit in the case of high demand. The large scale expansion has a zero profit for the case of low demand. Obviously, the greater risk comes from large scale expansion rather than low scale expansion.

An expected value is a forecasted value of a variable. A variable has numerous potential outcomes. The first step is determining the probability of occurrence of each outcome. By multiplying each possible outcomes by the probability of occurrence of that outcome and adding all those values, we will get the expected value. In order to choose the expansion option that is most likely to generate higher profit between large scale expansion and medium scale expansion, management need the expected value. The expected values of large scale expansion is $140 and medium scale expansion is $145.

The large scale expansion project has a lower expected value than the medium scale alternative. With that being said, the medium scale expansion is ideal for the objective of make the most of expected profit.

To make a knowledgeable decision, just knowing the expected value is not enough. Knowing how profit can differ from the expected value is also important. Variance is used for this reason. Variance measures the distance a set of random values are scattered from the mean value. A higher variance means that the random values are scattered far away from the mean. The ideal variance is a low variance. The variance of random variables is the expected value of squared deviation from the mean. Mathematically, variance of discrete random variables is calculated as: Var = E[(X-µ)² = Σ[P(X)*(X-µ)²]. The variance of large scale expansion projects are 12,400 and medium scale projects are 2,725. The variation for profit related with large scale expansion is far higher than the variation for profit related with medium expansion.

Standard deviation measures risk, it is a measure used to compute the amount of variation of a data set values. It is calculated as the square root of variance. A Low standard deviation shows that random values have a tendency to be close to the expected value. A lower standard deviation point toward low risk but a higher standard deviation point towards a higher risk. The standard deviation of medium scale is 52.202 and large scale is 111.355.

Since the value of the standard deviation of the medium scale expansion is lower than the value of the standard deviation of the large scale expansion, the medium scale expansion pose less risk. The medium scale expansion is ideal.

Judging from the information gathered, the medium scale expansion has a higher expected value than the large scale expansion and the medium scale incurs a lower risk than the large scale expansion. Therefore, the medium scale expansion should be the choice of management.

Kyle Bits and Bytes

Kyle Bits and Bytes is a retailer of computing products. The HP laser printer is the most popular product at Kyle’s Bits and Bytes. The HP laser printer average a weekly demand of 200 units and its lead time is one week but the demand for the HP printers are not constant. The weekly demand standard deviation is 30 for Kyle’s Bits and Bytes. Kyle need to know the inventory level and when they need to place order or the reorder point so that there is stock-out. Kyle will lose sales if Kyle is not able to fulfill orders due to stock-out and possible lose future sale. A maximum acceptable probability of stock has be set in any week to 6% by Kyle. Kyle wants to know how many HP laser printer should be in stock and what should be the re-order point with this target.

The inventory level at which orders should be replaced is the reorder point. The demand is variable in this case. It is implicit that demand can be defined by a normal distribution for variable demand. The sum of average daily demand for the number of days in lead time period is the average demand for the lead time. By multiplying average daily demand by the lead time, it can be measured. The variance of the distribution is measured as the sum of daily variance for the number of days in lead time. The reorder point R= dL + z*ơ*√L

d = average daily demand = 200/7 units

L= lead time = 7 days

ơ = standard deviation of daily demand = 30/7

z = number of standard deviations corresponding to the service level probability = 1.56.

The reorder point R = (200/7)*7 + 1.56*(30/7)*√7 = 200 + 17.69 = 217.69. So when inventory level reaches 218 units, Kyle should place an order.

There is a chance of stock-out when demand is variable. During the time of need stock-out can happen. To avoid the risk of stock-out the company needs to maintain safety stock. The additional inventory a firm maintains above expected demand to avoid stock out is the safety stock. To determine safety stock a company use service level. A company chooses what chance it can afford of stock-out. Probability of no stock out during lead time is the service level. This is called the service level. Safety stock is calculated as: safety stock = z*ơ*√L.

L = lead time = 7 days

ơ = standard deviation of daily demand = 30/7

z = number of standard deviations consistent to the service level probability = 1.56

Safety Stock = 1.56*(30/7)*√7 = 17.69 = 18 units. To avoid stock-out on the HP laser printer, Kyle should maintain 18 units of safety stock.

Citation

Black, K. (2017). Business Statistics: For Contemporary Decision Making , (9th Edition). Hoboken, NJ: Wiley.