Title CHAP 15-12 ✅

TA Mai Tuyền CHAP 15. SCHEDULING FOR THE SHORT-TERM I. SEQUENCING JOBS 1. Priority rules: - First come first serve - Shortest processing time - Earliest due date - Longest processing time ● Average completion time = Sum of total flow time Number of jobs ● Utilization metric= Total job work time Sum of total flow time ● Average number of jobs in the system = Sum of total flow time Total job work time ● Average job lateness = Total late days Number of jobs Example: Determine the sequence of processing according to FCFS, SPT, EDD, and LPT rules. Job Processing time (days) Job due date (days) A 6 8 B 2 6 C 8 18 D 3 15 E 9 23 2. Critical ratio: Critical ratio = = Time remaining Workdays remaining Due date − Today's date Work (lead) time remaining Example: Today is day 25 on Zyco Medical Testing Laboratories’s production schedule. Three jobs are on order, as indicated here: Job Due date Workdays remaining A 30 4 B 28 5 C 27 2
TA Mai Tuyền 3. Johnson’s Rule: Sequencing jobs on 2 machines Example: Five specialty jobs at a La Crosse, Wisconsin, tool and die shop must be processed through two work centers (drill press and lathe). The time for processing each job follows: Work (processing) time for jobs (hours): Job Work center 1 (Drill press) Work center 2 (Lathe) A 5 2 B 3 6 C 8 4 D 10 7 E 7 12 II. Assignment method Example 1: First Printing wants to find the minimum total cost assignment of 3 jobs to 3 typesetters. Typesetters Jobs A B C R-34 $11 14 6 S-66 $8 10 11 T-50 $9 12 7 Example 2: King Finance Corporation, headquartered in New York, wants to assign three recently hired college graduates, Julie Jones, Al Smith, and Pat Wilson, to regional offices. However, the firm also has an opening in New York and would send one of the three there if it were more economical than a move to Omaha, Dallas, or Miami. It will cost $1,000 to relocate Jones to New York, $800 to relocate Smith there, and $1,500 to move Wilson. What is the optimal assignment of personnel to offices? Office OMAHA MIAMI DALLAS
TA Mai Tuyền Hire Jones Smith Wilson $800 500 500 1,100 1,600 1,000 1,200 1,300 2,300 CHAP 12: MANAGING INVENTORY 1. ECONOMIC ORDER QUANTITY MODEL (EOQ) - P: price/cost per unit - Q: number of unit per order - EOQ (or Q*): optimal number of units per order - D: annual demand - S: Setup cost - H: Holding cost ● Annual setup cost: SD/Q = SN Number of order placed per year: N = D/Q ● Total Annual holding cost: HQ/2 Average inventory level: Q/2 ● When Annual setup cost = Annual holding cost SD/Q = HQ/2 → Q= : EOQ (Q*): optimal number of units per order 2SD H ● Time between orders: T = Number of working days per year N ● Total cost (per year) = Annual setup cost + Annual holding cost + Product cost = SD/Q + HQ/2 + PD Example 1: The Warren W. Fisher Computer Corporation purchases 8,000 transistors each year as components in minicomputers. The unit cost of each transistor is $10, and the cost of carrying one transistor in inventory for a year is $3. Ordering cost is $30 per order. What are (a) the optimal order quantity, (b) the expected number of orders placed each year, and (c) the expected time between orders? Assume that Fisher operates on a 200-day working year. Example 2: Southeastern Bell stocks a certain switch connector at its central warehouse for supplying field service offices. The yearly demand for these connectors is 15,000 units. Southeastern estimates its annual holding cost for this item to be $25 per unit. The cost to place and process an order from the supplier is $75. The company operates 300 days per year, and the lead time to receive an order from the supplier is 2 working days. a) Find the economic order quantity.
TA Mai Tuyền b) Find the annual holding costs. c) Find the annual ordering costs. d) What is the reorder point/ reorder level? ● Reorder point with Safety stock: ROP = d x L + Safety stock Safety stock = Z x σ x L σ : standard deviation (Variance) Example 1: The daily demand for 520 flat-screen TVs at Sarah’s Discount Emporium is a standard deviation of 2 units. The lead time for receiving a shipment of new TVs is 10 days and is fairly constant. Determine the reorder point and safety stock for a 95% service level. 2. QUANTITY DISCOUNT MODEL Example 1: Bell Computers purchases integrated chips at $350 per chip. The holding cost is $35 per unit per year, the ordering cost is $120 per order, and sales are steady, at 400 per month. The company’s supplier, Rich Blue Chip Manufacturing, Inc., decides to offer price concessions in order to attract larger orders. The price structure is shown below. Quantity purchased Price/unit 1-99 units $ 350 100-199 units $ 325 200 or more units $ 300 a) What is the optimal order quantity and the minimum annual cost for Bell Computers to order, purchase, and hold these integrated chips? b) Bell Computers wishes to use a 10% holding cost rather than the fixed $35 holding cost in (a). What is the optimal order quantity, and what is the optimal annual cost? Example 2: M. P. VanOyen Manufacturing has gone out on bid for a regulator component. Expected demand is 700 units per month. The item can be purchased from either Allen Manufacturing or Baker Manufacturing. Their price lists are shown in the table. Ordering cost is $50, and annual holding cost per unit is $5. ALLEN MFG BAKER MFG. QUANTITY UNIT PRICE QUANTITY UNIT PRICE 1–499 $16.00 1–399 $16.10