Consider an inventory system whereby an inventory replenishment order for Q units is placed whenever inventory reaches ROP units. The lead time for the order is LT days and daily demand is d units. Beginning on-hand inventory at time=0 is OH units.

Use these parameters:

Q = 1,500; ROP = 2,200; LT = 7; d = 300; OH = beginning on-hand inventory = 2,800.

and provide an answer for each of the following:

Long-run average inventory on-hand (note – don’t include the inventory in the first order cycle, since it depends on the beginning inventory, but determine what the long run average amount of on-hand inventory will be once order cycles and inventory amounts fall into a regular pattern):

Inventory on hand at time=10:

Number of orders outstanding (in the “pipeline” but not yet received) at time=10 (your number will be 0,1,2, or 3):

Order cycle length (time between orders): days.

(Draw yourself a “sawtooth diagram” for analyzing this, like we did in class and posted in an example on Blackboard. The diagram “maps out” inventory at discrete points in time t=0, 1 day, 2 days, etc., as though demand occurs between two points in time and order placement and order receipt occur at a specific point in time. So, inventory at time 1 = starting on-hand inventory – d units. If the result is equal to the reorder point (ROP), then an order for Q units should be placed at time 1 and will arrive at time 1+LT).

1 points

QUESTION 3

A local retailer of party supplies purchases special paper cups from a local distributor for \$12/case and sells them to customers for \$18.99 per case. Traditionally they have purchased in lot sizes of 500 cases, which means about ten orders per year given the average annual demand of 5,000 cases. Orders have a two week lead time. The company is currently doing an analysis of their ordering policies, including lot sizes. A recent project by a co-op student has estimated an annual inventory holding cost of 22% of unit cost, and a fixed cost to place an order, independent of order quantity, of \$37. For each of the following questions, provide answers to two decimals and without commas or dollar signs.

I. What is the annual ordering cost (of their current lot size)?

II. What is the annual holding cost, related to the cycle stock(again, based on current lot size)?

III. What is the optimal order quantity that minimizes the sum of annual holding and ordering costs?

1 points

QUESTION 4

The INDY Industrial Supply Company has finished a highly-sophisticated project where they separately determined order setup (S) costs for each of their main suppliers, based on the specific ordering process for that supplier. They have determined that the ACME Supplier, from which they order six different SKUs, the setup cost for an order (which has been highly automated) to be \$21.80 per order, with an additional cost of \$3.15 for each line on the order. Annual demand data and cost per unit for six SKUs is provided below; assume an annual inventory holding rate of 22%.

SKUDCost/unitSKU1500\$25SKU2900\$20SKU3600\$28SKU4450\$23SKU5700\$33SKU6200\$19

The optimal number of orders per year from this supplier is (to two decimals):

The amount of SKU3 that will be ordered each time (round to nearest integer):

The EOQ for SKU3, if ordered on its own, would be (round to nearest integer): . Note – use the major setup cost plus the setup cost for one line when finding the EOQ of an individual item. Also, your answer should make sense (i.e. you should think about whether you think the optimal order quantity for one SKU ordered alone should be higher or lower than the optimal order quantity for that SKU when it is combined with other SKUs on an order.)

1 points

QUESTION 5

CPC, a chemical processing company, uses a special catalyst chemical in some of their processing; they keep the chemical in a large vat that holds up to 1,000 litres. Daily demand for the chemical averages 24.6 litres with a standard deviation of 11.1. The vat is equipped with a sensor that can alert an operator when the amount of chemical in the vat reaches a pre-determined reorder point, at which time an order is placed with the supplier who will use a tanker truck to deliver more chemical (they refill the vat directly from the tanker). The leadtime on a replenishment order is three days (assume no variability in lead time), and a typical order size is Q=500 litres.

In general, if the vat runs out of the chemical before the tanker arrives with replenishment, CPC can delay production without much problems, and thus they are thinking of setting the reorder point quite low (also because the chemical is expensive). Help them with the math:

At how many litres should the reorder point sensor be set if the goal is to ensure that there is no more than a 5% chance of stocking out while waiting for the tanker to arrive (i.e. a 95% Cycle Service Level)?

At how many litres should the reorder point sensor be set if the goal is to ensure that there is no more than a 10% chance of stocking out while waiting for the tanker to arrive?

At how many litres should the reorder point sensor be set if the goal is to ensure that there is no more than a 15% chance of stocking out while waiting for the tanker to arrive?

(Round all answer to a whole number).

1 points

QUESTION 6

Assume demand to average 100 a week (5,200 per year) with a standard deviation of weekly demand of 30. The order quantity currently used is 500, the Reorder Point is 250, and the lead time is two weeks (assume no variability in lead time). The cycle service level (CSL) will be percent (please round two two decimals, e.g. 72.45).

1 points

QUESTION 7

For each answer, indicate ‘T’ for TRUE or ‘F’ for FALSE. (Please only specify ‘T’ or ‘F’ – the grading criteria requires only a single letter.) ***Read these carefully***

a) T or F: The more expensive the process for ordering replenishment inventory, the larger the cycle inventory should be.

b) T or F: The longer the lead time for replenishment of inventory, the larger the cycle inventory should be.

c) T or F: The Economic Order Quantity (EOQ) model is used to resolve the trade-off between total costs (holding plus ordering) and frequency of stock-outs.

d) T or F: Assuming that demand and lead time do not change, an increase in the ROP (reorder point) will result in a decrease in the number of annual inventory turns.

e) Doubling the lead time (e.g. from five to ten days) would mean that the average demand during the lead time increases by 2.00 times while the standard deviation of demand during the lead time increases by 4.00 times.

f) The role ofcycle stock (inventory) is to allow a firm to take advantage of economies of scale for fixed costs (such as ordering and/or transportation costs)

2 points

QUESTION 8

For each of the following, indicate ‘T’ for TRUE or ‘F’ for false. (Note – please only put in the letter ‘T’ or ‘F’, not the full word. ***Read these carefully***

T or F: (Assuming that no other factors are changed) Increasing the order quantity (Q) will increase the fill rate. (Indicate ‘T’ or ‘F’).

T or F: (Assuming that no other factors are changed) Increasing the Reorder Point (ROP) will increase the fill rate.

T or F: (Assuming that no other factors are changed) Increasing the order quantity (Q) will increase the cycle service level.

T or F: (Assuming that no other factors are changed) Increasing the Reorder Point (ROP) will increase cycle service level.

1 points

QUESTION 9

The HardCore battery company refurbishes vehicle and other battery “cores” and sells them to industrial customers. Part of their production process requires a small but expensive part that is purchased from a supplier in Quebec, in order quantities of 40,000, approximately every two weeks (the order quantity is given and is beyond the scope of this question). Demand for the product averages 2000 units per day with a standard deviation of daily demand equaling 425 units. They ship by LTL and have used a number of different carriers. Note that LTL carriers consolidate the cargo of different customers and thus LTL transport time is generally longer and with more variability than full truckload transport. HardCore would like to settle on one of the four carriers that they have used, and would like to consider the amount of safety stock that would be required, in each case, to achieve a 97.5% cycle service level (CSL). Average and standard deviation of lead time for each carrier is provided below.

Which of the following lists in ascending order the amount of safety stock that would be required in each case in (i.e. which one lists the carrier that would allow for the least amount of safety stock, followed by the next least, etc…)

*Note – take a moment to decide what you need to calculate in order to answer the question.a.Broad Street Logistics, NW Trucking, Rogie’s LTL, Spinners Transportb.Spinners Transport, NW Trucking, Rogie’s LTL, Broad Street Logisticsc.Broad Street Logistics, Rogie’s LTL, Spinners Transport, NW Truckingd.NW Trucking, Rogie’s LTL, Spinners Transport, Broad Street Logistics,

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