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Review questions (1-17 questions) a. What is the purpose of decision tree analysis? b. List three advantages and three weaknesses of decision tree analysis. Answer:A. Decision tree analysis gives a powerful strategy for Decision Making since they: Clearly spread out the issue with the goal that ever...

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Review questions (1-17 questions) 1. a. What is the purpose of decision tree analysis? b. List three advantages and three weaknesses of decision tree analysis. Answer: A. Decision tree analysis gives a powerful strategy for Decision Making since they: Clearly spread out the issue with the goal that every alternative can be tested or tested. Permit us to analyze completely the potential results of a choice. Give a system to measure the estimations of results and the probabilities of accomplishing them. Also, it gives an efficient system in analyzing a succession of interrelated choices which might be made after some time. The study and understandings of alternative scenarios are encouraged with the use of decision tree analysis. B. B.1. Advantages: 1. It forces the consideration of all possible outcomes of a decision and traces each path to a conclusion. 2. It creates a comprehensive analysis of the consequences along each branch and identifies decision nodes that need further analysis. 3. Encourages the focus on the relationship between current and future decisions. B.2. Weaknesses: 1. They are unsteady, implying that a little change in the information can prompt a huge change in the structure of the ideal decision tree. 2. Not all the decisions that must be made on a subject under analysis are listed because choices are usually not restricted to two or three. 3. Decision trees are prone to errors in classification problems with many class and relatively small number of training examples. 2.

Discuss some of the factors that must be considered in decision making that decision tree analysis does not incorporate.

Answer: A decision tree does not give management the answers to an investment problem. Also, it does not identify all the possible events or does it list all the decisions that must be made on the subject under analysis. The collaborations of such choice with the goal of different pieces of the business association would be too confounded to even think about computing physically. Decision tree analysis regards questionable choices as though they were discrete well-defined possibilities. It should be putted in mind that unsure circumstances depend not only on one variable as well as on a few autonomous or halfway related factors subject to such chance influences. 3. Identify two ways that PERT is superior to Gantt chart techniques for complex projects. Answer: PERT is superior to Gantt Charts in complex projects because:

a. PERT utilizes first before a project begins to plan and determine the duration of each task, while Gantt Charts is used while a project is happening to break projects into smaller tasks and highlight scheduling constraints. b. PERT gives users a birds-eye view of the entire project before it's started to avoid potential bottlenecks. On the other hand, Gantt charts are most useful to project managers during the project to make sure that each task is accomplished. 4. Discuss how PERT can be used in planning a complex project. Answer: PERT stands for Program Evaluation Review Technique, No matter how small or big a project is, using a PERT chart will help determine realistic estimates. This planning tool used to calculate the amount of time it will take to realistically finish a project and provides a structured foundation for planning complex projects in sufficient detail to facilitate effective control. The first thing to do is to identify a workable sequence of events comprising the project. Each key event should be a task; then the interdependent relationship between events is structured. After constructing the network of events, cost and time parameters are established for each package. Staffing plans are reviewed and analyzed. The critical path is the most important part of the diagram for managers: it determines the completion date of the project; its computation identifies sequence of key events with total time equal to the time allotted for the project’s completion. Delays in completing activities along the critical path necessitate an extension of the final deadline for the project. In order to avoid delay, it is possible to slow down jobs that are not on the critical path, and the slack resources available for these activities are reallocated to activities on the critical path. Moreover, the use of PERT allows sufficient scheduling of effort through functional areas and geographical location. It also enables scheduling efforts to be restructured and staff to be redeployed as required to compensate for delays or bottlenecks. It increases the possibility of completing this complex project on schedule and within the allocated budget. 5. Should management analyze time slippage on all activities? Answer: Time slippage may not need essential analysis in noncritical activities because of the availability of the slack. Furthermore, activity cost needs to be extensively monitored by the management because it usually increases with time 6. Define the term critical path and explain why it is considered critical. Answer: The critical path is the longest sequence of activities in a project plan which must be completed on time for the project to complete on due date. It is called a "critical path" because it cannot be started until its predecessor activity is complete; if it is delayed for a day, the entire project will be delayed for a day unless the activity following the delayed activity is completed a day earlier. 7. What is meant by crashing the network and what is differential of an activity? Answer:

Crashing refers to the efforts designed to complete the project ahead of schedule. And as for the term “Crashing the network” it means finding the minimum cost of completing the project in minimum time to achieve an optimum trade-off which is also referred to as PERT-Cost analysis between time and cost. On the other hand, the differential crash cost of an activity is the additional cost of that activity for each period of time saved. 8. What is slack and how can management utilize it? Answer: Slack time is defined as the time between the earliest and latest start time, or between the earliest and latest finish time of an activity. Moreover, slack is the amount of time an event can be delayed without affecting and compromising the project’s completion date. It can serve as a buffer against bottlenecks that may arise on the critical path, hence, it can be very helpful and useful for the management. 9. If we want to maximize profit, why do we use unit contribution margins in our analysis instead of unit gross margin? Answer: If we want to maximize profit, we should use unit contribution margin instead of unit gross margin as a basis. Contribution margin per unit helps us determine how an additional unit of a product affects the profit of the company. It is calculated by subtracting variable costs incurred while producing that additional unit of product from the sale of the product itself. Furthermore, it helps a business understand how profitable it is at the product level. It gives managers an essential insight into various aspects of the business and helps them come up with better-informed decisions. These decisions could include decisions on (1) which product to continue or discontinue producing and selling; (2) how many additional units of a product to be produced; (3) how to set the price of the product and; other critical decisions. On the other hand, unit gross margin is usually computed with an allocation of fixed costs. Generally, total fixed costs will not change with a change in volume within the relevant range. In fact, fixed costs allocations can distort the relative contributions which result in a poor decision. Truly, the contribution margin per unit is quite beneficial for managers to consider while maximizing their profits. However, decisions solely based on it might not always be the right decisions to make. It is of great importance that managers should also take into account the fixed costs associated with the production alongside. 10. Management notes that the contribution margin from one product is greater than the contribution from a second product. Hence, they conclude that the company should concentrate on production of the first product. Under what, if any, conditions, will this approach result in maximum profits? Answer: This approach will maximize profits only if production and sales has no constraints or if both products use scarce resources at an equal rate. Unless, otherwise the management would want to maximize the contribution per unit of scarce resource.

11. What do we mean by the opportunity cost of a constraint? 12. What is the feasible production region? Answer: The opportunity cost of a constraint is the cost of not having additional availability of the constrained resources. It is the monetary value of the contribution margin that would be lost by not adding an additional hour of capacity. This is also called a shadow price. 12. What is the feasible production region? Answer: It is the area in that contains all possible combinations of production outputs. It is bounded by the constraints imposed on production possibilities. The production schedule which management chooses must come from the feasible production region. In a graph, feasible region is the region of the graph which contains all the points which satisfy all the constraints of the system 13. What is the role of the accountant in the management decision uses linear programming models (or other mathematical programming techniques)? Answer: A business that uses linear programming can gain valuable insights to the business problems as it helps in finding the optimal solution with the use of productive resources. An accountant, in this business that uses such programming, usually provides the contribution margin that is vital in formulating profit-maximizing objective function. Accountant also supplies data that helps in the selection of investment mix and how to minimize costs while increasing the profit. Aside from that, accountant participates in the analysis of the program's output by assessing the costs of changes in product mix. With that, accountant equips decision makers with tools to make right decisions for the business through linear programming. 14. For each of the following costs, indicate whether the cost would be an out of-pocket carrying cost (C), or a cost of placing an order (P). If the item does not qualify for either of these categories, note that it as none of the above (N). Assume that wages vary with the level of work while are salaries fixed for a monthly or longer time period. a. b. c. d. e. f. g. h. i. j.

Hourly fee for inventory audit. Salary of purchasing supervisor. Costs to audit purchase orders and invoices, on a per-order basis. Taxes on inventory. Stockout costs. Storage costs charged per unit Fire insurance on inventory. Fire insurance on warehouse. Obsolescence costs on inventory. Shipping costs per shipment.

Answer:

a. Hourly fee for inventory audit b. Salary of purchasing supervisor c. Costs to audit purchase orders and invoices d. Taxes on inventory e. Stockout costs f. Storage costs charged per unit in inventory g. Fire insurance on inventory h. Fire insurance on warehouse i. Obsolescence costs on inventory j. Shipping costs per shipment

(C) (N) (P) (C) (P) (C) (C) (N) (C) (P)

15. Since the operations research specialists develop and maintain inventory models, why does the accountant become concerned with inventory policy decisions? Answer: Although the inventory models are developed by operations researchers, statisticians and computer specialists, the accountant should still be concerned with inventory policy decision since the areas of expertise of those developers are only limited to the costs as a given. Unlike accountants, they analyze and assess differential costs for the inventory models. In inventory costs, some costs increase with the quantities of inventory on hand while other costs decrease. It is the role of the accountant to determine which costs are suitable for inclusion in an inventory model. 16. Why is the cost of capital included as a carrying cost of inventory? ANSWER: Cost of capital represents the interest on funds if they were borrowed or opportunity cost if funds were internally provided by owners. It is included as carrying cost of inventory because funds are attached in inventory. 17. A review of the inventories of a company indicates the following cost data for a given item: Invoice price P 102.25 per unit Processing invoices and other documents P 21.45 per order + P1475.80 per month Permit fees for shipping P 201.65 per truckload Excise tax 4% of invoice price Inventory tax 2% of the invoice price Insurance on shipments P 1.50 per unit Insurance on inventory P 2.80 per unit Warehouse rental P 985.00 per month Stock out costs P 122.00 per order Cost of capital 25% Unloading - per order P 80.20 per order Show differential costs that would be included in an EOQ model.

ANSWER: Costs that vary with the average number of units in inventory:

Inventory insurance Inventory tax Total

P 2.80 2.05 (P102.25 x 2%) P 4.85

Costs that vary with the number of units purchased: Purchase price Insurance on shipment Total

P102.25 1.50 P103.75

Total carrying cost = (25% x P103.75) cost of capital + P4.85 = P25.94 + P4.85 = P30.79 Order costs: Shipping permit Costs to arrange for the shipment Unloading Stockout costs Total

P 201.65 21.45 80.20 122.00 P 425.30

PROBLEM 1 Metalworks, Inc., received four orders for specially designed gears. Each gear must go through two departments in sequence, Hobbing and Machining. The supervisors estimated the time required for each order. Expresses in days, these times are.

Orders Hobbing ……..… Machining.……..

1 4 3

2 7 2

3 5 5

4 8 9

There is no backlog in the departments on orders in process. To minimize time in departments, select the shortest times for orders in both departments. Then schedule first the order requiring the least amount of hobbing time. Schedule last the order requiring the least amount of machining time. Repeat this rule for each sequence until all orders are sequence. Required: a. Develop a Gantt chart for the four orders. Move each order from one department to the next minimizing the total time required to complete all orders. b. Determine how long it will take to complete work on all four orders.

ANSWER: Refer to last page.

PROBLEM 2 Ace Construction Company developed the following network for building complex equipment. Your assistance in using the program, evaluation review technique is required.

Required: With ANSWERS a. Determine the critical path.  The critical path is shown by path 0-1-6-7-8 with a total expected time of 40.

0-1-2-5-8 2 + 8 + 10 + 14 = 34 0-1-3-4-7-8 2+8+7+5+3= 25 0-1-6-7-8 2 + 26 + 9 + 3= 40 b. Determine the latest time for reaching Event 4.  40 - 3 - 5 = 32 c. Assume all other paths operate on schedule but path 4-7 has an unfavorable time variance of 10. What is the effect on the critical path?  There will be no effect on the critical path because path 0 - 1 - 3 - 4 - 7 – 8 will only have a total expected time of 35, unlike path 0 - 1 - 6 - 7 – 8 that has a total time of 40 which is still greater than path 0 - 1 - 3 - 4 - 7 – 8. d. Compute the earliest time for reaching event 5 via path 0-1-2-5.  The earliest time for reaching event 5 via path 0-1-2-5 is 20. 0-1-2-5 2 + 8 + 10 = 20

PROBLEM 3 Tower Company produces two types of gloves, G1 and G2. The cost and production data concerning these two products are as follows: Selling price Manufacturing costs: Materials Labor Fixed overhead Gross margin per unit Required production time/unit

G1 P12.00

G2 P14.00

4.00 3.00 2.50 P 2.50 2 hours

1.50 6.00 5.00 P 1.50 2 hours

Total production time available is 2,500 hours per month. Since production time is limited and gross margin unit for GI is higher than for G2, Tower Company management decided to produce and sell GI exclusively. Required: Did Tower Company management make the correct decision? Answer:No, they didn’t make a right decision, based from the data above they included fixed costs which do not vary in the short run. They would have had P5 for G1 and P6.50 for G2 if they had used contribution margin instead of gross margin, this will then result in the preferred output of G2 exclusively.

PROBLEM 4

A company uses 1,500 units of Zeron per year. Each unit has an invoice cost of P222, including shipping costs. Because of the volatile nature of Zeron, it costs P860 for liability insurance on each shipment. The costs of carrying the inventory amount to P65 per item per year exclusive of a 20 percent cost of capital. Other order costs amount to P18 per order. At present, the company orders 250 units at a time. Required: a. What is the annual cost of the company's current order policy? b. What is the annual cost of the optimal economic order policy?

Answer: Order cost= Insurance cost + Other order costs = P860+ P18 =P878 Carrying costs = Out-of-pocket costs + Cost of Capital Inventory =P65 + P44.40 (P222 * 20%) =P109. 40 What is the annual cost of the company’s current order policy? Carrying cost:

P 250 units∗P109.40 =P 13,675 2 Order Cost:

1,500∗P 878 =P 5,628 250units Carrying cost + Order cost = P18, 943 What is the annual cost of the optimal economic order policy?

√

2∗1500∗P 878 = √ P 24,077=155 units P109.40

Carrying cost:

155∗P 109.40 =P8,478.50 2 Order Cost:

1,500∗P 878 =P 8,496.77 155 Carrying costs + Order costs = P16, 975.27 Problem 5

Forest Products Corporation manufactures Maquis as one of its agricultural items. The manufacturing process requires several inputs including nitrogen fixer, NFX. The company uses 39,000 units of NFX per year and orders in economic lot sizes of 2,600 units. The cost to carry a unit of NFX is P24.40. If there is a stock out, a carload of NFX must be purchased at retail from a local supplier. The retail price is P1,650 greater than the price from the regular supplier. Looking at the past order records, it appears that certain safety-stock levels would result in stockouts according to the following schedule: Safety-Stock Quantity 0 150 175 250

Probability of Stockout 0.50 0.20 0.05 0.01

Required: What level of safety stock would result in the least cost to the company?

Answer: It is necessary to evaluate the annual carrying costs and expected stockout costs at each safety-stock level. The carrying cost will be P24.40 for each unit in safety stock. There are 15 orders placed a year (39,000/2,600 = 15). Below is the schedule: Safety

Carrying Costs

Stock

of Safety Stock

0 150 175 250

0

Expected Stockout

Total

Costs

Costs

a

P12,375

a

8,610

0.50 x 15 x P1,650 = P12,375

150 x P24.40 = P3,660 0.20 x 15 x P1,650 = P 4,950 a

175 x P24.40 = P4,270 0.05 x 15 x P1,650 = P 1,273.5 250 x P24.40 = P6,100b

0.01 x 15a x P1,650 = P

247.5

5,507.5 (optional) 6,347.5

Additional computations: a 15 number of orders per year. b It should be seen that at this level that the carrying costs exceed the total costs at a safety stock of 175 units. It can be seen that it is not possible for this or any safety-stock level larger than 250 to be less costly than 175 units. Given a total cost at 175 units of P5,507.5, stockout costs would have to occur with probability zero for any safety stock greater than 225.72 units (P5,507.5 / P24.40 = P225.72).

Problem 1

Requirement (a) Answer:

TASKS

Ho b b i n g

1

2

3

4

Order 1

Ma c h i n i n gX